Market for Lemons - Stennekstennek.se/onewebmedia/12 - Market for Lemons (slides).pptx.pdf ·...

1

Market for Lemons

Johan Stennek

Let’splayagame!

Game•  Halfofallusedcarsare“lemons”

–  Valuetoseller(currentowner)=0–  Valuetobuyer=100

•  Halfofallusedcarsare“peaches”–  Valuetoseller=200–  Valuetobuyer=300

•  InformaEon–  Onlythesellerknowsifthecarisalemonorapeach

•  Game–  AbrokersuggeststhepriceP–  Thebuyerandthesellersay”yes”or”no”simultaneously–  Onlyifbothsay”yes”thegoodwillbetraded

3

Game

•  Procedure–  Formpairs

–  SellerscomeforwardtocollectinformaEonabout

theircars–CheckinformaEonsecretly!

–  Iambrokerandwillsuggestaprice

–  Bothsellerandbuyerwritedownyourchoiceonapieceofpaper-Secretly

4

Priceannouncement

•  Halfofallusedcarsare“lemons”– Valuetoseller(currentowner)=0– Valuetobuyer=100

•  Halfofallusedcarsare“peaches”– Valuetoseller=200– Valuetobuyer=300

•  Price:125

5

–  Sellerswithpeach–pleasestandup:–  Raiseyourhandiftheresultwas….

–  Sellerswithlemon–pleasestandup:–  Raiseyourhandiftheresultwas….

6

Buy No

Sell ? ?

No ? ?

Buy No

Sell ? ?

No ? ?

Result?

InterpretaEon

7

Analysis

•  Q1:Howmanycarsshouldbesold,fromanefficiencypointofview?– All!

•  BuyersvaluepeacheshigherthanSellers•  BuyersvaluelemonshigherthanSellers

8

Analysis

•  Q2:Howmanycarswouldbe,accordingtoeconomicreasoning?– Difficult,let’scheck!

9

InterpretaEon

•  Seller’svalue–  Ifpeach=200–  Iflemon=0

•  Price125

•  Q:Seller’schoice?–  Ifpeach:keep–  Iflemon:sell

•  Q:Buyer’sexpectedvalueofbuying?–  100(=0·300+1·100)

•  Q:Buyer’schoice?–  don’tbuy

•  Conclusion:Marketbrakesdown!

10

Probabilityacarforsaleisapeach

Buyer’svaluaEonofpeach

InformaEon•  ImperfectinformaEon

–  Agentsdonotobserveallpreviousbehavior(orsimultaneousmoves)–  Example:Firmsdecideonpricesimultaneously

•  IncompleteinformaEon–  Agentsdonotknowalltheexogenousdata–  Example:Firmsmaynotknowdemand

•  AsymmetricinformaEon–  Someplayersknowsomeexogenousdata(=privateinformaEon)–  Othersdon’t

11

AsymmetricInformaEon•  Examples

–  Firmsmaynotknoweachother’scosts

–  Firmsmaynotknowconsumers’willingnesstopay

–  Consumermaynotknowqualityofgood

–  EmployersmaynotknowtheproducEvityofanapplicant

–  Banksmaynotknowthebankruptcyriskofentrepreneurs

–  Insurancecompanymaynotknowriskthatapersonfallsill

–  Governmentsmaynotknowfirms’costsofreducingpoluEon

12

AsymmetricInformaEon

•  But:Learning–  OjenpeopledisclosesomeoftheirprivateinformaEonwhentheyact

–  Otherswilllearn

•  Howdowemodellearning?–  BayesianupdaEng

13

Baye’sRule

14

Baye’sRule

•  ExampleofasymmetricinformaEon–  Entrepreneurs

•  Somebutnotenoughmoneytofinancetheirprojects

•  TheyknowrelaEvelywelliftheirprojectwillsucceedorfail

–  Banksdon’tknowtheifanewfirmwillsucceed•  Iftheprojectsucceeds=>Entrepreneurisabletopaytheloan•  Iftheprojectfails=>Bankruptcy

15

Baye’sRule

•  QuesEon– Howcanbankslearnabouttheentrepreneurs’privateinformaEon?

•  Answer–  Iftheentrepreneurbelievestheprojectwillsucceed,heiswillingtoriskhisownmoney.

– Otherwisenot.

16

Baye’sRule

•  Numericexample–  Twotypesofentrepreneurs

•  5withgoodprojects•  10withbadprojects

–  Amongentrepreneurswithgoodprojects80%believetheprojectisgoodandarewillingtorisktheirownwealth

–  Amongentrepreneurswithbadprojects10%believethattheprojectisgoodandarewillingtorisktheirownwealth

17

Baye’sRule

18

PopulaEon- 5entrepreneurswithgoodprojects- 10entrepreneurswithbadprojects

Baye’sRule

19

PopulaEon- 5entrepreneurswithgoodprojects

- 80%willingtoriskownmoney- 10entrepreneurswithbadprojects

- 10%willingtoriskownmoney

Baye’sRule

20

ExercisesWhatistheprobabilitythatarandomentrepreneurhasgoodproject?

1.  InpopulaEon2.  Amongthosewithsomeownfunding3.  Amongthosewithoutownfunding




Baye’sRule

21

Answers1.  5outof15(33%)entrepreneurs

inpopulaEonareprofitable.2.  4outof5entrepreneurs(80%)

withsomefundingareprofitable.3.  1outof10entrepreneurs(10%)

withoutfundingareprofitable.




Baye’sRule

•  Conclusion–  Byobservingloanapplicantsbehavior(howmuchoftheirownmoneytheyarewillingtorisk)abankmaylearnsomethingabouttheirprivateinforma2on(probabilityofsuccess).

22

Baye’sRule•  Example

–  Anemployerdoesn’tknowtheproducEvityofjobapplicants

–  Twotypesofapplicants•  500withhighproducEvity

•  500withlowproducEvity

–  AmongpeoplewithhighproducEvity90%investinamaster

–  AmongpeoplewithlowproducEvity10%investinamaster

•  Exercise1–  Whatistheprobabilitythatajobapplicantwithamasterhashigh

producEvity?

23

Baye’sRule

•  SoluEon1–  Numberofhigh-producEvethatinvestinmaster450=0.9*500

–  Numberoflow-producEvethatinvestinmaster50=0.1*500

–  Totalnumberofpeoplewithmaster500=450+50

–  Shareofpeoplewithmasterthatarehigh-producEve0.9=450/500

•  Note–  ShareofhighproducEveinpopulaEon50%<90%

24



–  Twotypesofapplicants•  500withhighproducEvity

•  500withlowproducEvity



•  Exercise2–  Whatistheprobabilitythatajobapplicantwithoutamasterhashigh

producEvity?

25

Baye’sRule

•  SoluEon2–  Numberofhigh-producEvewithoutmaster50=0.1*500

–  Numberoflow-producEvewithoutmaster450=0.9*500

–  Totalnumberofpeoplewithoutmaster500=50+450

–  Shareofpeoplewithoutmasterthatarehigh-producEve:0.10=50/500

•  Note–  ShareofhighproducEveinpopulaEon:50%–  ShareofhighproducEveamongpeoplewithmaster:90%

–  ShareofhighproducEveamongpeoplewithoutmaster:10%

26

Baye’sRule–MoreGenerally•  PopulaEonshares

–  P(H)=shareofpeoplewithhighproducEvityinpopulaEon–  P(L)=shareofpeoplewithlowproducEvityinpopulaEon

•  Behavior–  P(M:H)=likelihoodofgerngmaster,ifhighproducEve–  P(M:L)=likelihoodofgerngmaster,iflowproducEve

•  Exercise–  FindexpressionforP(H:M)=probabilityofbeinghighprod.ifmaster

27

P H :M( ) = Pr Master& High{ }Pr Master{ } =

P H( ) ⋅P M | H( )P H( ) ⋅P M | H( ) + P L( ) ⋅P M | L( )

=12 ⋅ 910

12 ⋅ 910 + 1

2 ⋅ 110=

99 +1



–  Twotypesofapplicants•  500withhighproducEvity,solve10problemsperhour

•  500withlowproducEvity,solve2problemsperhour



•  Exercise3–  WhatistheexpectedproducEvityinthepopulaEon?

–  WhatistheexpectedproducEvityamongpeoplewithmaster?

–  WhatistheexpectedproducEvityamongpeoplewithoutmaster?

29

Baye’sRule

•  Recall–  ShareofhighproducEveinpopulaEon:50%–  ShareofhighproducEveamongpeoplewithmaster:90%–  ShareofhighproducEveamongpeoplewithoutmaster:10%

•  ExpectedproducEvity–  PopulaEon:0.5*10+0.5*2=6–  Master:0.9*10+0.1*2=9.2

–  Without:0.1*10+0.9*2=2.8

30

Baye’sRule

•  EducaEonisasignalofproducEvity–  IF:DifferentproducEvity=>Differentprobabilitytogetmaster

–  THEN:MasterissignalofproducEvity

•  SignalprovidesvaluableinformaEon–  EmployerswhocannotobserveproducEvitydirectly

–  CanbasehiringdecisionorwageoneducaEon– MustuseBaye’srule

31

MarketforLemons

32

MarketforLemons•  Basicpoint

–  AsymmetricinformaEonaboutqualitymaydisruptamarket

•  IntuiEon–  Buyersdon’tobservequalityof(say)usedcars–  IF:Price=100–  THEN:Onlycarswithqualitybelow100willbesupplied–  THEN:Averagevalueofcarsactuallysuppliedislow,say50–  THEN:Buyersonlywillingtopay50

•  But–  IfbuyersandsellershavesufficientlydifferentvaluaEonsofquality,the

informaEonproblemmaybepartlyovercome

33

MarketforLemons

•  Usedcars–  Mass1ofsellerswithonecareach–  Qualityuniformlydistributedover[L,H]

34

L H

(H-L)-1 f(q)

q

MarketforLemons

•  ExpectedqualityinpopulaEon

35

L H

(H-L)-1 f(q)

qμ*

UniformdistribuEon=>Average=“midpoint” µ* = H + L2

MarketforLemons

•  Expectedquality

36

L H

(H-L)-1 f(q)

q

µ* = Eq = f q( )L

H

∫ ⋅q ⋅dq =1

H − LL

H

∫ ⋅q ⋅dq

µ* = 1H − L

q ⋅dqL

H

∫ = 1H − L

12q2⎡

⎣⎢⎤⎦⎥L

H

= 1H − L

12H 2 − L2⎡⎣ ⎤⎦ =

1H − L

12H − L[ ] H + L[ ] = H + L

2

μ*

MarketforLemons

•  InformaEon–  Buyerscannotobservequality

•  Note–  Equilibriumpricemustbethesameforallcars–  Allsellersclaimtheyhavehighquality

•  OtherwiseperfectcompeEEon–  ConEnuumofbuyersandsellers–  Bothbuyersandsellersareprice-takers

37

Buyers

38

Buyers•  Buyers

–  IdenEcal–  Mass=1

•  UElity–  withoutcar: m (income)–  withcar: ΘBq+m–p (q=quality)

•  Uncertainty–  Knowaveragequalityforsale: μ(Baye’srule)–  Risk-neutral

•  Demand–  Buyiff: ΘBμ≥p

39

Twopossiblereasons:-  Buyerscomputetheequilibrium-  Buyersknowaveragequalityfromownandfriendsexperience

Buyers

•  Marketdemand

40

!!

D =

0 p >ΘBµ

[0,1] if p =ΘBµ

1 p <ΘBµ

"

#$$

%$$

Sellers

41

Sellers•  Sellers

– Mass=1

•  UElity– withcar: ΘSq+m– withoutcar: m+p

•  InformaEon–  Knowqualityofowncar

•  Decision–  Selliff: ΘSq≤póq≤p/ΘS

42

Sellers

•  Assume – ΘB>ΘS– Buyers’willingnesstopayhigherthansellers’willingnesstoaccept

•  Efficiency– Allcarsshouldbesold

43

Sellers

•  AdverseselecEon

44

L H

(H-L)-1 f(q)

q

Selliffq≤p/ΘS

p/ΘS

LowerpriceèFewercarsforsale

Sellers

•  AdverseselecEon

45

L H

(H-L)-1 f(q)

q

Averagequalityinmarketμ=½[p/ΘS+L]

p/ΘSμ

LowerpriceèLoweraveragequality

Sellers

•  “BayesianupdaEng”– ExpectedqualityofcarsforsaleislowerthanaveragequalityofcarsinpopulaEon

46

MarketforLemons

•  Expectedquality

47

µ = E q for sale{ } = f q( ) ⋅Pr sale q{ }Pr sale{ }L

H

∫ ⋅q ⋅dq

=f q( ) ⋅1

Pr sale{ }L

B

∫ ⋅q ⋅dq +f q( ) ⋅0

Pr sale{ }B

H

∫ ⋅q ⋅dq

=1

Pr sale{ } f q( )L

B

∫ ⋅q ⋅dq

µ =B − LH − L

⎛⎝⎜

⎞⎠⎟−1 1

H − L⋅q ⋅dq

L

B

∫ =1

B − L⋅q ⋅dq

L

B

∫ =B + L

2

L H

(H-L)-1 f(q)

qB

Equilibrium

48

Equilibrium

49

Equilibrium- Apricesuchthatthemarketclears(Demand=Supply)- ThequanEtytradedatthisprice

Equilibrium

50

p

μ

Butwewillstudy- price- averagequality(“=quanEty”)

Equilibrium- Apricesuchthatthemarketclears(Demand=Supply)- ThequanEtytradedatthisprice

Equilibrium

51

p

μL (L+H)/2

Equilibrium-Apricesuchthatthemarketclears(Demand=Supply)

Wewillstudy- price- averagequality(quanEty)

Averagequalityifallcarssold

Averagequalityifonlylowestquality

carssold

Equilibrium

•  Equilibrium– SupplyrelaEon

•  μ=½[p/ΘS+L]óp=-ΘSL+2ΘSμ

52

Equilibrium

53

p

μL (L+H)/2

ΘSL

ΘSH

SupplyrelaEon-Higherprice=>higheraveragequalityoffered

Ifp=ΘSH,Thenallcarssold.Then:μ=(L+H)/2

Equilibrium

•  Equilibrium– SupplyrelaEon

•  μ=½[p/ΘS+L]óp=-ΘSL+2ΘSμ

– Demand

54

!!

D =

0 p >ΘBµ

[0,1] if p =ΘBµ

1 p <ΘBµ

"

#$$

%$$

Equilibrium

55

p

μ

D=1

D=0

D =

0 p >ΘBµ[0,1] if p =ΘBµ1 p <ΘBµ

⎧

⎨⎪⎪

⎩⎪⎪

Price=B’svalueofexpectedquality

Equilibrium

56

Demandrela:on-  Higherdemandif

-  Priceislow-  Averagequalityishighp

μ

D=1

D=0

Equilibrium

57

Givenp,sellerswillsupplyaveragequalityμ

p

μ

Consider(p,μ)onsupply-relaEon-S<1sinceμ<(L+H)/2

p

μ

Equilibrium

58

Given(p,μ)allbuyerswanttobuyacar

p

μ

Consider(p,μ)onsupply-relaEon-S<1sinceμ<(L+H)/2-D=1

Equilibrium

59

Excessdemand:Pricemustbeincreased(Alsoqualityisincreased)

p

μ

Consider(p,μ)onsupply-relaEon-S<1sinceμ<(L+H)/2-D=1

Equilibrium

60

Excesssupply:Pricemustbereduced(Alsoqualityisreduced)

p

μ

Consider(p,μ)onsupply-relaEon-S>0sinceμ>L-D=0

Equilibrium

61

p

μL (L+H)/2

ΘSL

ΘSHp=-ΘSL+2ΘSμ

p=ΘBμ

μ*

p*

Equilibrium

62

p

μL (L+H)/2

ΘSL

ΘSHp=-ΘSL+2ΘSμ

p=ΘBμ

μ*

p*

Ashareofsellersdecidetosell(thosewithlowquality)

Equallymanybuyerdecidetobuy(theorydoesn’ttellhowtheydecide)

Equilibrium:AllbuyersandsellerscanrealizetheirplansatthesameEme

Equilibrium

63

p

μL (L+H)/2

ΘSL

ΘSHp=-ΘSL+2ΘSμ

p=ΘBμ

μ*

p*

µ* = L2 − ΘB

ΘS

DespiteΘS<ΘBnotallcarsaresold,ieμ*<(L+H)/2

Equilibrium

64

p

μ

p=2ΘSμp=ΘBμ

μ*p*

IfL=0andΘS>½ΘBnocarssold

Whatifalluninformed?

65

IncompletebutSymmetricInformaEon

•  Ifnooneobservesquality– Buyif ΘBμ≥p– Sellif ΘSμ≤p

–  IfΘB≥ΘSthereexistsanequilibriumwhereallcarsaresold,atuniformpriceegp=μ(ΘB+ΘS)/2

•  Notuncertainty,butasymmetricinformaEoncausesadverseselecEon

66

ApplicaEons

67

InsuranceMarket

•  Problem:AdverseselecEonspiral– Peoplewithhighriskofbecomingillbuyinsurance–  Insurancecompanymustchargehighfees– Then,low-riskindividualsdon’tbuy

•  SoluEon– Mandatoryinsurance

•  E.g.:FinancedwithtaxesinEurope•  E.g.:Obama-careintheUS

68

LaborMarkets

•  Problem– PeoplewithlowproducEvityapplyfornewjobs– Employersmustsetlowwages– Then,high-producEvityworkersstayatoldjobs

•  PossiblesoluEons–  Internallabormarkets– Signalingandscreening

•  HigheducaEontoprovehighproducEvity

69

CreditMarket

•  Problem– Firmswithhighriskofbankruptcyborrow– Bankmustchargehighinterestrate– Then,low-riskfirmsdon’tborrow

(theirexpectedpriceishigher)

•  AsoluEon:CreditraEoning– Banksdon’tincreaseinterestrate,despiteexcessdemand

– RaEoncreditsinstead

70

Signaling&Screening

71

Signaling&Screening

•  Marketforlemons–  Akerlof(1970)

•  SoluEon1:Signaling–  Spence(1973)

•  SoluEon2:Screening–  RothchildandSEglitz(1976)

72

Signaling

73

Signaling

•  Problem– EmployerscannotobserveproducEvity

– Alsolow-producEvityworkershaveincenEvetoclaimhighproducEvity

74

Signaling

•  Basicidea– High-producEvityworkers:

•  investineducaEon– Employers:

•  higherwagetoeducated– LowproducEveworkers:

•  costofeducaEonhigher•  wagepremiumnotsufficient

75

Screening

76

Screening

•  Similartosignaling1.  Uninformedpartymovesfirst:Setsupmenuof

contractstosortinformed

2.  Informedself-select

•  Example– SeconddegreepricediscriminaEon

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