On Doctors, Mechanics, and Computer Specialists: The ... · PDF fileÒIf a mechanic...

5

lowast Dulleck Johannes Kepler University Linz andUniversity of Vienna Kerschbamer University of Innsbruckand CEPR Previous versions have benefitted from com-ments by and discussions with Heski Bar-Isaac GerhardClemenz Winand Emons Roger Gordon Ulrich KameckeGilat Levy John McMillan Dennis Mueller GerhardOrosel Carolyn Pitchik Larry Samuelson AndreasWagener Elmar Wolfstetter Asher Wolinsky and threeanonymous referees The first author gratefully acknowl-edges support by the DFG through SFB 373 at HumboldtUniversity Berlin and SFB 303 at the University of Bonn

1 Introduction

ldquoIf a mechanic tells you that he has toreplace a part in your car donrsquot forget

to ask him to put the replaced part into thetrunk of your carrdquo This is an example of day-to-day advice regarding the services of carmechanics One hopes to avoid two types offraud by following this advice On the onehand the mechanic has to change a part and

cannot only claim (and charge for) thereplacement of a part he or she did not actu-ally change On the other hand the cus-tomer might be able to verify that themechanic did not provide an unnecessaryrepair by inspecting the defect of theexchanged part

This example illustrates a situation wherean expert knows more about the type of goodor service the consumer needs than the con-sumer himself The expert seller is able toidentify the quality that fits a customerrsquos needbest by performing a diagnosis He can thenprovide the right quality and charge for it orhe can exploit the informational asymmetryby defrauding the customer

Goods and services where an expertknows more about the quality a consumerneeds than the consumer himself are called

Journal of Economic LiteratureVol XLIV (March 2006) pp 5-42

On Doctors Mechanics andComputer Specialists The Economics

of Credence Goods

UWE DULLECK AND RUDOLF KERSCHBAMERlowast

Most of us need the services of an expert when our apartmentrsquos heating or our wash-ing machine breaks down or when our car starts to make strange noises And for mostof us commissioning an expert to solve the problem causes concern This concern doesnot disappear even after repair and payment of the bill On the contrary one worriesabout paying for a service that was not provided or receiving some unnecessarytreatment This article studies the economics underlying these worries Under whichconditions do experts have an incentive to exploit the informational problems associ-ated with markets for diagnosis and treatment What types of fraud exist What arethe methods and institutions for dealing with these informational problems Underwhich conditions does the market provide incentives to deter fraudulent behaviorAnd what happens if all or some of those conditions are violated

Mar06_Art1 22006 634 PM Page 5

6 Journal of Economic Literature Vol XLIV (March 2006)

credence goods Michael R Darby and EdiKarni (1973) added this type of good toPhillip Nelsonrsquos (1970) classification of ordi-nary search and experience goods Theymention provision of repair services as atypical example Other examples includetaxicab rides where a stranger in a city can-not be sure that the driver takes the short-est route to his destination and medicaltreatments where doctors may providewrong diagnosis to sell the most profitabletreatment or where they can try to chargefor a more expensive treatment than pro-vided There are countless other examplesof situations were consumers face similarinformation problems and where theyworry about the two basic problemssketched out by the mechanic example topay for goods or services they did notreceive or to receive goods or services theydid not need in the first place

Consumersrsquo concerns about beingdefrauded by experts seem not to beunfounded Winand Emons (1997) cites aSwiss study reporting that the averagepersonrsquos probability of receiving one ofseven major surgical interventions is onethird above that of a physician or a mem-ber of a physicianrsquos family Asher Wolinsky(1993 1995) refers to a survey conductedby the Department of Transportation esti-mating that more than half of auto repairsare unnecessary He also mentions a studyby the Federal Trade Commission thatdocuments the tendency of optometriststo prescribe unnecessary treatmentThese examples reveal that the informa-tional asymmetry matters Monetaryincentives play a role too For the case ofthe health industry Jon Gruber JohnKim and Dina Mayzlin (1999) empiricallyshow that the frequencies of cesareandeliveries compared to normal child birthsreact to the fee differentials of healthinsurance programs A similar observationhas been made by David Hughes andBrian Yule (1992) who document that thenumber of cervical cytology treatments is

correlated with the fee for this treatmentThat treatment can also be affected bysupply of expert services is shown byVictor R Fuchs (1978) ldquoOther thingsequal a 10 percent higher surgeonpopu-lation ratio results in about a 3 percentincrease in the number of operations rdquo(p 54)

These observations suggest that weneed a more profound understanding ofthe specific problems associated with mar-kets for diagnosis and treatment Underwhich conditions do experts have anincentive to exploit the informationalproblems associated with markets fordiagnosis and treatment What types offraud exist What are the methods andinstitutions for dealing with these infor-mational problems Under which condi-tions does the market provide incentivesto deter fraudulent behavior And whathappens if all or some of those conditionsare violated

The existing literature on credence goodsdoes not help much to answer these ques-tions The studies performed up to nowcover very different and quite special situa-tions and in total they yield no clear pictureregarding the inefficiencies arising from theinformational asymmetry Rather theresults seem to depend sensitively on thespecific conditions of the settings consid-ered and the specific assumptions of themodels adopted in the analysis More dis-turbingly apparently similar models oftenlead to contradicting results (see section 2for details)

The present article presents a model ofcredence goods that highlights the informa-tion problems in markets for experts servic-es and clarifies the variety of results in thisarea The model provides a unifying frame-work for the analysis of the effects of differ-ent market institutions and informationstructures on efficiency and for the identi-fication of the forces driving the variousinefficiency results in the literature Inaddition the model allows us to generalize


Dulleck and Kerschbamer On Doctors Mechanics and Computer Specialists 7

some of the existing results and to show thelimits of other ones

The key feature of credence goods is thatconsumers do not know which quality of agood or service they need The provision ofa too low quality compared to the neededone is insufficient and the provision of a toohigh quality does not add extra value Withrespect to the auto repair example if a carbreaks down and only an adjustment to themotor is needed to put the car back on theroad then the replacement of the entireengine does not add to the utility the cus-tomer derives from the repair He does noteven perceive the difference That is thecustomer can ex post only observe (butmight be unable to verify) whether the prob-lem still exists If the problem no longerexists he can not tell whether he got theright or a too high treatment qualityFurthermore he may not even be able toobserve whether a suggested treatmentquality was actually provided or not

Credence goods can give rise to the fol-lowing two types of problem (1) The con-sumer requires a sophisticated complextypically expensive intervention butreceives a simple inexpensive treatmentand thus forgoes the benefits of the sophis-ticated intervention We refer to this kind ofinefficiency as undertreatment A secondtype of inefficiency arises if the consumerrequires an inexpensive treatment butreceives a sophisticated one The additionalbenefits to the consumer from the sophisti-cated intervention are less than the addi-tional costs We refer to this kind ofinefficient treatment problem as overtreat-ment (2) In addition to these inefficienttreatment problems surrounding credencegoods credence goods can also be associat-ed with pure transfers from consumers toproducers when a consumer requires andreceives an inexpensive treatment but ischarged for an expensive one In the longrun such overcharging also leads to an inef-ficiency if consumers postpone car repairsor medical check-ups and the like because

1 There are of course a number of other potentialproblems (and therewith a number of other sources offraud) in the credence goods market For example expertsmay differ in their ability to perform a diagnosis or atreatment and this ability may be their own private infor-mation Or the effort bestowed by an expert in the diag-nosis stage may be unobservable We ignore theseproblems here not because we regard them as less impor-tant but rather because they seem to be less specific tothe credence goods market For analyses of situationswhere effort is needed to diagnose the customer andwhere an expertrsquos effort investment is unobservable seeWolfgang Pesendorfer and Wolinsky (2003) and Dulleckand Kerschbamer (2005a) The former contribution focus-es on the effect that an additional diagnosis (by a differentexpert) has on the consumerrsquos evaluation of a givenexpertrsquos effort and the latter paper studies competitionbetween experts and discounters when customers can freeride on expertsrsquo advice

of the high prices they have paid for theseservices in the past1

A first step in the understanding of cre-dence goods is to identify the conditions thatdetermine which of these two basic prob-lems associated with markets for diagnosisand treatment is the more demanding oneTo get a first impression let us assume weown a garage and our customer cannotobserve the repair we perform but that hewill only pay us in case his car is functioningwell after the repair (thus undertreatment isruled out) If this is the case and if we planto defraud him we will claim that an expen-sive and difficult repair is needed even whena minor repair fixes the problem If the cus-tomer authorizes us to perform the repairwe will provide the minor treatment andcharge for a more expensive oneOvertreatment is a strictly dominated strate-gy in this setting because the higher cost ofthe expensive repair does not affect the pay-ment of the customer Next assume this cus-tomer follows the advice to ask for replacedparts and can thus verify the type of servicewe perform (but he is still technically notvery adept and therefore not able to deter-mine whether the provided service was actu-ally needed or not) In this case we cannotovercharge the customer but we will consid-er overtreating him whenever we make ahigher profit selling an expensive instead of



a cheap repair In other words overtreat-ment is only an issue if overcharging is notfeasible due to the specific situation

In general the legal framework as well astechnicalities and individual education andabilities determine whether and if yeswhich of the mentioned problems appearsOvercharging is only possible if the cus-tomer cannot control the service provided bythe expert Asking the mechanic for replacedparts is a way to avoid overcharging and ifone is able to inspect the exchanged part adevice to avoid overtreatment too If a cus-tomer is able to perform a diagnosis himselfthere might be no credence goods problemat all For instance a patient with a medicaleducation might be able to determinewhether the treatment proposed by a physi-cian is really necessary As the evidence citedabove reveals these differences in abilitiesaffect the treatment prescribed in medicalenvironments

Existing institutions address the informa-tional problems associated with markets fordiagnosis and treatment The problem ofundertreatment is most famously controlledfor by the Hippocratic Oath of a physicianand its counterpart in the law Warrantiesprovide similar incentives The separation ofdoctors and pharmacies is an institution toavoid overtreatment by disentangling theincentives to prescribe drugs from the profitmade selling them The fixed part of a taxiride tariff provides incentives for the driverto serve many individual customers andtherewith not to take longer routes than nec-essary To avoid overcharging as well asovertreatment in many repair industries thechamber of commerce issues standard work-times for some repairs to allow customers tobetter check upon a workmanrsquos billmdashby pro-viding a comparison to usual hours for theordered repair

We will see below that the market mecha-nism itself might discipline experts In theunifying model that we present experts havean incentive to commit to prices that inducenonfraudulent behavior and full revelation

of their private information if a small num-ber of critical assumptions are satisfiedThese conditions are (i) expert sellers face homogeneous customers (ii) largeeconomies of scope exist between diagnosisand treatment so that expert and consumerare in effect committed to proceed with anintervention once a diagnosis has beenmade and (iii) either the type of treatment(the quality of the good) is verifiable or a lia-bility rule is in effect protecting consumersfrom obtaining an inappropriate inexpensivetreatment (or verifiability and liability bothhold) In section 3 we will describe theseassumptions in more detail and in section 6we will discuss and review them in the lightof the examples given

These three basic assumptions are centralin our simple unifying model We show thatby relaxing them one by one a large part ofthe existing results on inefficiencies in thecredence goods market are obtained Thusthe analysis of our simple model sheds lighton the general structure of credence goodsmarkets This understanding of the generalstructure can help to make a next step fromthe fractional analysis of certain situationsand certain institutions (as done in the exist-ing literature) toward a more complete pic-ture of the issues involved Given thisunderstanding we are then in a position tojudge other situations and other institutionsand to assist in the design of new policies andinstitutions that remove the inefficienciessurrounding credence goods

The rest of the paper is organized as fol-lows The next section briefly reviews theexisting literature on credence goods In sec-tion 3 we introduce our model Section 4shows that market institutions solve thefraudulent expert problem at no cost whenconditions (i) (ii) and (iii) hold In the sub-sequent section we characterize the ineffi-ciencies that arise if at least one of theseconditions is violated Section 6 builds a linkto real world situations by returning to thekey motivating examples mentioned in thetext and discussing the plausibility of each of



these assumptions in each case This sectionalso contains a table where the existing liter-ature is categorized according to ourassumptions Section 7 concludes Someproofs are relegated to the appendix

2 On the Existing Literature

Before recapitulating the main contribu-tions of the literature within our model wewant to review briefly the existing literaturewith respect to assumptions and results

Models of credence goods markets needto make assumptions on at least three inter-related characteristics of the market consid-ered They have to specify (1) the technologyof the suppliers ie the costs for providingdifferent treatments (2) the degree of com-petition together with the organization(ldquomicrostructurerdquo) of the market and (3) theinformation structure of consumers andcourts ie whether consumers are able toobserve the quality provided and whetherthe quality provided and the result of treat-ment can be proven to the courts We nowturn to each of these points and discuss whatthe literature assumes

(1) There are several differences in theconsidered technologies Some authorsassume that experts can serve arbitrari-ly many customers at constant(Wolinsky 1993 and 1995 Curtis RTaylor 1995 Jacob Glazer and ThomasG McGuire 1996 Dulleck andKerschbamer 2005a and 2005b IngelaAlger and Franccedilois Salanieacute 2003 Yuk-Fai Fong 2005) or increasing (Darbyand Karni 1973) marginal cost in othercontributions experts are capacity con-strained (Emons 1997 and 2001 HughRichardson 1999) Also some authorsconsider models where the right treat-ment fixes the problem for sure(Carolyn Pitchik and Andrew Schotter1987 and 1993 Wolinsky 1993 and1995 Taylor 1995 Dulleck andKerschbamer 2005a and 2005b Fong2005) others focus on frameworks

2 Alger and Salanieacute (2003) focus on an intermediatecase where some but not all inputs needed for an inter-vention are observable and verifiable

where success is a stochastic functionof service input (Darby and Karni 1973Glazer and McGuire 1996 Emons1997 and 2001 Richardson 1999)

(2) The analyzed market conditions rangefrom experts having some degree ofmarket power (Pitchik and Schotter1987 Richardson 1999 Emons 2001Dulleck and Kerschbamer 2005bFong 2005) to competitive frameworks(Wolinsky 1993 and 1995 Taylor 1995Glazer and McGuire 1996 Emons1997 Alger and Salanieacute 2003 Dulleckand Kerschbamer 2005a) Also insome contributions experts are able tocommit ex ante to take-it-or-leave-itprices (Wolinsky 1993 Taylor 1995Glazer and McGuire 1996 Emons1997 and 2001 Dulleck andKerschbamer 2005a and 2005b Algerand Salanieacute 2003 Fong 2005) in othersprices are determined ex post in a bilat-eral bargaining process (Wolinsky 1995Richardson 1999) still others considermodels where prices are exogenouslygiven (Darby and Karni 1973 Pitchikand Schotter 1987 and 1993 Kai Suumllzleand Achim Wambach 2005)

(3) Without exception all contributions tothe credence goods literature implicit-ly or explicitly impose our condition(iii) That is either the type of treat-ment (the input) is assumed to beobservable and verifiable (our verifia-bility assumption) or the result (theoutput) is supposed to be verifiable anda liability rule is assumed to be in effectprotecting consumers from obtainingan inappropriate inexpensive treatment(our liability assumption)2 Which ofthese two conditions is implicitly orexplicitly imposed (none of the contri-butions imposes both) unambiguouslydetermines the problem on which the



3 In this context ldquosomerdquo means that one subgroup ofcustomers is treated efficiently while another subgroupreceives one and the same treatment independently of theoutcome of the diagnosis By contrast ldquoallrdquo means thateach treated customer gets the same treatment (againindependently of the type of problem he has) In bothcases some consumers might decide to remain untreated

respective author(s) focus(es) Emons(1997 and 2001) Richardson (1999)and Dulleck and Kerschbamer (2005aand 2005b) explicitly impose the verifi-ability assumption and study the prob-lems of over- and undertreatmentPitchik and Schotter (1987 and 1993)Wolinsky (1993 and 1995) Fong(2005) and Suumllzle and Wambach(2005) analyze expertsrsquo temptation toovercharge customers implicitlyassuming the liability assumption tohold and verifiability to be violatedTaylor (1995) imposes these assump-tions explicitly And in Darby and Karni(1973) the implicit assumption regard-ing verifiability varies according towhether capacity exceeds demand orvice versa For the former case theyanalyze expertsrsquo incentive to overtreatcustomers implicitly assuming verifia-bility to hold For the latter case theydiscuss the incentive to charge fortreatments not provided implicitlyassuming verifiability to be violated

Given the wide range of problems ana-lyzed in the literature it is not surprisingthat the proposed solutions exhibit a broadrange of different equilibrium behaviorthere are pure strategy equilibria in whichexperts ldquomistreatrdquo (ie under- or overtreat)some (Dulleck and Kerschbamer 2005b) orall (Darby and Karni 1973 Richardson1999 Alger and Salanieacute 2003) consumersand pure strategy equilibria which give riseto excessive search and diagnosis costs(Wolinsky 1993 Glazer and McGuire1996)3 There are pure and mixed strategyequilibria where the market outcomeinvolves fraud in the form of overchargingof consumers (Pitchik and Schotter 1987

4 Pitchik and Schotter (1993) claim that their formalframework encompasses both the verifiability and the non-verifiability case (p 818) In our view their assumptions onthe payoff structure (the profit of an expert authorized bya client to perform an expensive treatment is higher if theclient needs a cheap rather than the expensive treatment)hardly allow the verifiability interpretation however

and 1993 Wolinsky 1995 Fong 2005 Suumllzleand Wambach 2005) And there are alsoequilibria where the only inefficiencies inthe credence goods market are expertsrsquoinefficient capacity levels (Emons 1997)Thus the overall picture is rather blurredAt least for the nonexpert reader it is fairlydifficult to judge which set of conditionsdrives the presented results

The unifying model that we present facili-tates the identification of the criticalassumptions that lead to the striking diversi-ty of results In addition it helps to removesome ambiguities in the literature Forinstance Emons (2001) attributes the maindifference between his own work and thepapers by Pitchik and Schotter (1987 and1993) and Wolinsky (1993) to the fact thatldquothey all (implicitly) assume unnecessaryrepairs to be costless whereas our expertneeds resources for unnecessary treatmentsThis implies that overtreatment is alwaysprofitable in their set-up In contrast theprofitability of overtreatment in our modeldepends on demand conditions and is deter-mined endogenouslyrdquo (p 4) Our analysisbelow suggests that differences in two of thethree conditions specified in the previous(and further discussed in the next) sectionare more important First Pitchik andSchotter (1987 and 1993) and Wolinsky(1993) implicitly assume verifiability to beviolated and liability to hold whereas Emons(2001) considers the opposite constellation4

Thus the former papers focus on the prob-lem of overcharging while the latter studiesexpertsrsquo incentive to over- or undertreat cus-tomers Secondly Pitchik and Schotter(1987 and 1993) and Wolinsky (1993)assume that the efficiency loss of diagnosinga consumer more than once is rather low

Mar06_Art1 22006 634 PM 0


5 Many of results can also be obtained in an extendedmodel that allows for more than two types of problem andmore than two types of treatment (see Dulleck andKerschbamer 2005b for such a model) However since ourgoal is to provide a simple unifying framework we stick toa binary model

6 For convenience both the type of treatment and theassociated cost is denoted by c

(low economies of scope between diagnosisand treatment) while Emons (2001)assumes this loss to be high (profoundeconomies of scope between diagnosis andtreatment)

Below we will reproduce the main resultsof these studies in our framework and discusswhich assumptions are crucial to get them

3 A Basic Model of Credence Goods

To model credence goods we assumethat each customer (he) has either a (minor)problem requiring a cheap treatment cndash or a(major) problem requiring an expensivetreatment cndash5 The customer knows that hehas a problem but does not know howsevere it is He only knows that he has an exante probability of h that he has the majorproblem and a probability of (1 minus h) that hehas the minor one An expert (she) on theother hand is able to detect the severity ofthe problem by performing a diagnosis Shecan then provide the appropriate treatmentand charge for it or she can exploit theinformation asymmetry by defrauding thecustomer

The cost of the expensive treatment is cndashand the cost of the cheap treatment is cndash withcndash gt cndash6 The expensive treatment fixes either

7 Of course not all credence goods have such a simplepayoff structure For instance in the medical example thepayoff for an appropriately treated major disease mightdiffer from that of an appropriately treated minor diseaseSimilarly the payoff for a correctly treated minor diseasemight differ from that of an overtreated minor diseaseIntroducing such differences would burden the analysiswith additional notation without changing any of theresults however

problem while the cheap one is only good forthe minor problem

Table 1 represents the gross utility of aconsumer given the type of treatment heneeds and the type he gets If the type oftreatment is sufficient a consumer gets util-ity v Otherwise he gets 0 To motivate thispayoff structure consider a car with either aminor problem (car needs oil in the engine)or a major problem (car needs new engine)with the outcomes being ldquocar worksrdquo (ifappropriately treated or overtreated) andldquocar does not workrdquo (if undertreated)7

An important characteristic of credencegoods is that the customer is satisfied in threeout of four cases In general he is satisfiedwhenever he gets a treatment quality at leastas good as the needed one Only in one casewhere he has the major problem but gets thecheap treatment will he discover ex postwhat he needed and what he got

Consumers may differ in their valuationfor a successful intervention or in their prob-ability of needing different treatments Weintroduce heterogeneous customers in sec-tion 5 In section 4 we follow the main bodyof the literature on credence goods inassuming that customers are identical Werefer to this as the homogeneity assumption(Assumption H)

TABLE 1UTILITY FROM A CREDENCE GOOD

Customerrsquos utility Customer needscminus

minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11


8 Since provision of treatment without diagnosis isassumed to be impossible an increase in diagnosis costmeans that consulting more than one expert becomes lessattractive

ASSUMPTION H (HOMOGENEITY)All consumers have the same probability hof having the major problem and the samevaluation v

An expert needs to perform a diagnosisbefore providing a treatment Regarding themagnitude of economies of scope betweendiagnosis and treatment there are two dif-ferent scenarios to consider If theseeconomies are small separation of diagnosisand treatment or consultation of severalexperts may become attractive With pro-found economies of scope on the otherhand expert and customer are in effect tiedtogether once the diagnosis is made In sec-tion 5 we take the diagnosis cost d as ameasure of the magnitude of economies ofscope between diagnosis and treatment anddiscuss conditions under which expert andconsumer are in effect tied together8 Insection 4 we work with the following short-cut assumption which we refer to as thecommitment assumption (Assumption C)

ASSUMPTION C (COMMITMENT)Once a recommendation is made the cus-tomer is committed to undergo a treatmentby the expert

As mentioned before the focus of thecredence goods literature has beentwofold inefficient treatment eitherunder- or overtreatment and overchargingThe inefficiency of treatment can bedescribed by referring to table 1 The caseof undertreatment is the upper right cornerof the table the case of overtreatment isthe lower left corner Note that overtreat-ment is not detected by the customer(v = v) and hence cannot be ruled out byinstitutional arrangements This is not thecase with undertreatment it is detected bythe customer (0 v) and might even beverifiable If this is the case and if a legal

9 An undercharging incentive only exists if the price ofthe expensive treatment is such that customers reject a minuscrecommendation and if the price of the cheap treat-ment exceeds the cost of the expensive one Such pricecombinations are not observed in equilibrium

rule is in effect that makes an expert liablefor the provision of inappropriate low qual-ity we say that the liability assumption(Assumption L) holds

ASSUMPTION L (LIABILITY) Anexpert cannot provide the cheap treatment cndashif the expensive treatment cndash is needed

Referring again to table 1 the secondpotential problem is that the customer mightnever receive a signal that discriminatesbetween the upper left and the lower rightcell of the table If this is the case an expertwho discovers that the customer has theminor problem can diagnose the major oneso that the customer might authorize andpay for the expensive treatment althoughonly the cheap one is provided This over-charging is ruled out if the customer is ableto observe and verify the delivered quality(he knows and can prove whether he is in thetop or the bottom row of the table) and werefer to situations in which consumers havethis ability as cases where the verifiabilityassumption (Assumption V) holds9

ASSUMPTION V (VERIFIABILITY)An expert cannot charge for the expensivetreatment cndash if she has provided the cheaptreatment cndash

Let us now describe the market environ-ment There is a finite population of n ge 1identical risk-neutral experts in the cre-dence goods market Each expert can servearbitrarily many customers The expertssimultaneously post take-it-or-leave-itprices Let pminusi (pminus

i respectively) denote theprice posted by expert i isin 1 n for theexpensive (cheap) treatment cndash (cndash) Anexpertrsquos profit is the sum of revenues minuscosts over the customers she treated Byassumption an expert provides the appro-priate treatment if she is indifferentbetween providing the appropriate and

Mar06_Art1 22006 634 PM Page 12


10 Introducing some guilt disutility associated with pro-viding the wrong treatment would yield the same qualita-tive results as this common knowledge assumptionprovided the effect is small enough to not outweigh thepecuniary incentives

11 The diagnosis cost d is assumed to include the timeand effort cost incurred by the consumer in visiting a doc-tor taking the car to a mechanic etc It is also assumed toinclude a fair diagnosis fee paid to the expert to cover heropportunity cost A more elaborate model would distin-guish between a search and diagnosis cost dc borne direct-ly by the consumer a diagnosis cost de borne by the expert(where d = dc + de) and a diagnosis fee p charged by theexpert Since one of our goals is to reproduce many of theexisting results on inefficiencies and fraud in credencegoods markets in a simple framework and since the bulk ofthe literature takes diagnosis fees as exogenously given (tothe best of our knowledge the only exceptions arePesendorfer and Wolinsky 2003 Alger and Salanieacute 2003and Dulleck and Kerschbamer 2005a) we do not endoge-nize the price for diagnosis (but rather assume that p = de)for easier comparison

12 Here the implicit assumption is that the outsideoption is not to be treated at all Again the car exampleprovides a good illustration A car may be inoperable for aminor or a major reason with the lack of treatment givingthe same outcome (lsquocar does not workrsquo) as undertreatmentThe medical example behaves differently For instanceletting a cancerous growth go untreated is much differentthan letting a benign growth go untreated See footnote 7above however

providing the wrong treatment and this factis common knowledge among all players10

There is a continuum with mass one ofrisk-neutral consumers in the market Eachconsumer incurs a diagnosis cost d perexpert he visits independently of whether heis actually treated or not11 That is a con-sumer who resorts to r experts for consulta-tion bears a total diagnosis cost of rd Thenet payoff of a consumer who has been treat-ed is his gross valuation as depicted in table1 minus the price paid for the treatmentminus total diagnosis cost The payoff of aconsumer who has not been treated is equalto his reservation payoff which we normal-ize to zero minus total diagnosis cost12 Byassumption it is always (ie even ex post)efficient that a consumer is treated when hehas a problem That is v minus cndash minus d gt 0 Also byassumption if a consumer is indifferentbetween visiting an expert and not visiting an expert he decides for a visit and if a

13 That consumers know expertsrsquo costs of providing dif-ferent treatments is obviously a very strong assumptionSince it is explicitly or implicitly imposed by all authorswho work with the verifiability assumption and since weneed it to replicate their results we introduce it here

14 Here note that from a game-theoretic point of viewthere is no difference between a model in which naturedetermines the severity of the problem at the outset andour model where this move occurs after the consumer hasconsulted an expert (but before the expert has performedthe diagnosis)

15 We take the convention that each consumer can visita given expert at most once

16 Throughout we assume that an expertrsquos agreement toperform the diagnosis means a commitment to provide atreatment even if treatment-provision is not profitable forthe expert This assumption is not important for our resultsand we mention in footnotes what changes if the expert isfree to send off the customer after having conducted thediagnosis

customer who decides for a visit is indifferentbetween two or more experts he randomizes(with equal probability) among them

Figure 1 shows the game tree for the spe-cial case where a single expert (n = 1) courts asingle consumer The variables v h cndash and cndashare assumed to be common knowledge13 Atthe outset the expert posts prices pminus and pminus forcndash and cndash respectively The consumer observesthese prices and then decides whether to visitthe expert or not If he decides against thevisit he remains untreated yielding a payoff ofzero for both players If he visits the expert arandom move of nature determines the sever-ity of his problem14 Now the expert diagnosesthe consumer In the course of her diagnosisshe learns the customerrsquos problem and recom-mends either the cheap or the expensivetreatment Next the customer decideswhether to accept or reject the recommenda-tion If he rejects his payoff is minus d while theexpertrsquos payoff is zero15 Under the commit-ment assumption (Assumption C) this deci-sion node of the consumer is missing If theconsumer is committed or if he accepts underthe noncommitment assumption then theexpert provides some kind of treatment andcharges for the recommended one16 Underthe verifiability assumption (Assumption V)this decision node is degenerate the expertsimply provides the recommended treatment

Mar06_Art1 22006 634 PM Page 13


Figure 1 Game Tree for the Credence Goods Problems

overprovisionovercharging

underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices

consumer decideswhether to visit theexpert or not

nature deter-mines severityof problem

expert recom-mends (andcharges ifaccepted)

consumeraccepts or rejects

expert provides

c

c

c ccc

c

Under the liability assumption (AssumptionL) this decision node is degenerate wheneverthe customer has the major problem then theexpert must provide the expensive treatmentThe game ends with payoffs determined inthe obvious way

The game tree for the model with manyconsumers and a single expert (n = 1) can bethought of as simply having many of thesesingle-consumer games going on simultane-ously with the fraction of consumers withthe major problem in the market being hWith more than one expert (n gt 1) theexperts simultaneously post prices pminus

i and pminusi

(i isin 1 n) for cndash and cndash respectively17

17 In the efficiency results of section 4 the distinctionbetween the setting where there is only one expert and theone where there are many experts is simply a matter ofdetermining whether the surplus in the market is trans-ferred to consumers or experts For the results in subsec-tion 51 experts need to have market power In our simplemodel market power corresponds to the single expert caseIn subsection 52 we discuss the case of multiple diagnosisa frequent phenomenon in markets for expert services Toanalyze this phenomenon we need more than one expert

Consumers observe these prices and thendecide whether to undergo a diagnosis by anexpert or not and if yes by which expertThus with n gt 1 a consumerrsquos decisionagainst visiting a given expert (the ldquooutrdquodecision in the game tree) doesnrsquot mean thathe remains untreated he might simply visita different expert Similarly a consumerrsquospayoff if he rejects a given expertrsquos treatmentrecommendation depends on whether hevisits a different expert or not

With commitment the game justdescribed is a multistage game withobserved actions and complete informationsee Drew Fudenberg and Jean Tirole (1991chapter 3)18 The natural solution conceptfor such a game is subgame-perfect equilib-rium and we will resort to it in section 4Subgame-perfection loses much of its bite inthe noncommitment case where the less-informed customer has to decide whether to

18 Tirole (1990 chapter 11) refers to such games asldquogames of almost perfect informationrdquo

Mar06_Art1 22006 634 PM Page 14


stay or to leave without knowing whether thebetter-informed expert has recommendedthe right or the wrong treatment To extendthe spirit of subgame-perfection to this gameof incomplete information we require thatstrategies yield a BayesndashNash equilibriumnot only for each proper subgame but alsofor continuation games that are not propersubgames (because they do not stem from asingleton information set) That is we focuson perfect Bayesian equilibria in the non-commitment case

4 Efficiency and Honesty with Credence Goods

We start by stating our efficiency resultPROPOSITION 1 Under Assumptions H

(Homogeneity) C (Commitment) and eitherL (Liability) or V (Verifiability) or bothmarket institutions solve the fraudulentexpert problem at no cost

The proof for this result as well as theintuition behind it relies on three observa-tions that are reported as Lemma 1ndash3 belowLemma 1 discusses the result under the ver-ifiability assumption With verifiability alone(ie without liability) experts find it optimalto charge a uniform margin over all treat-ments sold and to serve customers honestlyas the following result shows

LEMMA 1 Suppose that Assumptions H(Homogeneity) C (Commitment) and V(Verifiability) hold and that Assumption L(Liability) is violated Then in any sub-game-perfect equilibrium all consumers areefficiently served under equal markupprices The equilibrium prices satisfy pminus minuscndash = pminus minus cndash = v minus d minus cndash minus h(cndash minus cndash) if a singleexpert provides the good (n = 1) and pminus minuscndash = pminus minus cndash = 0 if there is competition in the

credence goods market (n ge 2)PROOF First note that with verifiability

each expert will always charge for the treat-ment she provided The treatment qualityprovided depends upon the type of price vec-tor (tariff) under which the customer isserved There are three classes of tariffs to

19 The assumption that it is common knowledge amongplayers that experts provide the appropriate treatmentwhenever they are indifferent plays an important role inLemma 1 in generating a unique subgame-perfect equilib-rium outcome Without this assumption there exist othersubgame-perfect equilibria which are supported by thebelief that all experts who post equal markup pricesmdashorthat experts who post equal markup prices that are too low(in the monopoly case too high)mdashdeliberately mistreattheir customers We regard such equilibria as implausible(see footnote 10 above) and have therefore introduced thecommon knowledge assumption which acts as a restrictionon consumersrsquo beliefs

consider tariffs where the markup for themajor treatment exceeds that for the minorone (pminus minus cndash gt pminus minus cndash) tariffs where the markupof the minor treatment exceeds that for themajor one (pminus minus cndash lt pminus minus cndash) and equal markuptariffs (pminus minus cndash = pminus minus cndash) A consumer under a tar-iff in the first class will always get the major aconsumer under a contract in the secondclass always the minor interventions Onlyunder contracts in the last class is the expertindifferent between the two types of treat-ment and therefore behaves honestly19

Consumers infer expertsrsquo incentives fromtreatment prices Thus if a single expert pop-ulates the market (n = 1) the maximal profitper customer the monopolist can realize withequal markup prices is v minus d minus cndash minus h(cndash minus cndash)the maximal obtainable profit with tariffs sat-isfying pminus minus cndash gt pminus minus cndash is v minus d minus cndash and the max-imal profit with tariffs satisfying pminus minus cndash lt pminus minus cndashis (1 minus h)v minus d minus cndash Thus since v gt cndash minus cndash theexpert will post the proposed equal markuptariff and serve customers honestly Next sup-pose that n gt 1 Further suppose that at leastone expert attracts some customer(s) under atariff (pminus pminus) that violates the equal markuprule Then she can increase her profit byswitching to an equal markup tariff (pminuspminus) satisfying either pminus minus cndash = pminus minus cndash = pminus minus cndash + (1 minus h)(cndash minus cndash) (if the old tariff had pminus minus cndash gtpminus minus cndash) or pminus minus cndash = pminus minus cndash = pminus minus c+ h(v minus cndash + cndash) (inthe opposite case) Thus only equal markupprices can attract customers in equilibriumThe result then follows from the observationthat pminus minus cndash = pminus minus cndash = 0 is the only equal markupconsistent with Bertrand competition

Mar06_Art1 22006 635 PM Page 15


Figure 2 Consumersrsquo Expected Utility with Verifiability

)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~

Figure 2 illustrates the equal markupresult graphically In this figure theterm tu(pminuspminus) denotes the expected net payoffof a consumer who resorts to an expert withposted price-vector (pminuspminus) First notice thatverifiability solves the problem of overcharg-ing that is the seller cannot claim to havesupplied the expensive treatment when sheactually has provided the cheap one Thereremains the incentive to provide the wrongtreatment Such an incentive exists if theintervention prices specified by the tariff aresuch that providing one of the treatments ismore profitable than providing the other Soif we fix the markup for the cheaper inter-vention at pminus minus cndash and increase the markup forthe expensive intervention from 0 (as it isdone in figure 2) then the expertrsquos incen-tives remain unchanged over the interval(0 pminus minus cndash) she will always recommend andprovide the cheap treatment at the price pminusConsequently a consumerrsquos expected utilityis constant in this interval at (1 minus h)v minus d minus pminusand there is an efficiency loss from under-treatment of size h(v minus cndash + cndash) Similarly if westart at pminus minus cndash and increase pminus minus cndash then theexpert will always recommend and provide

the expensive treatment at the price pminus so thatthe consumerrsquos utility is v minus pminus minus d implying anefficiency loss from overtreatment of size(1 minus h)(cndash minus cndash) Only at the single point wherethe markup is the same for both treatments(pminus minus cndash = pminus minus cndash = ∆ say) will the expert per-form a serious diagnosis and recommend theappropriate treatment At this point there isno efficiency loss and consumerrsquos expectedutility jumps discontinuously upward to v minus pminus minus h(cndash minus cndash) minus d

Consumers infer the expertsrsquo incentivesfrom the intervention prices So expertscannot gain by cheating Consequently thebest they can do is to post equal markup tariffs and to behave honestly In themonopoly case (n = 1) the expert has all themarket power Hence posted prices aresuch that the entire surplus goes to theexpert With two or more experts on theother hand Bertrand competition drivesprofits down to zero and consumers appro-priate the entire surplus as experts are notcapacity constrained in our model

The verifiability assumption is likely to besatisfied in important credence goods mar-kets including dental services automobile

Mar06_Art1 22006 635 PM Page 16


and equipment repair and pest control Formore sophisticated repairs where the cus-tomer is usually not physically present dur-ing the treatment verifiability is oftensecured indirectly through the provision ofex post evidence In the automobile repairmarket for instance it is quite common thatbroken parts are handed over to the cus-tomer to substantiate the claim that replace-ment and not only repair has beenperformed Similarly in the historic carrestoration market the type of treatment isusually documented step by step in pictures

Is there any evidence of equal markups inthese markets Many suppliers in the autorepair and historic car restoration market setstandard job-completion times and thencharge a uniform hourly rate This might beinterpreted as evidence for uniform marginsover all treatments sold

Equal markup prices are also plausible incases with expert sellers Computer storesare an obvious example Customers can con-trol which quality they receive Other exam-ples of uniform margins are the pricingschemes of insurance brokers and travelagents The markup insurance brokers andtravel agent charge (the margin plus anybonuses to the agent offered by theprovider) are similar for all products Oftenalso a fixed fee is involved independent ofwhat insurance is bought or which bookingis made

Lemma 1 facilitates the interpretation ofthe Emons (1997) result on the provisionand pricing strategy of capacity constrainedexperts Emons considers a model in whicheach of a finite number of identical poten-tial experts has a fixed capacity Shebecomes an active expert by irreversiblydevoting this capacity to the credence goodsmarket Once she has done this she can useher capacity to provide two types of treat-ment at zero marginal cost up to the capac-ity constraint One type of treatmentconsumes more units of capacity than thesecond Total capacity over all potentialexperts exceeds the amount necessary to

serve all customers honestly Emons propos-es a symmetric equilibrium in which eachpotential expertrsquos entry decision is strictlymixed Thus active experts may either haveto ration their clientele due to insufficientcapacity or they may end up with idle capac-ity In the former case they charge pricessuch that (1) all the surplus goes to theexperts and (2) the price for the morecapacity-consuming treatment exceeds theprice of the second treatment by such anamount that the profit per unit of capacityconsumed is the same for both types oftreatment In the latter case all expertscharge a price of zero for both types oftreatment In both cases experts serve cus-tomers honestly This is exactly what ourLemma 1 would predict the situationwhere demand exceeds total capacity corre-sponds in our model to a situation wheren = 1 since experts have all the marketpower in that case and since n is our param-eter for market power With all the marketpower experts appropriate the entire sur-plus and consumers get only their reserva-tion payoff of zero Furthermore withinsufficient capacity equal markup pricesimply a higher price for the more capacity-consuming treatment since the opportunitycost in terms of units of capacity used ishigher By contrast if capacity exceedsdemand the opportunity cost is zero forboth types of treatment Thus the price hasto be the same for both treatments to yieldequal markups Furthermore with idlecapacity experts have no market power(which corresponds in our model to a situa-tion where n ge 2) Without market powercompetition drives prices down to opportu-nity costs and customers appropriate theentire surplus

To summarize our analysis shows thatmany specific assumptions made by Emons(eg that there is a continuum of cus-tomers that capacity is needed to providetreatments that success is a stochasticfunction of the type of treatment providedetc) are not important for his efficiency

Mar06_Art1 22006 635 PM Page 17


20 The only inefficiency that remains in the Emonsmodel is the suboptimal amount of capacity provided inequilibrium This inefficiency has nothing to do with thecredence goods problem however It is rather a coordina-tion failure type of inefficiency similar to that arising in thesymmetric mixed strategy equilibrium of the grab-the-dollar game prominent in Industrial Organization

21 In the Emons model the inefficiencies described insubsection 51 arise for any n since experts have marketpower whenever capacity is insufficient to cover demand

22 Assumption C is not important for the Emons resultas Lemma 8 below shows

23 If the expert is not obliged to treat the customer afterhaving conducted the diagnosis the price charged in equi-librium changes to tp = minusc +(v minus d minus minusc) where = 1 forn = 1 and = 0 otherwise The rest of Lemma 2 remainsunaffected

result20 What is important however is thatconsumers are homogeneous (see Proposition2 below)21 and that the type of treatment isverifiable (see Proposition 4 below)22

Let us turn now to the liability caseUnder the liability assumption expertscharge a uniform price for both types oftreatment and serve customers honestly asthe following result shows

LEMMA 2 Suppose that Assumptions H(Homogeneity) C (Commitment) and L(Liability) hold and that Assumption V(Verifiability) is violated Then in any sub-game-perfect equilibrium each expertcharges a constant price for both types oftreatment and efficiently serves her cus-tomers The price charged in equilibrium isgiven by tp = v minus d if a single expert providesthe good (n = 1) and by tp = cndash + h(cndash minus cndash) ifthere is competition in the credence goodsmarket (n ge 2)23

PROOF Obvious from the discussionbelow and therefore omitted

Figure 3 depicts the expected utility of aconsumer under the conditions of Lemma 2In the setting under consideration the cus-tomer cannot control the service provided bythe expert In this case overtreatment is astrictly dominated strategy because the high-er cost of the expensive repair does not affectthe payment of the customer Also under-treatment is no problem because of the lia-bility assumption So each expert efficiently

24 As a referee pointed out this may be a too naive viewon HMOs In section 6 we discuss the plausibility ofAssumptions L in this context

serves her customers There remains theincentive to overcharge that is to alwaysclaim that an expensive and difficult repair isneeded even when a minor treatment fixesthe problem Such an incentive exists when-ever pminus ne pminus Consumers know this and expectthe expert to charge the higher price andthen to provide the cheapest sufficienttreatment Thus their behavior depends ontp = maxpminus pminus only The rest is trivial In themonopoly case (n = 1) the expert has all themarket power Thus she charges tp = v minus dWith n gt 1 the price-posting game is a stan-dard Bertrand game Thus the pricecharged in equilibrium is tp = cndash + h(cndash minus cndash) bythe usual price-cutting argument

Lemma 2 offers an explanation for the fre-quently observed fixed prices for expertservices in environments where experts haveto provide reliable quality because otherwisethey are punished by law or by bad reputa-tion One example is health maintenanceorganizations (HMOs) providing medicalservice to members at an individualizedconstant price per customer Our analysissuggests that the schemes offered by theHMOs are cheaper than a health insurancesystem Under insurance the customer doesnot care about the price after having paid theinsurance premium With the HMO thecompany will make sure that the cheapestsufficient quality will be provided24

Lemma 2 facilitates the identification ofthe driving forces behind Taylorrsquos (1995)efficiency results Taylor studies an elaboratemodel of a durable credence good whichmay be in one of three states health dis-ease or failure The good begins in the stateof health passes over to the state of diseaseand from there either to the state of failureor if efficiently treated back to the state ofhealth The amount of time spent in each ofthe first two states is governed by an expo-nential distribution When the good enters

Mar06_Art1 22006 635 PM Page 18


Figure 3 Consumersrsquo Expected Utility with Liability

0

pdv

p p

ppdv max

)(~ ppu

the state of failure it remains there foreverThe main problem for the owner of the goodis that he never discovers whether the goodis healthy or diseased An expert on theother hand can observe this by performing adiagnostic check If the check reveals thegood to be diseased she can perform thenecessary treatment Taylor shows that ifexperts post treatment prices ex ante thenthey essentially offer fair insurance againstthe presence of disease by charging a fixedprice equal to the expected treatment costas our Lemma 2 would predict However inthe Taylor model this insurance solution isnot efficient since the good also needs main-tenance by the owner for survival If theowner opts for low maintenance then themaintenance cost per unit of time is low butthe good is later more expensive to treatwhen it becomes diseased Obviously in thisset up fixed prices are inefficient since theyprovide poor incentives for owners to per-form maintenance Taylor proposes twoalternative ways to solve this problem expost contracts where experts commit totreatment prices only after having learnedthe ownerrsquos level of care and multiperiodcontracts for settings with repeated interac-tions between an owner and an expert

These solutions would dominate the simplefixed price rule in our setup too if weassumed that the good needs costly mainte-nance and that the ownerrsquos level of care isrevealed to the expert in the diagnosticcheck as is assumed by Taylor

Our framework shows that many detailsof the more sophisticated Taylor model arenot important for the efficiency resultsWhat is important however is that a liabili-ty rule protects consumers from obtaininginsufficient treatment (without liabilityexperts would never cure the good exceptfor the prospect of repeat business) and thatthe type of treatment is not verifiable (oth-erwise equal markup prices would provideincentives for maintenance)

Let us now consider the case where boththe liability and the verifiability assumptionhold In this case a lower markup for themajor than for the minor intervention is suf-ficient to induce nonfraudulent behavior asthe following result shows

LEMMA 3 Suppose that Assumptions H (Homogeneity) C (Commitment) L(Liability) and V (Verifiability) hold Then in any subgame-perfect equilibrium eachexpert posts and charges prices yielding alower (le) markup for the more expensive

Mar06_Art1 22006 635 PM Page 19


25 Obviously if an expert is not obligated to treat a cus-tomer after having conducted the diagnosis equilibriumprices will also satisfy the condition minusp ge minusc

treatment and efficiently serves her cus-tomers Posted (and charged) equilibriumprices satisfy pminus + h(pminus minus pminus) = v minus d and pminus minuscndash le pminus minus cndash if a single expert provides the good(n = 1) and pminus + h(pminus minus pminus) = cndash + h(cndash minus cndash) and pminus minus cndash le pminus minus cndash if there is competition in the credence goods market (n ge 2)25

PROOF The proof is similar to that ofLemma 1 the only difference being that theliability rule prevents the expert from profit-ing by providing the cheap treatment whenthe expensive one is needed

Under the conditions of Lemma 3 verifi-ability prevents an expert from claiming tohave supplied the major treatment when sheactually has provided the minor one (ieovercharging is ruled out) In addition lia-bility prevents her from providing the minorintervention when her customer needs themajor one (ie undertreatment is ruled outtoo) There remains the incentive to providea major treatment when the consumer onlyneeds the minor one This overtreatmentincentive disappears if prices are such thatthe markup for the minor treatment exceedsthat of the major treatment

Lemmas 1ndash3 discussed possible idealenvironments that imply that the pricemechanism solves the credence goods prob-lem at no cost This no-fraud result suggeststhat asymmetric information alone cannotexplain expertsrsquo cheating

Table 2 recapitulates the role our fourassumptions play for the efficiency result Ifconsumers are homogeneous price discrimi-nation is no issue As we will see below pricediscrimination in expert markets proceedsalong the dimension of quality of adviceoffered

The commitment assumption preventsconsumers from visiting more than oneexpert This assumption is important forefficiency if liability holds while verifiabilityis violated Why Because then a constant

26 As one of the referees pointed out a second diagno-sis is not necessary in many settings Our assumption thatprovision of treatment without diagnosis is impossibleshould not be taken literally however but rather as a shortcut for situations in which there exist economies of scopebetween diagnosis and treatment As Darby and Karni(1973 footnote 2) have put it ldquo it is easier to repair anydamage while the transmission or belly is open to see whatis wrong than to put everything back together and goelsewhere to repeat the process for the actual repairrdquo

price across treatments is necessary to pre-vent experts from overcharging (see Lemma2) A constant price across treatmentsimplies that consumers with minor prob-lems subsidize those with major ones Ifconsumers are not committed to undergo atreatment once a diagnosis has been madeand if the cost of getting a second opinion islow such cross-subsidization becomes infea-sible because it invites cream skimming by adeviating expert who sells the minor inter-vention only at a lower price Nondeviatingexperts who charge a constant price acrosstreatments will realize that only consumerswho need a major intervention visit themand they will adjust their prices accordinglyThe result is specialization some expertssell only the minor others only the majorintervention Specialization is inefficientbecause it implies a duplication of searchand diagnosis costs26

The verifiability assumption preventsovercharging while the liability assumptionprevents undertreatment If none of theseassumptions holds each expert will alwaysprovide the minor and charge for the majorintervention Thus undertreatment of con-sumers who need the major treatmentresults Consumers anticipate this and iftheir valuation for a successful treatment istoo low they leave the market

In the next section we will discuss these(and other) inefficiencies in more detail

5 Various Degrees of Inefficiencies andFraud in the Credence Goods Market

In this section we characterize the ineffi-ciencies that might arise if at least one of the

Mar06_Art1 22006 635 PM Page 20


TABLE 2ASSUMPTIONS AND THEIR IMPORTANCE FOR THE EFFICIENCY RESULT

Assumption Effect

Homogeneity prevents price discrimination

Commitment prevents consumers from visiting more than one expert

Liability prevents undertreatment

Verifiability prevents overcharging

conditions of Proposition 1 is violated Webegin with the homogeneity assumption(Assumption H)

51 Heterogeneous Consumers InefficientRationing and Inefficient Treatment ofsome Consumer Groups

Dropping the homogeneity assumptioncan give rise to two different kinds of ineffi-ciency inefficient rationing of consumersandor inefficient treatment of some con-sumer groups To show this we consider asetting in which a single expert (n = 1) sellsverifiable treatments (Assumption V holds)to heterogeneous consumers (Assumption His violated) To keep things simple we con-centrate on the case where consumers onlydiffer in their expected cost of efficient treat-ment More precisely we assume that a con-sumer of type h has the major problem withprobability h and the minor problem withprobability (1 minus h) Since this assumptionimplies that higher type consumers have ahigher expected cost of efficient treatmentwe refer to them as high cost consumersConsumersrsquo types (ie the probabilities h)are drawn independently from the sameconcave cumulative distribution functionF() with differentiable strictly positive den-sity f() on [01] F() is common knowledgebut a consumerrsquos type is the consumerrsquos pri-vate information If a consumer gets a treat-ment that fixes his problem he obtains atype-independent gross utility of v and if notone of zero exactly as in our basic model

Let us start with a setting in which theexpert cannot price discriminate among

consumers Without price discriminationthe expert chooses equal markup pricesWhy Because consumers infer the expertrsquosincentives from the intervention pricesThus the expert cannot gain from cheatingConsequently the best she can do is to postan equal markup tariff and to provide seriousdiagnosis and appropriate treatment Withan equal markup tariff the monopolisticexpert is interested in two variables only inthe magnitude of the markup and in thenumber of visiting customers If consumersare very similar the expert finds it profitableto serve all consumers Otherwise prices aresuch that some consumers do not consult hereven though serving them would be effi-cient This is nothing but the familiarmonopoly-pricing inefficiency We record itin Lemma 4

LEMMA 4 Suppose that Assumptions C(Commitment) and V (Verifiability) holdand that Assumptions H (Homogeneity)and L (Liability) are violated Further sup-pose that a single expert (n = 1) who cannotprice-discriminate among customers servesthe market and that consumers differ intheir expected cost of efficient treatmentonly Then in the unique subgame-perfectequilibrium the expert posts and chargesequal markup prices (pminus minus cndash = pminus minus cndash) If thedifference in expected cost between the bestand the worst type is large relative to theefficiency gain of treating the worst type(cndash minus cndash gt (v minus d minus cndash)f(1)) then prices aresuch that (i) high cost consumers decide toremain untreated (pminus gt v minus d) and (ii) allother types visit the expert (pminus lt v minus d) and

Mar06_Art1 22006 635 PM Page 21


27 That the condition minusc minus minusc gt (v minus d minus minusc)f (1) is necessaryand sufficient for an interior solution is easily verified bychecking that the expertrsquos profit is an increasing function of∆ at ∆ = v minus minusc minus d if and only if this condition is satisfied

get serious diagnosis and appropriate treat-ment Otherwise all consumers are effi-ciently served under equal markup prices(pminus le v minus d)

PROOF From the proof of Lemma 1 weknow that for given net utilities for the con-sumers the monopolistrsquos profit is highestwith an equal markup tariff Thus themonopolist will choose such a tariff and shewill provide the appropriate treatment to allof her customers With an equal markup tar-iff the monopolistic expert is interested intwo variables only in the magnitude of themarkup (pminus minus cndash = pminus minus cndash = ∆ say) and in thenumber of visiting consumers The resultthen follows from the observation that theexpertrsquos problem is nothing but the familiarmonopoly pricing problem for demandcurve D(pminus) = F[(v minuspminus minus d)(cndash minus cndash)] and netrevenue per customer ∆ = pminus minus cndash27

For our next result we allow the expert topost more than one tariff Since consumersdiffer in their expected cost of efficienttreatment the monopolist might want to tar-get a specific tariff for each consumer or atleast different tariffs for different consumergroups However in the absence of informa-tion about the identity of each consumer(the expert only knows the aggregate distri-bution of probabilities of needing differenttreatments) the expert must make sure thatconsumers indeed choose the tariff designedfor them and not the tariff designed forother consumers This puts self-selectionconstraints on the set of tariffs offered by themonopolist As our next result shows themonopolist uses the quality of advice offeredas a self selection device

LEMMA 5 Suppose that the generalconditions of Lemma 4 hold except that theexpert can now price discriminate amongconsumers (rather than being restricted toa single price vector only) Then in any

subgame-perfect equilibrium the expertposts two tariffs one with equal markupsand one where the markup for the majortreatment exceeds that for the minor one28

Both tariffs attract customers and in totalall consumers are served Low cost con-sumers are served under the former tariffand always get serious diagnosis andappropriate treatment high cost con-sumers are served under the latter andalways get the major treatment sometimesinefficiently

PROOF The proof parallels Dulleckand Kerschbamerrsquos (2005b) proof of (their)Proposition 2 We reproduce it here in theappendix to this paper

When price discrimination is possiblethe expert finds it optimal to provide high-quality diagnosis and appropriatetreatment to low-cost consumers onlyHigh-cost consumers are potentiallyovertreated that is they are induced todemand a high-quality intervention withoutan honest diagnosis

Why is such a policy optimal The reasonis simple Under perfect price discrim-ination the monopolist would providehigh-quality diagnosis and appropriatetreatment to all consumers and gain theentire surplus by charging customer specif-ic prices In the absence of informationabout the identity of consumers perfectdiscrimination is infeasible With imperfectdiscrimination the expert sells seriousdiagnosis and appropriate treatment at arelative high price to low-cost consumersonly For the rest of the market this policyis unattractive since the expected price islarger than the valuation of a successfulintervention Offering efficient diagnosisand treatment at a lower expected price tothe residual demand is impossible becausethis would induce low-cost consumers toswitch to the cheaper policy So the expert

28 The menu may contain some redundant price vectorstoo ie some tariffs that attract no consumers

Mar06_Art1 22006 635 PM Page 22


offers in addition to the expensive efficientdiagnosis and treatment policy a cheaperbut also less efficient one Her difficulty indesigning this second policy is to preventthe low-cost segment from choosing thecheaper policy The solution is to potential-ly overtreat the residual demand consistingof high-cost consumers that is to inducethem to demand a high-quality interven-tion (a new engine) without a serious diag-nosis For low-cost consumers this policy isunattractive since their problem is mostlikely to be a minor one implying that buy-ing the expensive efficient diagnosis andtreatment policy still entails a lower expect-ed cost than buying the high quality inter-vention (without an honest diagnosis) at abargain price

While the equilibrium behavior outlinedin Lemma 5 is obviously an abstraction andit is probably impossible to point out anindustry that features exactly this kind ofprice discrimination the result identifiesan element that may be present in the con-duct of some industries The IT industryfor example features some degree of sec-ond degree price discrimination there arePC manufacturers who distribute theirequipment through IT warehouses thatoffer only selected qualities of equipmentat a relatively low price and through spe-cialized dealers that offer the entire assort-ment as well as advice on choosing the rightquality some consumers (presumably theless profitable ones) buy from warehousesellers others consult an expert seller andget serious diagnosis and appropriateequipment

The equilibrium outlined in Lemma 5 isessentially the overtreatment equilibrium ofDulleck and Kerschbamer (2005b) Dulleckand Kerschbamer go on to show that theresult changes dramatically when con-sumers differ in their valuation for a suc-cessful intervention (rather than in theirexpected cost of efficient treatment) In thiscase no overtreatment will be observed butundertreatment appears

29 To the best of our knowledge there are only threefurther contributions with heterogeneous consumers oneof them is the more verbal paper by Darby and Karni(1973) the second is the 1993 article by Pitchik andSchotter and the third is Fong (2005) In the former twoarticles heterogeneity is only used to purify a mixed strat-egy equilibrium in the third contribution consumersrsquo lackof commitment power plays an important role for theresultmdashwe therefore relegate the discussion of that articleto the next subsection

Dulleck and Kerschbamerrsquos undertreat-ment result stands in sharp contrast to thefindings in another credence goods paperthat has the verifiability assumption andheterogeneous consumers29 In a modelwith capacity constrained experts who pro-vide procedures to consumers who differ intheir valuation for a successful interven-tion Richardson (1999) finds that all treat-ed consumers are overtreated that is theyget a high-quality intervention independ-ently of the outcome of the diagnosis Acloser look at his paper reveals differentdriving forces behind the Richardsonovertreatment and the Dulleck andKerschbamer (over- and undertreatment)results The Dulleck and Kerschbamerresults are driven by a combination of mar-ket power and the ability to price discrimi-nate among heterogeneous consumersObviously the type of treatment must alsobe verifiable (otherwise overtreating wouldbe strictly dominated by overcharging) Bycontrast Richardsonrsquos findings result froma lack of commitment power Consider anexpert who can ex ante precommit only tothe price for a low quality basic interven-tion At the diagnosis stage the expert cantell the consumer that the basic interven-tion is insufficient to cure his problem andinform him about the additional amount hewould have to pay if he accepts an upgradeto a more advanced procedure The con-sumer knows that he might have a seriousproblem and that the basic interventionfails in this case He is therefore preparedto pay some additional amount for astronger intervention If this amountexceeds the difference in treatment costs

Mar06_Art1 22006 635 PM Page 23


30 Here remember that equal markup prices are nec-essary to induce an expert to perform serious diagnosis andto provide the appropriate treatment (see the discussion ofLemma 1)

(as is the case under Richardsonrsquos assump-tions) then the expert has an incentive toalways recommend a stronger treatmenteven if the basic intervention would havebeen sufficient to cure the problem30

Before proceeding further notice thatthe inefficiencies of lemmas 4 and 5 disap-pear if experts have no market power Withn gt 1 price-competing experts provide bothtypes of treatment at marginal cost leavingno leeway for inefficiencies of any kindNote here that the relevant condition is notn = 1 but rather that experts have marketpower in providing treatments In a modelin which capacity is required to serve cus-tomers (cf eg Emons 1997 and 2001 orRichardson 1999) experts have marketpower (independently of n) whenever tightcapacity constraints hamper competitionSimilarly consumer loyalty travel coststogether with location search costs collu-sion and many many other factors mightgive rise to market power

We summarize the results of this subsec-tion in the following proposition

PROPOSITION 2 Subgame-perfect equi-libria exhibiting inefficient rationing andorinefficient treatment of some consumergroups can exist if Assumption H(Homogeneity) is violated and experts havemarket power

52 No Commitment Overcharging andDuplication of Search and DiagnosisCosts

In this subsection we drop the commit-ment assumption Under certain condi-tions this gives rise to two different typesof equilibriamdashovercharging equilibria andspecialization equilibria In both the cre-dence goods problem manifests itself ininefficiently high search and diagnosis costsas some consumers end up visiting morethan one expert and being diagnosed more

31 If experts are not committed to treat their customersafter having conducted a diagnosis then a lower bound forthe price of the expensive treatment (minusp ge minusc) emergesendogenously So only the upper bound for prices (minusp le minusc + d)is required in this case to prove part (i) of the lemma

than once We begin with the overchargingscenario To get the overcharging resultstudied in the literature firmsrsquo price settingpower needs to be restricted In part (i) ofLemma 6 this is captured by referring to a(legal) rule requiring experts to choose theprice for the expensive treatment from agiven range of cost-covering prices Such arule is of course unrealistic Part (ii) of thelemma shows that the overcharging equi-librium ceases to exist if prices are fullyflexible

LEMMA 6 (i) Suppose that AssumptionsH (Homogeneity) and L (Liability) hold andthat Assumptions C (Commitment) and V(Verifiability) are violated Further supposethat there is some competition in the cre-dence goods market (n ge 2) that economiesof scope between diagnosis and treatmentare relatively low (d lt (cndash minus cndash)(1 minus h)) andthat a (legal) rule is in effect requiringexperts to choose the price for the expensivetreatment from a given range of cost-cover-ing prices (pminus isin [cndash cndash + d])31 Then thereexists a symmetric weak perfect Bayesianequilibrium in which experts overchargecustomers (with strictly positive probabili-ty) In this equilibrium experts post pricessatisfying pminus = cndash + ∆ and pminus = cndash gt cndash + ∆ Experts always recommend the expensivetreatment if the customer has the majorproblem and they recommend cndash with proba-bility ω isin (01) if the customer has the minorproblem Consumers make at least one atmost two visits Consumers at their first visitalways accept a cndash recommendation and theyaccept a cndash recommendation with probability isin (01) and reject it with probability (1 minus) Consumers who reject visit a second(different) expert and on that visit theyaccept both recommendations with certain-ty A customer who accepts to be treatedalways gets the appropriate treatment

Mar06_Art1 22006 635 PM Page 24


32 For experts to be indifferent between recommend-ing the minor and recommending the major interventionwhen the customer has the minor problem the probabili-ties and ω and the markup ∆ must satisfy ∆ [1 + ω(1 minus)] = (minusc minus minusc)[ + ω (1 minus )] To understand this equationnote that recommending the cheap treatment guarantees aprofit of minusp minus minusc = ∆ gt 0 for sure while recommending theexpensive treatment when only the cheap one is requiredis like playing in a lottery yielding a payoff of minusp minus minusc gt ∆ withprobability [ + ω (1 minus )] [1 + ω (1 minus )] and zero oth-erwise This probability takes into account that a fraction1[1 + ω (1 minus )] of customers are on their first visit (andhence are accepting the minusc recommendation with probabil-ity ) while the remaining fraction ω (1 minus )[1 + ω (1 minus )]are on their second visit (accepting the minusc recommendationfor sure)

(ii) The strategy profile sketched in part (i)of this lemma ceases to form part of a weakperfect Bayesian equilibrium if experts arecompletely free in choosing prices

PROOF See the appendix

In the setting under consideration verifi-ability is violated In this case overtreat-ment is a strictly dominated strategybecause the higher cost of the expensiverepair does not affect the payment of thecustomer Also undertreatment is no issuebecause of the liability assumption So eachexpert efficiently serves her customersThere remains the incentive to overchargethat is to claim that a major intervention isneeded when a minor one fixes the prob-lem Such an incentive exists in the equilib-rium characterized in Lemma 6 since minusp gt minuspIn the equilibrium experts do not over-charge their customers all the time (butonly with strictly positive probability)because recommending the cheap treat-ment guarantees a positive profit of minusp minus cminus= ∆ gt 0 for sure while recommending theexpensive treatment when only the cheapone is required is like playing in a lotteryyielding a payoff of minusp minus minusc gt ∆ if the con-sumer accepts and zero otherwise By con-struction the expected payoff under thelottery equals ∆ making experts exactlyindifferent between recommending honest-ly and overcharging32

The overcharging equilibrium sketched inpart (i) of Lemma 6 is essentially the equi-librium outlined by Pitchik and Schotter

33 Suumllzle and Wambachrsquos (2005) paper is essentially acomparative statics study on the overcharging equilibriumof Lemma 6 The main focus is on the effect of insurancearrangements on the (mixed strategy) equilibrium behaviorof consumers and experts

34 See Andreu Mas-Colell Michael Whinston andJerry R Green (1995) for the definition of weak perfectBayesian equilibrium Roger B Myerson (1991) calls thesame concept a weak sequential equilibrium

(1987)mdashand further studied by Suumllzle andWambach (2005)mdashfor a setting with exoge-nously given payoffs33 Wolinsky (1993)argues that the equilibrium might also existwith flexible prices if sufficiently few expertscompete for customers Lemma 6 shows thatthe overcharging configuration of part (i)continues to form part of a weak perfectBayesian equilibrium if experts have somefreedom to choose prices but that it ceasesto form part of such an equilibrium if pricesare fully flexible34

The reason for why overcharging equilib-ria with the essential features as outlined inpart (i) of the lemma cease to exist if expertsare completely free in choosing prices is thatthe markup minusp minus minusc = ∆ which is necessary tosupport the described behavior as a weakperfect Bayesian equilibrium invites priceundercutting by a deviating expert who spe-cializes in the minor intervention How can adeviating expert specialize in the minorintervention In the present model whereeach expertrsquos decision variables are her post-ed prices and her recommendation policyspecialization on the minor interventionoccurs via the commitment to a tariff whichinduces customers who are diagnosed torequire the major intervention to rejecttreatment and to visit another expert Howdoes such a specialization tariff look In theequilibrium of Lemma 6 all experts post (minusp minusp) = (minusc + ∆ minusc) Thus by posting a tariffthat has minusp gt minusc + d a deviating expert cancredibly signal that she will provide reliablediagnosis and only the minor treatment Thepoint is that when the customer has themajor problem the expert cannot sell theminor intervention because of liability Thusshe will reveal his true condition And if the

Mar06_Art1 22006 635 PM Page 25


customer has the minor problem the expertwill not recommend the major treatmentbecause the customer would reject it and hewould visit a nondeviating expert (if heaccepts he pays minusp gt minusc + d if he rejects andvisits a nondeviating expert his cost is minusc + d)Under the conditions of part (i) of Lemma 6such specialization tariffs are infeasible Ifthey become feasible because prices areflexible (as in part (ii) of the lemma) theovercharging configuration ceases to formpart of a weak Bayesian equilibrium

The ldquoequilibrium with fraudrdquo discussedby Darby and Karni (1973) resembles apurified version of the overcharging equilib-rium of Lemma 6 In their analysis ldquo increasing the amount of services pre-scribed on the basis of the diagnosisincreases the probability of entering thecustomerrsquos critical regions for going else-where [ ] Taking this consideration intoaccount the firm will take fraud up to thepoint where the expected marginal profit iszerordquo (p 73) Adapting Lemma 6 to an envi-ronment where consumers are heteroge-neous with respect to their search costwould yield an equilibrium with these prop-erties (see Pitchik and Schotter 1993) Theanalogy is not perfect however as the prob-lem discussed by Darby and Karni is that ofovertreating and not that of overchargingcustomers Overtreatment can only poseproblems if the customer can observe andverify the type of treatment he gets (ourAssumption V) since if he cannot over-charging is always more profitable But withverifiability and flexible prices there are noequilibria exhibiting fraud as Lemma 8below shows In other words to support theDarby and Karni (1973) configuration withfraud as an equilibrium payoffs again needto be exogenously fixed as they are in theirenvironment

A result that resembles a degenerate ver-sion of the overcharging equilibrium ofLemma 6 is the ldquono-cheating resultrdquo ofFong (2005) In Fongrsquos basic model there is a single expert who offers two types of

35 Since in Fongrsquos model there is a single expertAssumption C is not required to get this result

36 With a fixed price below minusc the expert turns downconsumers with a major problem with a fixed price aboveminusc no consumer will ever consult the expert (as minusc is abovev minus d by Fongrsquos first departing assumption)

37 If the cminus recommendation is accepted for sure theexpert will always recommend cminus if only cminus recommenda-tions are accepted she will always recommend cminus Thus inan equilibrium in pure strategies a price vector with pminus ne pminusis equivalent to a fixed price contract

treatment to a continuum of homogeneousconsumers in an environment in which lia-bility holds while verifiability is violatedSince the expert is completely free in choos-ing prices our model would predict that shesets a single price for both treatments at theconsumersrsquo net valuation for a successfulintervention (that is minusp = minusp = v minus d seeLemma 2)35 However this solution is infea-sible in Fongrsquos setup due to a combinationof two assumptions First consumersrsquo valu-ation for a successful intervention isassumed to be small in comparison to treat-ment costs Translated to the present con-text Fongrsquos assumption amounts tov minus d lt minusc lt v while we assume minusc lt v minus d Thismodification alone would not change any-thing provided that it is ex ante efficient tovisit the expert (ie v minus d minus minusc minus h(minusc minus minusc) ge 0)The experts would still offer to fix bothtypes of problem at the price v minus d cross-subsidizing the losses made on selling cminus bythe gains made on selling minusc Fongrsquos seconddeparture from our assumptionsmdashthat theexpert has the option to reject a customerafter performing a diagnosismdashimplies thattreatment prices cannot be lower than treat-ment costs and thereby prevents this (andany other) fixed price solution36 Also purestrategy equilibria in which the expert poststwo different prices cannot exist because insuch an equilibrium it must be commonknowledge that only one of the prices willbe charged by the expert37 It remains asthe only possibility an equilibrium in mixedstrategies In such an equilibrium theexpert posts two prices (minusp = v minus d (1 minus h)minusp = v) and nevertheless behaves honestly

Mar06_Art1 22006 635 PM Page 26


38 In Fongrsquos model where consumers who reject do notreenter the market for the expert to be indifferentbetween recommending the minor and recommendingthe major treatment when the customer has the minorproblem the probability must satisfy = (_p minus _c)(

_p minus _c)

= [_v minus _d(1 minus _h) minus _c](_v minus _c)

The intuition behind this ldquono-cheatingresultrdquo parallels that for Lemma 6 Theexpert does not recommend the majorintervention when the minor one fixes theproblem because customers accept themajor treatment with a low enough proba-bility while they accept the minor one forsure38 The only difference to the over-charging equilibrium in Lemma 6 is thatconsumers who get a minusc recommendation arenot kept indifferent between accepting andrejecting by the expertrsquos cheating behaviorbut rather by the fact that the price chargedfor the major treatment equals exactly theirvaluation for a successful intervention (minusp = v) Although there is no duplication ofsearch and diagnosis costs in Fongrsquos modelthe equilibrium is still inefficient because afraction of consumers who need the majortreatment remain untreated to keep theexpert indifferent

Based on this basic model Fong derivestwo overcharging equilibria both based onidentifiable heterogeneity among con-sumers To see how they work assume thatthere exist two groups of consumersmdashonewith valuation minusv the other with valuation minusv gt minusv where minusv minus d lt minuscmdashand that a con-sumerrsquos valuation is observable to theexpert Obviously from the expertrsquos pointof view it would be ideal if she could pricediscriminate between the two groups Thisis assumed to be impossible that is theexpert is constrained to post a single pricevector only With a single vector she canimplement the no-cheating result for a sin-gle customer group only If the fraction ofminusv consumers is large she will implementthe no-cheating result for those consumersand ignore the rest of the market By con-trast if there are many minusv consumers theexpert tailors the no-cheating tariff to their

39 One difference between the overcharging equilibri-um of Lemma 6 and Fongrsquos overcharging equilibriumdeserves mentioning In the equilibrium of Lemma 6 con-sumersrsquo incentive to reject a cminus recommendation increasesin ω because a higher ω implies that the consumer has ahigher probability to pay less for the treatment on his sec-ond visit By contrast in Fongrsquos model consumers have noopportunity to visit a second expert Thus an additionalassumption is needed to keep consumers indifferentnamely that the loss born by the consumer if his problemis left untreated is greater if cminus rather than minusc is required

40 In the Wolinsky (1993) model where experts committo an unobservable recommendation policy at the price-posting stage of the game an additional restriction onbeliefs is required to prove the result In the presentmodel that requirement is implied by the notion of perfectBayesian equilibrium

valuation (minusp = minusv minus d (1 minus h) minusp = minusv) and shewill sometimes overcharge minusv consumers tokeep them indifferent between acceptingand rejecting a minusc recommendation (exactlyas in our Lemma 6)39

To summarize our analysis shows thatmany specific assumptions made by Fong(eg that there is no diagnosis cost or thatthe treatments for the two problems are notsubstitutable) are not important for his find-ings What is important however is that lia-bility holds while verifiability is violatedthat consumers are not committed that theexpert is not committed either and that con-sumersrsquo valuation for successful treatment israther low

Overcharging equilibria with the essentialfeatures as outlined in Lemma 6 cease toexist if there is more than one expert and if experts are free in choosing prices With fully flexible prices a continuum of experts and low economies of scopebetween diagnosis and treatment the onlyperfect Bayesian equilibria that survivewhen Assumptions H and L hold whileAssumptions C and V are violated are spe-cialization equilibria similar to the one out-lined in the next lemma This has beenshown by Wolinsky (1993)40

LEMMA 7 Suppose that Assumptions H(Homogeneity) and L (Liability) hold andthat Assumptions C (Commitment) and V(Verifiability) are violated Further suppose

Mar06_Art1 22006 635 PM Page 27


41 If experts are not committed to treat their customersafter having conducted the diagnosis the condition d lt(minusc minus minusc)(1 minus h) changes to d lt (minusc minus minusc)(1 minus h)h

that there is enough competition in the cre-dence goods market (n ge 4) and thateconomies of scope between diagnosis andtreatment are relatively low (d lt (minusc minus minusc)(1 minus h))41 Then there exists a perfectBayesian equilibrium exhibiting specializa-tion In this equilibrium some experts (atleast two) post prices given by minusp = minusc and minusp gt minusc + d (we call such experts ldquocheap expertsrdquo)and some other experts (again at least twoldquoexpensive expertsrdquo) post prices given by pminus le minusp = minusc Cheap experts always recommendthe appropriate treatment expensive expertsalways the expensive one Consumers firstvisit a cheap expert If this expert recom-mends minusc the customer agrees and gets minusc Ifthe cheap expert recommends minusc the cus-tomer rejects and visits an expensive expertwho treats him efficiently


In the specialization equilibrium ofLemma 7 liability (again) solves the prob-lem of undertreatment and the cost differ-ential minusc minus minusc that of overtreatment Theincentive to overcharge customers is elimi-nated because cheap experts lose their cus-tomers if they recommend the expensivetreatment (see the discussion above)

Is there any supporting evidence for verti-cal specialization as outlined in Lemma 7 inthe market place Wolinsky (1993) mentionsthe automobile repair industry as an exam-ple of a market featuring some degree ofspecialization of this kind there are back-yard garages who specialize in minor repairsand there are certified dealer garages whooffer the whole spectrum of treatmentssome consumers (presumably those with alower opportunity cost of time) first visit abackyard garage and if the problem turnsout to be a major one they turn to a certifieddealer

Note that the condition for the strategiesdescribed in Lemma 1 to form part of a

42 Glazer and McGuire (1996) characterize a similarequilibrium for a setting in which there are (by assump-tion) two types of experts safe ones who can successfullyserve all consumers and risky ones whose treatmentmight fail The focus of their work is on optimal referralfrom risky to safe experts after risky expertsrsquo diagnosis of aconsumerrsquos problem

43 Wolinsky (1993) doesnrsquot explicitly impose the liabilityassumption This assumption is implicit in his specificationof consumer payoffs however

perfect Bayesian equilibrium even if thecommitment assumption (Assumption C) isnot imposed and even if n ge 4 is exactly thatthe restriction imposed by Lemma 7 on d isviolated that is the diagnosis cost d mustexceed (1 minus h)(minusc minus minusc) To verify this noticethat a deviation that might jeopardize theequilibrium of Lemma 1 is a specializationtariff that has minusp lt minusc + h(minusc minus minusc) and minusp ge minusc + h(minusc minus minusc) + d The expected cost to aconsumer who visits the deviator first and ifrecommended the expensive treatmentresorts to a nondeviating expert is d + (1 minus h)

minusp + h[minusc + h(minusc minus minusc) + d] Consulting only anondeviating expert on the other handcosts d + minusc + h(minusc minus minusc) Thus to attract cus-tomers the deviator must post a price vectorwith a minusp such that d + minusc + h(minusc minus minusc) ge d +(1 minus h) minusp + h[minusc + h(minusc minus minusc) + d] which isequivalent to minusp le minusc + h[(minusc minus minusc) minus d (1 minus h)]But if d gt (1 minus h)(minusc minus minusc) then such a pricevector doesnrsquot cover cost and no deviation isprofitable

The equilibrium outlined in Lemma 7 isessentially the specialization equilibrium ofWolinsky (1993) the only difference beingthat experts can refuse to provide a treatmentafter having conducted the diagnosis in theWolinsky model while they cannot refuse inour present framework42 What drives theWolinsky result is the combination of twoassumptions the assumption that consumersare neither able to observe the type of treat-ment they need nor the type they get (ourAssumption V is violated) and the assumptionthat experts are liable for providing the cheaptreatment when the expensive one is needed(our Assumption L holds)43 Specialization

Mar06_Art1 22006 635 PM Page 28


44 Since the uniform price charged by the monopolisticexpert under the conditions of Lemma 1 does not exceedconsumersrsquo gross utility v they will not quit even if notcommitted for their only alternative is to remain withoutany treatment

equilibria cease to exist if Assumption L is violated and they also cease to exist ifAssumption V holds We postpone the discus-sion of the case where neither liability norverifiability holds to the next subsection andrecord the rest of the result as Lemma 8

LEMMA 8 Suppose that prices are flexi-ble that consumers are homogeneous(Assumption H) and that the type of treat-ment is verifiable (Assumption V) Then theequilibria summarized in Lemma 1 (for thecase where Assumption L is violated) andLemma 3 (for the case where Assumption Lholds) remain the only perfect Bayesianequilibria even if Assumption C is violated

PROOF The proof is similar to that ofLemma 1 and therefore omitted

Why is it that specialization equilibriainvolving costly double advice exist if liabilityholds while verifiability is violated while theycease to exist if verifiability holds The pointis that verifiability allows experts to set treat-ment prices close to marginal cost Withprices close to marginal cost consumers haveno incentive to search for a second opinion

For obvious reasons perfect Bayesianequilibria exhibiting specialization and per-fect Bayesian equilibria in which expertsovercharge customers also cease to exist if asingle expert serves the market44


PROPOSITION 3 Perfect Bayesian equi-libria exhibiting specialization and perfectBayesian equilibria in which experts over-charge their customers might exist ifAssumption C (Commitment) is violated

53 Neither Liability Nor Verifiability TheCredence Goods Market Breaks Down

In this subsection we consider an envi-ronment resembling a hidden action version

45 Proposition 4 relies on the assumption that con-sumers are able to verify whether some kind of treatmenthas been provided or not If this is not the case eachexpert always has an incentive to provide no treatment atall and the credence goods market ceases to exist for anyvalue of v (see also the next footnote)

of George A Akerlofrsquos (1970) lemons modelconsumers can neither observe the type oftreatment they get (Assumption V is violat-ed) nor can they punish the expert if theyrealize ex post that the type of treatmentthey received is not sufficient to solve theirproblem (Assumption L is violated too)Under these adverse conditions theexpert(s) always provide(s) the cheap (andcharge(s) for the expensive) treatmentConsumers anticipate this and consult anexpert only if the price of the expensivetreatment is such that getting the minorintervention at this price for sure increasestheir expected utility If there is no minusp ge minusc thatattracts customers no trade takes place andthe credence goods market ceases to exist45

PROPOSITION 4 Suppose that AssumptionH (Homogeneity) holds and that AssumptionsV (Verifiability) and L (Liability) are violat-ed Then there is no perfect Bayesian equilib-rium in which experts serve customersefficiently If consumers valuation v is suffi-ciently high (minusv ge (minusc + d)(1 minus minush)) then eachexpert charges a constant price (given by tp =(1 minus h)v minus d if a single expert provides thegood and by tp = minusc if there is competition inthe credence goods market) and always pro-vides the cheap treatment If the consumersrsquovaluation is too low then the credence goodsmarket ceases to exist

PROOF Obvious and therefore omitted

The assumption that one treatment ismore expensive than the second one isimportant for the negative result inProposition 4 Without this assumption(that is if minusc = minusc) expert(s) have no incentiveto mistreat customers and therefore behavehonestly This helps to explain the Emons(2001) results In his 2001 contributionEmons investigates the same basic model

Mar06_Art1 22006 635 PM Page 29


as in the 1997 paper (see our discussion insection 4) That is again capacity isrequired to provide treatments to homo-geneous consumers and once a givencapacity level has been installed bothtypes of treatment can be provided at zeromarginal cost up to the capacity con-straint Again one type of treatment con-sumes more units of capacity than thesecond Also there is no liability rule ineffect that protects consumers from get-ting an inappropriate cheap treatmentThe major difference between the twoEmons contributions is (1) that the 2001article considers a credence goodsmonopolist while the earlier paper isabout competing experts and (2) that the2001 article distinguishes between thecases of verifiable and unverifiable treat-ment and between observable and unob-servable capacity while the earlier articledeals only with the case of verifiable treat-ment together with observable capacityThe major result of Emons (2001) is thatfor three out of the four possible constel-lations the monopolist always behaveshonestly Only when capacity and treat-ment are both unobservable no tradetakes place

Efficiency with homogeneous consumersand verifiable treatments is exactly whatone would expect given our Lemma 8What is more intriguing is that Emonsobtains efficiency even in one of the non-verifiability cases The intuition for thisresult is as follows With observable capaci-ties the expert can publicly precommit to atechnology (ie to a capacity level) thatallows her to provide the right treatment toall consumers at zero marginal cost (cminus = cminus= 0) Consumers observe capacity andsince they know that there is nothing themonopolist can do with her technology butto provide honest services they trust theexpert and get honest treatment By con-trast with unobservable capacities theexpert has no precommitment technologyat hand and the credence goods market

46 In the Emons paper the credence good marketbreaks down even if consumersrsquo gross valuation v is highThe reason is the Emons assumption that not only the typeof treatment is unobservable but also whether treatmenthas been provided at all or not Under this assumptionexpertrsquos capacity investment is zero irrespective of con-sumersrsquo valuation v If only the type of treatment wereunobservable as is the case in the present paper and if vwere high enough then the expert would install a capacitylevel that allows her to sell cminus to all consumers exactly asone would expect from our Proposition 4

47 Wolinsky (1993) and In-Uck Park (2005) study cre-dence goods models where the reputation mechanismincreases efficiency That the possibility of reputationbuilding may also go in the opposite direction has beenshown by Jeffrey C Ely and Juuso Vaumllimaumlki (2003) and byEly Fudenberg and David K Levine (2005) in theirpapers on ldquobad reputationrdquo

breaks down46 To summarize our analysisshows that many specific assumptions madeby Emons (eg that capacity is needed toprovide treatments that success is a stochas-tic function of the type of treatment provid-ed etc) are not important for his findingsWhat is important however for the positivepart of his result is that consumers are homo-geneous with heterogeneous customers theeffects described in subsection 51 abovewould emerge and inefficiency would appear

The equilibrium of Proposition 4 is ratherextreme and one is tempted to argue infavor of public intervention eg the intro-duction of a legal rule that makes the expertliable for providing an inappropriately inex-pensive treatment In reality liability rulesare far from being perfect mechanismshowever (see the discussion in section 6) Isthere a way out In practice experts mightbe kept honest by their need to maintaintheir reputation (if bad reputation spreadsreputation considerations might mitigate theproblem even if consumers are expected tobuy only once) or by their desire to retaincustomers who are expected to frequentlyneed a treatment47

6 Discussion Theory and Real WorldExamples

We started our analysis by showing thatexperts have an incentive to commit to

Mar06_Art1 22006 635 PM Page 30


prices that induce nonfraudulent behaviorand full revelation of their private informa-tion if a small set of critical assumptionshold These conditions are (1) expert sellersface homogeneous customers (AssumptionH) (2) large economies of scope existbetween diagnosis and treatment so thatexpert and consumer are in effect commit-ted to continue with a treatment once adiagnosis has been made (Assumption C)and (3) either the type of treatment (thequality of the good) is verifiable(Assumption V) or a liability rule is in effectprotecting consumers from obtaining aninappropriately inexpensive treatment(Assumption L) This positive result temptsone into thinking that problems in credencegoods markets are not very prevalentHowever some of our organizing assump-tions sound more innocent than they reallyare In this section we make the link to realworld situations by returning to the keymotivating examples mentioned in theintroduction and discussing the plausibilityof Assumptions C V and L in each case(strictly speaking Assumption H is neversatisfied in practice) This section also pro-vides a table where the existing literature iscategorized according to our assumptions

Let us start by considering the example ofcar repairs and other repair services Withrepair services strict liability is difficult toimpose in practice For instance an insuffi-ciently repaired item may work for sometime and problems may develop later on Tomitigate the undertreatment problem insuch a situation the liability needs to cover alonger period But during this longer periodthe item may stop working for reasons unre-lated to the expertrsquos behavior Also anextended liability period introduces a moralhazard problem on the consumersrsquo side insituations where the eventual performanceof the product depends not only on theexpertrsquos but also on the consumerrsquos behaviorIf the consumer is fully compensated for abreakdown during the extended liabilityperiod then he has no incentive to take care

48 Casual observation suggests that seemingly less tech-nically able customers face a higher risk of becoming vic-tim of overtreatment than seemingly more able customersSee for example the article in the Los Angeles Times fromthe 23rd of February 2000 ldquoYour Wheels More WomenAre Beginning To Take A Peek Under The Hoodrdquo statingthat women are more likely to be defrauded by mechanics

of the product (see Taylor 1995 for a modelcapturing this feature)

The verifiability assumption poses similarproblems For instance the advice that opensthe article urging customers of repair servicesto ask the expert for replaced parts is soundonly if the consumer can verify that the partsactually came from his product and if he hasenough knowledge to identify the parts asthose he is charged for The latter problem ispronounced by the fact that most real-worldrepair settings feature a large number of pos-sible treatments (Is the presented part an oilor an air filter Did my brakes get their drumsground and new brake shoes or just newbrake shoes) Some customers may haveenough expertise to secure verifiability othersdo not Thus technical expertise or expertrsquosexpectation of its existence on the consumerrsquosside may affect market outcomes48 Theexisting literature has ignored consumersrsquoheterogeneity in expertise so far We thinkthis is an interesting area for future research

Next consider the commitment assump-tion This assumption may be a reasonableapproximation to reality for complicatedproblems where repair is more or less a by-product of diagnosis and where an addition-al diagnosis adds nothing to the informationthat is revealed during the repair processanyway (for example if the problem is a bro-ken part in the gear box of a car) Howeverit may be violated in many other cases

With respect to taxicab rides the taxime-ter registering time and distance travelledensures verifiability and paying on reachingyour destination ensures liability Thisimplies that the only problem to worry aboutis overtreatment that is the driverrsquos incen-tive to take a circuitous route Obviouslysuch an incentive only exists if the driver

Mar06_Art1 22006 635 PM Page 31


feels that her passenger is a stranger in thecity (and it is therefore often helpful todemonstrate onersquos knowledge of the city bygiving the driver details on which route totake) Thus again heterogeneity in con-sumersrsquo knowledgemdashsome consumers needrecommendation and treatment others canself-diagnose the problem and need only theexpertrsquos treatmentmdashis an important featureof the market For market segments withmany strangers our model would predictthat drivers commit to prices where themarkups for shorter routes exceed those forlonger ones (Lemma 3) The usual two-parttariff consisting of a fixed fee and a meterapproximates such a tariff The approxima-tion is not perfect however An importantaspect of the taxicab-rides market is that thecost of selling minusc instead of minusc varies with thetime of the day during peak times theopportunity cost for the driver to use a cir-cuitous route is high while it approximateszero during off-peak times To incorporatesuch variations in opportunity cost into atime-invariable two part tariff the variablepart of the tariff has to be set equal to zero sothat consumers essentially pay a fixed priceA fixed price over all destination is infeasibleof course given the large heterogeneity inrides However for more homogeneousmarket segments fixed price contracts maywell be optimal And in some segments theyindeed exist for instance in many cities taxi-cabs charge a fixed price for trips to andfrom the airport and from one city to thenext independently of the exact pick-uplocation andor the concrete destination

Finally consider the commitment assump-tion In the case of taxicab rides this assump-tion is implicitly enforced by not asking thedriver for the route he plans to take

Medical treatments offer the most compli-cated and maybe the most important envi-ronment Strict liability is difficult to imposein this context With many sicknesses there isno sufficient treatment with others successis only random Thus a failing treatment isno perfect signal of undertreatment Also

49 We thank a referee for suggesting this discussionHeshe mentions federal lawsmdashERISAmdashthat preemptstate suits and state and (proposed) federal limits on med-ical malpractice awards A (possibly too naive) alternativeexplanation for the undertreatment complaints againstHMOs is that they result from HMOsrsquo incentive to providean inexpensive treatment whenever it is sufficient Bydoing so they prescribe the inexpensive treatment moreoften than it is prescribed under an insurance scheme

treatment success is often impossible or verycostly to measure for a court while stillbeing observed by the consumer (how canone prove the presenceabsence of pain forinstance) In such a situation a patient maymisreport treatment success to sue thephysician for compensation Similarly thephysician may claim that the treatment wassuccessful even if she knows it was not Withindividual physicians the Hippocratic Oath(andor intrinsic motivation) may work rea-sonable well as a substitute for formal liabil-ity With profit seeking institutions thissolution does not work This may explain thecomplaints against HMOs in the UnitedStates that they often provide inexpensivetreatment where expensive ones are neededThe undertreatment problem is worsenedby the fact that HMOs have sought andsometimes received relief from liabilitythrough government intervention49

Verifiability is also a too demandingassumption with medical treatmentsPatients usually are either physically not ableto observe treatmentmdashas during an opera-tionmdashor simply lack the education to verifythe treatment delivered by a physician (did Iget a root canal and a crown or just a crownfrom the dentist)

The commitment assumption (as a short-cut for situations where there are largeeconomies of scope between diagnosis andtreatment) seems reasonable for some butnot for all cases For instance in surgery theassumption of profound economies of scopeis reasonable whereas for the prescriptionand preparation of drugs it is not

Insurance coverage seems to be a peculi-arity of the market for medical treatments

Mar06_Art1 22006 635 PM Page 32


and asks for some attention On the onehand patients have less incentive to proper-ly take care of themselves because healthrisks are covered by insurance On the otherhand they are less worried about overtreat-ment as they do not carry the full socialcosts For treatments with positive sideeffects (for example vitamin treatments ormassages) patients may even actively ask forovertreatment But given that overtreat-ment is often associated with negative sideeffects (for example a chemo therapy in thecase of cancer) patientsrsquo interests are at leastin some cases realigned with parsimonioustreatment On the supply side insurancecompanies may have an interest to colludewith physicians in expensive cases such thatsome patients get inefficiently undertreatedas long as this cannot be proven All theseindirect incentive effects are not addressedin our model

Table 3 provides a summary of our find-ings and categorizes the literature First sup-pose that the homogeneity and thecommitment assumption hold Then themarket provides incentives to deter fraudu-lent behaviour provided either the verifiabil-ity or the liability assumption is satisfied Ifa liability rule protects consumers fromobtaining insufficient treatment while thetype of intervention is not verifiable thenexperts are tempted to overcharge cus-tomers while to overtreat customers is astrictly dominated strategy because the high-er cost of the major intervention does notaffect the payment of the customer In thiscase a fixed price agreement is an efficientway to solve the credence goods problem(Case 1) Similarly if verifiability holds sothat overcharging is no problem while liabil-ity is violated (so that experts might not onlybe tempted to over- but also to undertreatconsumers) then expertsrsquo commitment toequal markup pricesmdashie to tariffs wherethe differences in intervention prices reflectthe differences in treatment costsmdashprovidesincentives for nonfraudulent behaviour(Case 2) If consumers can observe and ver-

ify the type of treatment they get (verifiabil-ity holds) and punish the expert if they real-ize ex post that the type of intervention theyreceived was insufficient to solve their prob-lem (liability holds too) then the onlyremaining problem is overtreatment In thiscase expertsrsquo commitment to prices wherethe markup for the minor interventionexceeds (weakly) that for the major oneinduces truthful behaviour (Case 3)

If the homogeneity assumption is droppeddifferent consumers might be treated differ-ently High quality advice and appropriatetreatment might be provided to the mostprofitable market segment only Less prof-itable consumers might be induced todemand either unnecessary or insufficientprocedures (Case 4)

Dropping the commitment assumption(and assuming low economies of scopebetween diagnosis and treatment) opens upproblems of multiple diagnoses Customerswho are not happy with the repair price pro-posed by the first expert they visit can searchfor a second opinion This search for a secondopinion makes fraudulent behaviour by thefirst expert less attractive (she knows that shewill lose the business of some consumers shediagnoses as requiring a major intervention)but it also leads to duplication of search anddiagnosis costs As table 3 reveals droppingthe commitment assumption (and assuminglow economies of scope) alone is not enoughto get equilibria characterized by multiplediagnosis The type of treatment has also tobe nonverifiable Why is it that specializationequilibria involving costly double advice arisewhen Assumptions C and V are violated (as inCase 5 in the table) while efficiency prevailswhen Assumption C alone or Assumptions Cand L are violated (Cases 2 and 3) Undernonverifiability an expert who has recom-mended the major intervention to a con-sumer with a minor problem will not have toprovide it anyway Consequently overtreat-ment is not a problem in this setting Thereremains the incentive to overcharge In anefficient equilibrium this incentive is

Mar06_Art1 22006 635 PM Page 33


removed by expertsrsquo commitment to charge aconstant price across treatments (Case 1 inthe table) The reason why this solution is notattainable with low economies of scope is thatthe constant price across treatments impliesthat consumers with minor losses subsidizethose with major losses If consumers are notcommitted and if the cost of getting a secondopinion is low (low economies of scope) thiscross-subsidization invites ex ante creamskimming by a deviating expert who special-izes in the minor intervention (by committingto prices that induce the customer to rejectthe expensive recommendation with certain-ty see Case 5 in the table) By contrast if the

type of intervention is verifiable treatmentprices can be set close enough to marginalcost to deter cream skimming (Case 2)Dropping assumptions C and V might alsolead to overcharging equilibria (Case 6 in thetable) In such an equilibrium liabilityremoves the under- the cost differentialbetween the interventions the overtreatmentincentive So only expertsrsquo temptation toovercharge consumers remains In equilibri-um experts do not overcharge their customersall the time (but only with strictly positiveprobability) because recommending thecheap treatment guarantees a small positiveprofit (minusp minus minusc gt 0) for sure (because customers

TABLE 3CREDENCE GOODS ASSUMPTIONS PREDICTIONS AND LITERATURE

Assumptionslowast Equilibrium Equilibrium Case treated inCase dropped characterized by prices Section (S) Lemma (L) Prop (P) Literature

1 V Full Efficiency and minusp = pminus S 4 L 2 Emons (1997)

2 L L and C Truthful Revelation minusp minus minusc = pminus minus cminus S 4 L 1 S 52 L 8 Taylor (1995)

3 none C of Private information minusp minus minusc le pminus minus cminus S 4 L 3 S 52 L 8

Price Discrimination

4 H and LOver- andor minusp minus minusc ne pminus minus cminus S 51 L 5

Dulleck amp

Undertreatment for some customers Kerschbamer (2005b)

(exp having market power)

Specializationsome exp pminus = cminus minusp =

Wolinsky (1993)

5 C and V Duplication of Searchother exp pminus le minusp = minusc

S 52 L 7 GlazerampMcGuire (1996)

and Diagnosis Cost

Overcharging

Duplication of search minusp = minusc gt pminus gt cminus PitchikampSchotter (1989)

and diagnosis cost Wolinsky (1993)

6 C and V (when prices inflexible) S 52 L 6 SuumllzleampWambach (2003)

Some Consumers Untreated

(when valuation low and minusp = v gt pminus = v minus minusd(1minusminush)minus Fong (2005)

monopolistic expert not committed)

Lemons Problem Akerlof (1970)

7 L and V+ Undertreatment constant price S 53 P 4 Emons (2001)

MarketBreak Down

lowast - H Homogenity - all customers have the same v and h- C Commitment - customers are commited to undergo treatment once a diagnosis has been performed- V Verifiability - customers observe and are able to verify to courts the quality of treatment received (rules out overcharging)- L Liability - experts cannot provide minusc when minusc is needed (rules out undertreatment)

+- and the following combinations of Assumptions dropped C LampV H LampV C H LampV

Mar06_Art1 22006 635 PM Page 34


accept such a recommendation with certain-ty) while recommending the expensive treat-ment when only the cheap one is required islike playing in a lottery yielding a high payoff(minusp minus minusc gt minusp minus minusc) if the consumer accepts andzero otherwise By construction the expect-ed payoff under the lottery equals minusp minus minusc mak-ing the expert exactly indifferent betweenrecommending honestly and overchargingAs we have shown in subsection 52 this over-charging equilibrium ceases to exist if expertsare completely free in choosing prices Thena deviating expert can again specialize on theminor intervention and thereby attract allconsumers on their first visit

Whenever neither verifiability nor liabilityholds an expert has an incentive to providelow quality but to charge for high quality Inthis situation we have Akerlofrsquos (1970) marketfor lemons problem and the market maybreak down all together (Case 7 in table 3)

7 Conclusions

Information asymmetries in expertndashcus-tomer relationships are an everyday life phe-nomenon Education and experience giveexperts the ability to diagnose the exactneeds of customers who themselves are onlyable to detect a need but not the most effi-cient way to satisfy it The information prob-lems in markets for diagnosis and treatmentsuggest that experts may be tempted todefraud customers The present article hasshown that the price mechanism alone is suf-ficient to solve the fraudulent expert prob-lem if a small set of critical assumptions aresatisfied and that most existing results oninefficiencies and fraud in credence goodsmarkets can be reproduced by dropping oneof those assumptions

Our systematic approach is newPrevious work has fostered the impressionthat the equilibrium behavior of expertsand consumers in the credence goods mar-ket delicately depends on the details of themodel By contrast the present paper hasshown that the results for the majority of

the specific models can be reproduced in asimple unifying framework

Our analysis suggests that market institu-tions solve the fraudulent expert problem atno cost if (1) expert sellers face homoge-neous customers (2) large economies ofscope exist between diagnosis and treatmentso that expert and consumer are in effectcommitted to continue with a treatmentonce a diagnosis has been made and (3)either the type of treatment is verifiable or aliability rule is in effect protecting con-sumers from obtaining an inappropriateinexpensive treatment

We have shown that inefficient rationingand inefficient treatment of some consumergroups may arise if condition (i) fails to holdthat equilibria involving overcharging of customers or specialization of expertsmdashbothleading to a duplication of search and diag-nosis costsmdashmay result if condition (ii) isviolated and that the credence goods mar-ket may break down altogether if condition(iii) doesnrsquot hold

Our model might be considered restric-tive in several respects It rests on theassumption that there are only two possibletypes of problem that only two types oftreatment exist that treatment costs areobservable that posted prices are take-it-or-leave-it prices that experts can diagnose aproblem perfectly and so on This is certain-ly a justified criticism Nevertheless oursimple model is sufficient to derive mostresults of that class of models that have beenthe focus of research in the credence goodsliterature50 Thus our simple model pro-vides a useful benchmark for the develop-ment of more general frameworks whichallow for an assessment of the robustness ofthe results

50 Our model is insufficient however to reproduce theWolinsky (1995) result which relies on the assumptionthat posted prices are bargaining prices It is also insuffi-cient to provide Taylorrsquos (1995) theoretical micro-founda-tions of several features observed in markets for diagnosisand treatment

Mar06_Art1 22006 635 PM Page 35


51 We thank an anonymous referee for suggesting thisdiscussion

With respect to robustness a comparisonof common experience with the results ofthis paper suggests that something is missingfrom existing models of credence goods51

As discussed earlier one common problemin such markets is that of overtreatment thatis that a more expensive treatment is pro-vided than is needed Suppose for examplethat our car needs either a new fuse or a newengine A common fear is that the garagewill sell us an engine even when the fusewould be sufficient because it is more prof-itable to replace the engine Some of uswould suspect this will be the case even if wecan tell whether the car is fixed when thegarage is done (and we refuse payment if thecar is not fixed) and even though we can seewhether the engine has been replaced ieeven if liability and verifiability are satisfiedProposition 1 of this article tells us that suchfraud cannot occur if liability and verifiabili-ty as well as homogeneity and commitmentare satisfied whereas common experiencesuggests the opposite What accounts for thisdissonance The answer appears to be thatin such situations prices should adjust sothat the firm can make just as much profit onselling us the fuse (when we only need thefuse) as on selling us the engine What doesthis mean For experts facing tight capacityconstraints (for example work time) therequirement is that the markup on theengine must exceed the markup on the fuseby such an amount that the profit per unit ofcapacity consumed is the same for bothtypes of intervention Such markups are like-ly to be feasible By contrast if experts holdidle capacities then the absolute markup hasto be the same for both types of treatmentBut are consumers really prepared to paythe same absolute markup for a fuse as foran engine Common experience tells us thatthey are not to the contrary most of uswould punish an expert who charges a highabsolute margin on a fuse with malicious

gossip Is there a way out For some of us afeasible solution might be to follow the day-to-day advice mentioned in the beginning ofthe article to ask the mechanic to put thereplaced part in the back of the car and toinspect the defect of this part It remains tohope that future research comes up withsolutions for this problem that are both moreefficient (in the sense that consumers do nothave to investigate exchanged parts) and fea-sible also for the less technically adept Forthe meantime a valuable advice might be toconsult an expert featuring a lengthy queueof customers waiting for service

Appendix

Proofs of lemmas 5 6 and 7 followPROOF OF LEMMA 5 The proof pro-

ceeds in four steps In Step 1 we show thatany arbitrary menu of tariffs partitions thetype-set into (at most) three subintervalsdelimited by cut-off values h10 h12 and h02with 0 le h10 le h12 le h02 le 1 and either h12 = h02

or h02 = 1 (or both) such that (i) the optimalstrategy of types in [0h10) is to choose a tar-iff where the markup for the minor treat-ment exceeds that for the major one (ii) theoptimal strategy of types in (h10h12) is todecide for an equal markup tariff and (iii)the optimal strategy of types in (h121) iseither to choose a tariff where the markupfor the major treatment exceeds that for theminor one (h02 = 1] or to remain untreated(h12 = h02)

52 Our strategy is then to show inStep 2 that an optimal price-discriminatingmenu cannot have h10 = h12 (that is there

52 The borderline types h10 and h12 are indifferentbetween the strategies of the types in the adjacent inter-vals (whenever such intervals exist) Here note that weallow for h12 = 1 (all consumers are served and no con-sumer chooses a tariff where the markup for the majortreatment exceeds that for the minor one) for h10 = h12 (noconsumer is attracted by an equal markup tariff) and forh10 = 0 (no consumer is attracted by a tariff where themarkup for the minor treatment exceeds that for the majorone) Price discrimination requires however that at leasttwo of the three relations hold as strict inequalities

Mar06_Art1 22006 635 PM Page 36


53 An immediate implication of this observation is thatsuccessful price discrimination requires that some typesare mistreated with strictly positive probability WhySince at least two tariffs must attract a positive measure ofconsumers and since only one of them can be an equalmarkup tariff

54 Under a tariff where the markup for the major treat-ment exceeds that for the minor one neither the con-sumer nor the expert cares about the associated minusp Alltariffs in this group that have the same ∆02 can thereforebe thought off as being a single tariff without any loss ingenerality The argument for tariffs where the markup forthe minor treatment exceeds that for the major one issymmetric

must be an equal markup tariff which attractsa strictly positive measure of types) to shownext (in Step 3) that h10 = 0 whenever h10 lt h12

(that is the expert has never an incentive topost a menu where both an equal markuptariff and a tariff with a higher markup forthe cheap treatment attract types) and toshow in the end (Step 4) that the expert hasindeed always a strict incentive to cover astrictly positive interval by a tariff where themarkup for the major treatment exceeds thatfor the minor one (h12 lt h02 = 1)

Step 1 First note that any arbitrary menuof tariffs can be represented by (at most)three variables by the lowest ∆02 equiv minusp minus minuscfrom the class of tariffs where the markupfor the major treatment exceeds that for theminor one (we denote the lowest ∆02 in thisclass by ∆ l

02) by the lowest ∆10 equiv minusp minus minusc fromthe class of tariffs where the markup for theminor treatment exceeds that for the majorone (we denote the lowest ∆10 in this class by∆l

10) and by the lowest equal markup∆12 equiv minusp minus minusc = minusp minus minusc from the class of allequal markup tariffs in the menu (denotedby ∆l

12) 53 To see this note that each possi-

ble tariff is member of exactly one of thesethree classes and that a customer whodecides for a tariff in a given class willalways decide for the cheapest one54 Animmediate implication is that each menu oftariffs partitions the type-set into the abovementioned three subintervals This followsfrom the fact that the expected utility underthe ∆ l

02 tariff is type-independent (implying

that either h12 = h02 or h02 = 1 or both) whilethe expected utility under both the ∆l

12 tariffand the tariff where the markup for theminor treatment exceeds that for the majorone is strictly decreasing in h and from v gt minusc minus minusc (implying that the ∆l

10-function issteeper than the ∆l

12-function)Step 2 To see that h10 lt h12 suppose to the

contrary that h10 = h12 Then h10 gt 0 sinceh10 = h12 = 0 is incompatible with price-dis-crimination (and sincemdashby Lemma 4mdashanon-price-discriminating expert will alwaysdecide for an equal markup tariff) But sucha menu is strictly dominated since the ∆l

10

tariff can always be replaced by a tariff withequal markups of ∆12 = ∆l

10 + h10(v minus minusc + minusc)the latter attracts exactly the same types asthe replaced one and yields a strictly higherprofit

Step 3 To see that h10 = 0 wheneverh10 lt h12 suppose to the contrary that0 lt h10 lt h12 Then the expertrsquos profit is strict-ly increased by removing all tariffs where themarkup for the minor treatment exceeds thatfor the major one from the menu This fol-lows from the observation that (by themonotonicity of the expected utilitymdashin hmdashunder equal markup tariffs) all types in[0h10) switch to ∆l

12 when all tariffs wherethe markup for the minor treatment exceedsthat for the major one are removed from themenu and from the fact that the expectedprofit per customer is strictly higher under∆l

12 than under ∆l10 whenever 0 lt h10 lt h12

since ∆l12 le ∆l

10 is incompatible with theshape of expected utilities (∆l

12 le ∆l10 implies

that v minus d minus minusc minus h(minusc minus minusc) minus ∆l12 gt (1 minus h)v minus d minus

minusc minus ∆l10 for all h gt 0 contradicting h10 gt 0)

Thus h10 = 0 lt h12 le h02 le 1 So if price dis-crimination is observed in equilibrium it isperformed via a menu that contains two tar-iffs one with equal markups and a tariffwhere the markup for the major treatmentexceeds that for the minor one55

55 The menu might contain some redundant vectorstoo which can safely be ignored however

Mar06_Art1 22006 635 PM Page 37


Step 4 We now show that the expert hasalways a strict incentive to post such a menuConsider the equal markup tariff posted bythe expert under the conditions of Lemma 4The markup in this vector is at least ∆12 = v minus d minus minusc in an interior solution evenhigher First suppose that the monopolistrsquosmaximization problem under the conditionsof Lemma 4 yields an interior solution (ie∆12 gt v minus d minus minusc) Then the expert can increaseher profit by posting a menu consisting oftwo tariffs the one chosen under the condi-tions of Lemma 4 and a second tariff wherethe markup for the major treatment exceedsthat for the minor one with minusp = v minus d Thelatter vector guarantees each type an expect-ed utility equal to the reservation utility of 0Thus all types that remain untreated underthe conditions of Lemma 4 will opt for itsince they are indifferent Also all typesserved under the conditions of Lemma 4 stillchoose the equal markup vector since v minus d minusminusc minus h(minusc minus minusc) is strictly decreasing in h Hencesince v minus d gt minusc and since all types in [01]have strictly positive probability the expertrsquosexpected profit is increased56 Now supposethat the monopolistrsquos maximization problemunder the conditions of Lemma 4 yields thecorner solution ∆12 = v minus d minus minusc Then again themonopolist can increase her profit by postinga menu consisting of two tariffs a tariff wherethe markup for the major treatment exceedsthat for the minor one with minusp = v minus d and an equal markup tariff that maximizesπ(∆12) = ∆12F[(v minus d minus cminus minus ∆12)(minusc minus minusc)] + (v minusd minus minusc)(1 minus F[(v minus d minuscminus minus ∆12)(minusc minus minusc)]) Sinceπ(∆12) is strictly increasing in ∆12 at ∆12 = v minusd minus minusc an interior solution is guaranteed

56 Here note that the expert can do even better byincreasing ∆ l

12 This follows from the observation that theexpertrsquos trade-off under the conditions of Lemma 4 isbetween increasing the markup charged from the types inthe segment of served customers and losing some types tothe unprofitable segment of not served consumers whilethe trade-off here is between increasing the markupcharged from the types in the segment of customers servedunder the more profitable equal markup vector and losingsome types to the segment of customers served under theless profitable ∆ l

12 tariff

PROOF OF LEMMA 6 Part (i) Firstnotice that under the conditions of Lemma6 liability prevents undertreatment and thecost differential (minusc minus minusc) prevents overtreat-ment So each expertrsquos provision policy istrivial and we will therefore focus in the restof the proof on expertsrsquo price-posting andrecommendation policy and on consumersrsquovisiting and acceptance decisions For therecommendation and acceptance behaviordescribed in part (i) of the lemma to poten-tially form part of a (weak) Perfect BayesianEquilibrium (henceforth PBE) the equilib-rium probabilities ω lowast and lowast and themarkup ∆lowast must satisfy

(1)

and

(2)

The first of these two equations guaran-tees that consumers who get a cminus recommen-dation are indifferent between accepting and rejecting57 the second equation guar-antees that experts are indifferent betweenrecommending minusc and recommending cminus when the consumer has the minor problem58

∆lowastlowast lowast lowast

lowast lowast= minus+ minus( )

+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus

minus( ) minus( )+ minus( )

lowastlowast lowast

lowast( )∆1 1

1ω ω

ω

57 If a consumer rejects he incurs an additional diagno-sis cost of d for sure His benefit is to pay less for the treat-ment on his second visit with probability [(1 minus ωlowast)ωlowast

(1 minus h)][h + (1 minus h)ωlowast] because he has the minor problemwith probability [ωlowast(1 minus h)][h + (1 minus h)ωlowast] given that theexpert has recommended minusc

58 Recommending the cheap treatment guarantees aprofit of ∆lowast gt 0 for sure while recommending the expen-sive treatment when only the cheap one is required is likeplaying in a lottery yielding a payoff of minusp minus cminus gt ∆lowast withprobability [αlowast + ωlowast(1 minus αlowast)][1 + ωlowast(1 minus αlowast)] and zerootherwise This probability takes into account that a frac-tion 1[1 + ωlowast(1 minus αlowast)] of customers are on their first visit(and hence are accepting the minusc recommendation withprobability αlowast) while the remaining fraction ωlowast(1 minus αlowast)[1 + ωlowast(1 minus αlowast)] are on their second visit (accepting the minuscrecommendation for sure) Here notice that a consumerwho is indifferent between accepting and rejecting a minusc rec-ommendation on his first visit will accept the minusc recommen-dation on his second visit because the probability ofneeding the minor treatment is lower on the second thanon the first visit

Mar06_Art1 22006 635 PM Page 38


Obviously consumers who get a minusc recom-mendation will accept with certainty Alsosince minusp lt minusc and since a minusc recommendation isalways accepted experts will always recom-mend cminus when the consumer has the majorproblem So if prices are exogenously fixed at(minusp minusp) = (minusc + ∆lowast minusc) and if ∆lowast is such that theprobabilities lowast and ωlowast satisfying equations (1)and (2) above are in (01) then the behaviordescribed in the lemma forms part of a PBE59

To show that this behavior continues toform part of a weak PBE even if experts arefree to choose minusp while minusp can vary within therange specified in part (i) of the lemma wehave to specify out-of-equilibrium beliefsand strategies that support the equilibriumEach expertrsquos strategy consists of a price vec-tor (minusp minusp) and a recommendation policy forall possible price vectors Each consumerrsquosstrategy consists of a visiting strategy for eachset of posted price vectors and an acceptancebehavior for each price vector We first spec-ify consumersrsquo beliefs and acceptance behav-ior and expertsrsquo recommendation policy foreach subgame beginning at the moment aconsumer visits an expert characterized byher price vector (minusp minusp) Then we specify con-sumersrsquo visiting and expertsrsquo price postingstrategy In the end we verify that we haveindeed identified a weak PBE

Let ω i denote the probability that theexpert recommends treatment minusc given that consumerrsquos problem is diagnosed to bei isin m M where m stands for minor andM for major Also let minusmicro (minusmicro) be the proba-bility a consumer assigns to the event thathe has the major problem given that theexpert has recommended treatment minusc (minusc)Similarly let minus (minus) be the probability that aconsumer accepts the recommendation cminus (minusc) Finally let k denote a consumerrsquosexpected cost if he follows the proposedequilibrium strategy (that is k = (1 minus h)(1 minus ω lowast)(minusc + ∆lowast) + [h + (1 minus h)ω lowast]minusc + d =

59 Here note that for any (minusc cminus d h) with d lt (minusc minus cminus)(1 minus h) there always exists a ∆lowast such that both αlowast and ωlowast

are in (01)

(minusc + ∆lowast) + (minusc minus minusc minus ∆lowast)[h + (1 minus h)ω lowast] + d)and let π denote expertsrsquo profit per customer if they follow the proposed equi-librium strategy (that is π = (1 minus h)[1 + ωlowast(1 minus lowast)]∆lowast) Suppose that con-sumersrsquo beliefs are correct at the proposedprice vector and that consumersrsquo beliefs atother price vectors are given by (i) minusmicro(minusp pminus)= 1 and minusmicro(minusp minusp) = 0 iff p le d + (1 minus ω lowast)(minusc + ∆lowast) + ωlowastminusc and minusp isin [minuscminusc + d) and (ii)minusmicro(minusp minusp) = h and minusmicro(minusp minusp) = 0 in any othercase Further suppose that consumersrsquoacceptance decisions are given by (i) minus(minuspminusp) = 1 iff minusp le d + (1 minus ω lowast)(minusc + ∆lowast) + ωlowastminuscand minus(minusp minusp) = 0 otherwise and (ii) minus(minusp minusp) = 1 iff either minusp le d + (1 minus ω lowast)(minusc + ∆lowast) + ωlowast

minusc and minusp le minusc + d or pminusgt d + (1 minus ω lowast)(minusc +∆lowast)+ωlowastcminus and minusp le k and minus(minusp minusp) = 0otherwise Also suppose that deviatingexpertsrsquo recommendation policy is given byωm(minusp minusp) = ωM(minusp minusp) = 160 Finally supposethat consumersrsquo visiting strategy prescribesnot to visit a deviating expert and thatexpertsrsquo price-posting strategy prescribesnot to deviate to a price vector differentfrom the proposed one

Now we verify that we have indeed identi-fied a weak PBE First observe that con-sumersrsquo acceptance strategies are indeedoptimal given their beliefs If a single expertdeviates the proposed price vector is stillavailable since at least two experts post thisvector in equilibrium The expected cost tothe consumer under that vector is k withprior beliefs it reduces to d + (1 minus ωlowast)(minusc + ∆lowast) + ωlowastminusc if the consumer believes toneed the cheap treatment for sure and itincreases to minusc + d if the consumer believes toneed the expensive treatment for sureGiven this consumersrsquo acceptance strategies

60 Here note that for out-of-equilibrium price-vectorssatisfying minusp le d + (1 minus ωlowast)(cminus + ∆lowast) + ωlowastcminus and pminus [minusc cminus + d]the proposed beliefs are not consistent with the proposedequilibrium strategies Sequential rationality and full consis-tency of beliefs at all information sets (full PBE) wouldrequire that for all out-of-equilibrium price-vectors withthese properties experts and consumers play mixed strategiessimilar to the ones specified in Lemma 6

Mar06_Art1 22006 635 PM Page 39


are indeed optimal given their beliefs Nextobserve that ωm(minusp minusp) = ωM(minusp minusp) = 1 isindeed optimal for a deviating expert eitherbecause minus(minusp minusp) = 1 and minusp ge minusc or because

minus(minusp minusp) = minus(minusp minusp) = 0 Given deviatingexpertsrsquo recommendation policy and minusp ge minuscconsumers obviously prefer to ignore anydeviating expert This establishes that no devi-ation to an alternative price vector will attractany customers and so (and since π gt 0) nodeviation will occur

Part (ii) To verify part (ii) of the lemma itsuffices to specify a profitable deviationConsider a deviation to a price vector (minusp minusp)with minusp isin (minuscd + (1 minus ωlowast)(minusc + ∆lowast) + ωlowast minusc) andminusp gt minusc + d First observe that for a consumerserved under such a price vector it is optimal to set minus(minusp minusp) = 1 and minus(minusp minusp) = 0 forany belief that he might have61 Given con-sumersrsquo acceptance behavior sequentialrationality for the expert requires that shechooses ωm = 0 and ωM = 162 Given deviat-ing expertsrsquo recommendation- and con-sumersrsquo acceptance-behavior the expectedcost to a first-time consumer who plans tovisit the deviator is k = d + (1 minus h)minusp + h(d + minusc)63 So if k lt k then the deviatorattracts all first-time consumers and servesthem at an expected profit of π = (1 minush)(minusp minusminusc) per customer The inequality k lt k isequivalent to minusp lt minusc + ∆lowast + ωlowast(minusc minus minusc minus ∆lowast) minusdh(1minush) which (using the indifferenceequations (1) and (2) above) is again equiva-lent to minusp lt minusc + ∆lowast + dω lowast[(1 minus ω lowast)(1 minus h)]Now suppose the deviating expert sets minusp =minusc + ∆lowast + dω lowast[(1 minus ω lowast)(1 minus h)] minus with

61 This follows from the fact that the only alternativeprice vector available if a single expert deviates is (minusp minusp) =(cminus + ∆lowast cminus) and that the cost to the consumer under thatvector is d + (1 minus ωlowast)(cminus + ∆lowast) + ωlowastcminus if the consumerbelieves to need the cheap treatment for sure while it iscminus + d if the consumer believes to need the expensivetreatment for sure

62 This follows from minusp gt cminus (so that it is indeed optimal torecommend cminus to a consumer with the minor problem) and

minusp lt cminus (so that it is never optimal to recommend cminus to a con-sumer who needs cminus) where the latter inequality is impliedby consumersrsquo indifference between accepting and reject-ing a cminus recommendation under (minusp minusp) = (cminus + ∆lowast cminus) and by

minusp lt d + (1 minus ωlowast)(cminus + ∆lowast) + ωlowastcminus

strictly positive but smaller than dωlowast[(1 minus ωlowast)(1 minus h)] Then she attracts all consumers andthus makes an expected profit π gt (1 minus h)∆lowastThe expected profit per expert in the pro-posed symmetric overcharging equilibriumis π n = (1 minus h)[1 + (1 minus lowast)ωlowast]∆lowastn which isstrictly less than (1 minus h)2∆lowastn implying thatπ lt πn even for n = 2 This establishes thatthe weak PBE sketched in part (i) of thelemma ceases to exist if experts are complete-ly free in choosing prices since a profitabledeviation always exists

PROOF OF LEMMA 7 Again liabilityprevents undertreatment and the cost dif-ferential (minusc minus minusc) prevents overtreatment Soeach expertrsquos provision policy is again trivialand we will therefore again focus on expertsrsquoprice-posting and recommendation policyand on consumersrsquo visiting and acceptancedecisions To show that the proposed strate-gies are part of a (full) PBE we have to spec-ify reasonable out-of-equilibrium beliefs andstrategies that support the equilibriumUsing the notation introduced in the proofof Lemma 6 we first specify consumersrsquobeliefs and acceptance behavior and expertsrsquorecommendation policy for each subgamebeginning at the moment a consumer visitsan expert characterized by her price vector(minusp minusp) Then we specify consumersrsquo visitingand expertsrsquo price posting strategy In theend we verify that we have indeed identifieda PBE

Let k denote the expected cost to the cus-tomer if he follows the proposed equilibriumstrategy that is k = d + (1 minus h)minusc + h(minusc + d)Suppose that consumersrsquo beliefs are correctat the proposed price vectors and that con-sumersrsquo beliefs at other price vectors aregiven by (i) minusmicro(minusp minusp) = 0 and minusmicro(minusp minusp) = 1 ifeither minusp = minusp le minusc + d or minusp gt minusc + d and

minusp lt minusc (ii) minusmicro(minusp minusp) = h and minusmicro(minusp minusp) = 1 if minusp gt minusc + d and minusp gt minusc (iii) minusmicro(minusp minusp) = 0 and

63 With probability (1 minus h) the consumer has the minorproblem and gets treated for the price minusp by the deviatorwith probability h he has the major problem the deviatorrecommends cminus the consumer rejects visits a nondeviatorand gets the right treatment for the price cminus

Mar06_Art1 22006 635 PM Page 40


minusmicro(minusp minusp) is such that a customer who gets a minusc recommendation is indifferent betweenaccepting and rejecting whenever minusp isin(k minusc + d) and minusp lt minusc + d and (iv) minusmicro(minusp minusp) = 0 and minusmicro(minusp minusp) = h in any other caseAlso suppose that new consumersrsquo (first timevisitorsrsquo) acceptance decisions are given by(i) minus(minusp minusp) =1 for minusp le k and minus(minusp minusp) = 0 for

minusp gt k whenever minusp gt minusc + d and minusp gt minusc and

minus(minusp minusp) =1 for minusp le minusc + d and minus(minusp minusp) = 0 for

minusp gt minusc + d whenever either minusp le minusc + d or

minusp le minusc and (ii) minus(minusp minusp) = 1 whenever minusp lt k minus(minusp minusp) is such that an expert who observesthat the customer has the minor problem isexactly indifferent between recommending cminusand recommending minusc whenever minusp isin(k minusc + d)and minusp lt minusc + d and minus(minusp minusp) = 0 for any otherprice vector Further suppose that theacceptance decisions of consumers on theirsecond visit are given by (i) minus(minusp minusp) =1 for

minusp le k and minus(minusp minusp) = 0 for minusp gt k whenever minusp gt minusc + d and minusp gt minusc and minus(minusp minusp) =1 for

minusp le minusc + d and minus(minusp minusp) = 0 for minusp gt minusc + dwhenever either minusp le minusc + d or minusp gt minusc and (ii) minus(minusp minusp) = 1 whenever minusp le minusc + d and minus(minusp minusp) = 0 otherwise Also suppose thatexperts recommend in accordance with con-sumersrsquo beliefs Finally suppose that con-sumers visiting strategy prescribes not todeviate from the proposed visiting behaviorprovided no deviating expert offers either

minusp lt minusc and minusp gt minusc + d or minusp lt minusc and thatexpertsrsquo price-posting strategy prescribes notto deviate to price vectors different from theproposed ones

Now we verify that we have indeed identi-fied a PBE First observe that customersbeliefs reflect expertsrsquo incentives The expertrecommends honestly (ie ωm = 0 andωM = 1) if minusp lt minusc + d and minusp = minusp and if minusp gt minusc + dand minusp lt minusc either since minus(minusp minusp) = minus(minusp minusp) = 1and minusp = minusp (in the former case) or since

minus(minusp minusp) = 1 minus(minusp minusp) = 0 and minusp lt minusc (in the lattercase) the expert always recommends

minusc (ie ωm = 0 and ωM = 0) if minusp gt minusc + d and

minusp gt minusc since minus(minusp minusp) = 0 and minusp gt minusc the expertrecommends minusc if the consumer has themajor problem and she randomizes between

recommending minusc and recommending cminus if hehas the minor problem (ie ωm isin(01) andωM = 1) whenever minusp isin (kminusc + d) and minusp isin(minusc minusc + d) since minus(minusp minusp) =1 and minus(minusp minusp) is suchthat she is exactly indifferent between bothrecommendations and the expert recom-mends the expensive treatment (ie ωm = 1and ωM = 1) in all other cases either becauseminus(minusp minusp) = 1 and minusp gt minusp or because minus(minusp minusp) =minus(minusp minusp) = 0 Next observe that customersrsquostrategies are optimal given their beliefsFirst consider consumersrsquo acceptance strate-gies If a single expert deviates the proposedequilibrium offers are still available since atleast two experts make each offer Thus theabove described acceptance strategies areoptimal given consumersrsquo beliefs Next con-sider new consumersrsquo visiting strategy If noexpert deviates the relevant alternatives are(i) to visit a cheap expert first and to rejectthe minusc recommendation as proposed or (ii) tovisit an expensive expert first and to acceptthe minusc recommendation The former strategyhas an expected cost of d + (1 minus h)minusc +h(minusc + d) the latter a cost of minusc + d while thebenefit is the same Since (minusc minus minusc)(1 minus h)h gt (minusc minus minusc)(1 minus h) gt d the former cost isstrictly lower and customersrsquo visiting strategyis optimal if no expert deviates Given thatthe equilibrium offers are still available if asingle expert deviates and given the abovespecified beliefs no customer has an incen-tive to visit a deviating expert if her postedprices do not satisfy either minusp lt minusc and minusp gt minusc + d or minusp lt minusc Finally observe that noexpert has an incentive to deviateDeviations to prices satisfying minusp lt minusc and minusp gt minusc + d are unattractive since only the

minusc recommendation is accepted Devia-tions to price vectors where minusp gt minusc and minusp ge minusc are unattractive since they attract no customers Price vectors where minusp lt minusc are unprofitable too if they only attractcustomers who first visit a cheap expert andif recommended the expensive treatmentresort to the deviator The expected cost to the customer of this latter strategy is d + minusc + h(p + d minus minusc) where p is the price

Mar06_Art1 22006 635 PM Page 41


posted by the deviator for the expensivetreatment Going directly to the deviator andaccepting her recommendation on the otherhand costs at most p + d Thus in order to avoid being visited only by consumerswith the major problem the deviation mustsatisfy d + minusc + h(p + d minus minusc) gt d + p which is equivalent to p lt minusc + dh (1 minus h) To cover expected treatment cost the price p must also satisfy p ge minusc + h(minusc minus minusc) But

minusc + h(minusc minus minusc) gt minusc + dh (1 minus h) since (1 minus h)(minusc minus minusc) gt d This proves that no deviation byan expert is profitable

REFERENCES

Alger Ingela and Franccedilois Salanieacute 2003 ldquoA Theory ofFraud and Over-Consumption in Experts MarketsrdquoBoston College Mimeo

Akerlof George A 1970 ldquoThe Market for lsquoLemonsrsquoQuality Uncertainty and the Market MechanismrdquoQuarterly Journal of Economics 84(3) 488ndash500

Darby Michael R and Edi Karni 1973 ldquoFreeCompetition and the Optimal Amount of FraudrdquoJournal of Law and Economics 16(1) 67ndash88

Dulleck Uwe and Rudolf Kerschbamer 2005aldquoExperts vs DiscountersmdashCompetition and MarketUnravelling When Customers Do Not Know WhatThey Needrdquo University of Vienna Mimeo

Dulleck Uwe and Rudolf Kerschbamer 2005b ldquoPriceDiscrimination Via the Choice of DistributionChannelsrdquo University of Vienna Department ofEconomics Working Paper 0511

Ely Jeffrey C Drew Fudenberg and David K Levine2005 ldquoWhen is Reputation Badrdquo UCLA LevinersquosWorking Paper Archive

Ely Jeffrey C and Juuso Vaumllimaumlki 2003 ldquoBadReputationrdquo Quarterly Journal of Economics118(3) 785ndash814

Emons Winand 1997 ldquoCredence Goods and FraudulentExpertsrdquo RAND Journal of Economics 28(1) 107ndash19

Emons Winand 2001 ldquoCredence Goods MonopolistsrdquoInternational Journal of Industrial Organization19(3-4) 375ndash89

Fong Yuk-Fai 2005 ldquoWhen Do Experts Cheat andWhom Do They Targetrdquo Rand Journal ofEconomics 36(1) 113ndash30

Fuchs Victor R 1978 ldquoThe Supply of Surgeons andthe Demand for Operationsrdquo Journal of HumanResources 13 35ndash56

Fudenberg Drew and Jean Tirole 1991 Game

Theory Cambridge and London MIT PressGlazer Jacob and Thomas G McGuire 1996 ldquoPrice

Contracts and Referrals in Markets for Servicesrdquo TelAviv University Working Paper 1096

Gruber Jon John Kim and Dina Mayzlin 1999ldquoPhysician Fees and Procedure Intensity The Caseof Cesarean Deliveryrdquo Journal of Health Economics18(4) 473ndash90

Hughes David and Brian Yule 1992 ldquoThe Effect ofPer-Item Fees on the Behaviour of GeneralPractitionersrdquo Journal of Health Economics 11(4)413ndash37

Mas-Colell Andreu Michael Whinston and Jerry RGreen 1995 Microeconomic Theory New YorkOxford University Press

Myerson Roger B 1991 Game Theory Analysis ofConflict Cambridge and London HarvardUniversity Press

Nelson Phillip 1970 ldquoInformation and ConsumerBehaviorrdquo Journal of Political Economy 78(2)311ndash29

Park In-Uck 2005 ldquoCheap-Talk Referrals ofDifferentiated Experts in Repeated RelationshipsrdquoRand Journal of Economics 36(2) 391ndash411

Pesendorfer Wolfgang and Asher Wolinsky 2003ldquoSecond Opinions and Price CompetitionInefficiency in the Market for Expert AdvicerdquoReview of Economic Studies 70(2) 417ndash37

Pitchik Carolyn and Andrew Schotter 1987 ldquoHonestyin a Model of Strategic Information TransmissionrdquoAmerican Economic Review 77(5) 1032ndash36

Pitchik Carolyn and Andrew Schotter 1988ldquoHonesty in a Model of Strategic InformationTransmission Correctionrdquo American EconomicReview 78(5) 1164

Pitchik Carolyn and Andrew Schotter 1993ldquoInformation Transmission in Regulated MarketsrdquoCanadian Journal of Economics 26(4) 815ndash29

Richardson Hugh 1999 ldquoThe Credence GoodProblem and the Organization of Health CareMarketsrdquo Texas AampM University Mimeo

Suumllzle Kai and Achim Wambach 2005 ldquoInsurance ina Market for Credence Goodsrdquo Journal of Risk andInsurance 72(1) 159ndash76

Taylor Curtis R 1995 ldquoThe Economics ofBreakdowns Checkups and Curesrdquo Journal ofPolitical Economy 103(1) 53ndash74

Tirole Jean 1988 The Theory of IndustrialOrganization Cambridge and London MIT Press

Wolinsky Asher 1993 ldquoCompetition in a Market forInformed Expertsrsquo Servicesrdquo RAND Journal ofEconomics 24(3) 380ndash98

Wolinsky Asher 1995 ldquoCompetition in Markets forCredence Goodsrdquo Journal of Institutional andTheoretical Economics 151(1) 117ndash31

Mar06_Art1 22006 635 PM Page 42


credence goods Michael R Darby and EdiKarni (1973) added this type of good toPhillip Nelsonrsquos (1970) classification of ordi-nary search and experience goods Theymention provision of repair services as atypical example Other examples includetaxicab rides where a stranger in a city can-not be sure that the driver takes the short-est route to his destination and medicaltreatments where doctors may providewrong diagnosis to sell the most profitabletreatment or where they can try to chargefor a more expensive treatment than pro-vided There are countless other examplesof situations were consumers face similarinformation problems and where theyworry about the two basic problemssketched out by the mechanic example topay for goods or services they did notreceive or to receive goods or services theydid not need in the first place

Consumersrsquo concerns about beingdefrauded by experts seem not to beunfounded Winand Emons (1997) cites aSwiss study reporting that the averagepersonrsquos probability of receiving one ofseven major surgical interventions is onethird above that of a physician or a mem-ber of a physicianrsquos family Asher Wolinsky(1993 1995) refers to a survey conductedby the Department of Transportation esti-mating that more than half of auto repairsare unnecessary He also mentions a studyby the Federal Trade Commission thatdocuments the tendency of optometriststo prescribe unnecessary treatmentThese examples reveal that the informa-tional asymmetry matters Monetaryincentives play a role too For the case ofthe health industry Jon Gruber JohnKim and Dina Mayzlin (1999) empiricallyshow that the frequencies of cesareandeliveries compared to normal child birthsreact to the fee differentials of healthinsurance programs A similar observationhas been made by David Hughes andBrian Yule (1992) who document that thenumber of cervical cytology treatments is

correlated with the fee for this treatmentThat treatment can also be affected bysupply of expert services is shown byVictor R Fuchs (1978) ldquoOther thingsequal a 10 percent higher surgeonpopu-lation ratio results in about a 3 percentincrease in the number of operations rdquo(p 54)

These observations suggest that weneed a more profound understanding ofthe specific problems associated with mar-kets for diagnosis and treatment Underwhich conditions do experts have anincentive to exploit the informationalproblems associated with markets fordiagnosis and treatment What types offraud exist What are the methods andinstitutions for dealing with these infor-mational problems Under which condi-tions does the market provide incentivesto deter fraudulent behavior And whathappens if all or some of those conditionsare violated

The existing literature on credence goodsdoes not help much to answer these ques-tions The studies performed up to nowcover very different and quite special situa-tions and in total they yield no clear pictureregarding the inefficiencies arising from theinformational asymmetry Rather theresults seem to depend sensitively on thespecific conditions of the settings consid-ered and the specific assumptions of themodels adopted in the analysis More dis-turbingly apparently similar models oftenlead to contradicting results (see section 2for details)

The present article presents a model ofcredence goods that highlights the informa-tion problems in markets for experts servic-es and clarifies the variety of results in thisarea The model provides a unifying frame-work for the analysis of the effects of differ-ent market institutions and informationstructures on efficiency and for the identi-fication of the forces driving the variousinefficiency results in the literature Inaddition the model allows us to generalize






































Mar06_Art1 22006 634 PM Page 10
















minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM 0



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42





































Mar06_Art1 22006 634 PM Page 10
















minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM 0









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42





























Mar06_Art1 22006 634 PM Page 10
















minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM 0
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42




















Mar06_Art1 22006 634 PM Page 10
















minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42
















minusc

Customer cminus v 0

gets minusc v v

Mar06_Art1 22006 634 PM Page 11














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42














Mar06_Art1 22006 634 PM Page 12













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42













Mar06_Art1 22006 634 PM Page 13




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42




underprovision

(pp)

out in

c

c c

c cc c

r r

r

ra a

a

a

expert postsprices





expert provides

c

c

c ccc

c



i and pminusi






Mar06_Art1 22006 634 PM Page 14













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42













Mar06_Art1 22006 635 PM Page 15



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42



)( cchpdv

)( ccpdv

pdvh)1(

0 cp cp

u( p p)~





Mar06_Art1 22006 635 PM Page 16








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42








Mar06_Art1 22006 635 PM Page 17















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42















Mar06_Art1 22006 635 PM Page 18



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42



0

pdv

p p

ppdv max

)(~ ppu






Mar06_Art1 22006 635 PM Page 19















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42















Mar06_Art1 22006 635 PM Page 20



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42



Assumption Effect











Mar06_Art1 22006 635 PM Page 21













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42













Mar06_Art1 22006 635 PM Page 22







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42







Mar06_Art1 22006 635 PM Page 23












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42












Mar06_Art1 22006 635 PM Page 24











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42











Mar06_Art1 22006 635 PM Page 25









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42









Mar06_Art1 22006 635 PM Page 26



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42



_p minus _c)










Mar06_Art1 22006 635 PM Page 27













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42













Mar06_Art1 22006 635 PM Page 28

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42

















Mar06_Art1 22006 635 PM Page 29










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42










Mar06_Art1 22006 635 PM Page 30









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42









Mar06_Art1 22006 635 PM Page 31










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42










Mar06_Art1 22006 635 PM Page 32







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42







Mar06_Art1 22006 635 PM Page 33











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42











Dulleck amp




Wolinsky (1993)



and Diagnosis Cost

Overcharging









MarketBreak Down



Mar06_Art1 22006 635 PM Page 34




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42




7 Conclusions








Mar06_Art1 22006 635 PM Page 35






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42






Appendix






Mar06_Art1 22006 635 PM Page 36

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42

















10













Mar06_Art1 22006 635 PM Page 37





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42





12 tariff


(1)

and

(2)




+ minus( )( ) c c

ωω

11 1

d c ch

h h= minus minus


lowastlowast lowast

lowast( )∆1 1

1ω ω

ω




Mar06_Art1 22006 635 PM Page 38






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42






are in (01)





Mar06_Art1 22006 635 PM Page 39














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42














Mar06_Art1 22006 635 PM Page 40
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42
















Mar06_Art1 22006 635 PM Page 41




REFERENCES































Mar06_Art1 22006 635 PM Page 42




REFERENCES































Mar06_Art1 22006 635 PM Page 42

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