1

Economie Publique IIFebruary-May 2010

Prof. A. Estache

Lecture 2Regulating Monopolies Under

information symmetry

Brief reminder• Monopoly = market failure

• Non convex production set because of increasing returns to scale in production (locally or constantly)

• Market failure = inefficient allocation of resources

• Inefficient allocation of resource = scope for government intervention

• Typical government interventions in the case of monopolies are:– 1. nationalize– 2. regulate: the focus of this course

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So what’s the problem with studying regulation?

• What the overview last week showed is that it is difficult to come up with a single clean story on how to regulate due to heterogeneity of:– Initial conditions– Variables monitored– Economic as well as Political dimensions of regulation– Sectoral diversity– Degree and type of information asymmetry between operators and

regulators

• But plenty of actions in the real world to learn how regulation sometimes works in practice

• Also lots of good theory work to learn to teach a few trick to practictioners!

• So what this course does is to provide you with an overview of where the theory stands as well as a sense of how best practice works

Here, we focus for now on Economic regulation

• Although…not quite since we will really look at economic + some social regulation– Economic = price, entry, quality of product– Social= environment, safety, …

• To learn more and faster…useful to distinguish between regulation with

• Symmetric vs asymmetric information• Single product vs multiple products• Barriers to entry vs contestable markets

– This week we focus on the simplest:• Symetric, simple, with barriers

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Why Monopolies again???• What causes monopolies?

– Natural monopolies • One general definition that can work for an industry is that this industry

is said to be a natural monopoly if one firm can produce a desired output at a lower social cost than two or more firms (i.e deadweight loss is lower!)

• SO what’s clear is that this natural monopoly is associated with a predictable cost structure

– high fixed cost, extremely low constant marginal cost, declining long run average cost, MC always below AC.

• Typical examples include rail, telecoms, water, electricity, ports

– But also “legal” monopolies, • ie. those due to

– a legal fiat; e.g. US Postal Service

– a patent; e.g. a new drug

– sole ownership of a resource; e.g. a toll highway

– formation of a cartel; e.g. OPEC

• This concept of monopoly is more about market power than about costs structures

So what is “Pure Monopoly (PM)”?

• A monopolized market has a single seller.

• Its demand curve is the (downward sloping) market demand curve.

• =>the monopolist can alter the market price by adjusting its output level.

Note (1)• Common, roughly correct but misleading definition: a pure

monopoly is when we have declining AC and MC curves…very restrictive

• More precise definition: an industry is a natural monopoly only if its cost function is subadditive; this focus is more encompassing (i.e.having declining AC, increasing returns to scale=> subadditivity) – The cost function C(q) is subadditive at some output level if and only if:

This says that the cost function is subadditive if a single firm could produce the same output for less cost=> no need to focus only on the shape of average costs to get a sense of what a monopoly is

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1

1

ni

i

ni

i

C q C q

q q

Note (2)• Subadditivity?

– Costs can be subadditive even if diseconomies exist (near the total output q1+q2).

– BUT in the single product case, scale economies is a sufficient condition for subadditivitity.

– HOWEVER, in the multiproduct case, product-specific scale economies is not a sufficient condition. Economies of scope matter

– NOTE THAT economies of scope is a necessary but not sufficient condition for subadditivity.

– SO even Economies of scale and scope is no guarantee of cost subadditivity

8

Note (3)

D

A monopoly can be temporary… (common in congestion related problems where demand drives the nature of the market!)

D D1

D1

Q*

e of scale Natural Monopoly

Constant Returns To scale

diseconomies of scale

So what does subadditivity mean in practice?

– It tells you when you should have a monopoly in the delivery of a service or a bundle of service and when you should allow an unbundling of the delivery of these services into two or more companies

– But to see in details what it means in practice…useful to conceptualize!

– Assume a cost function based on two inputs:

Thus, each of i firms produce ai % of output q1 and bi % of the output q2.

1 2 1 2, , 1,

1 1 0 0

i ii

i i i ii i

C a q b q C q q i n

a b a b

From a policy viewpoint what does this mean?

• If the cost function is subadditive => the technology implies a natural monopoly: only allow 1 firm!

• But what if we find the opposite when we measure???• If the cost function is superadditive => the firm could save

money by breaking itself up into two or more divisions.

• => from a policy viewpoint, essential to see how you want to structure your industry (i.e. when you need to clear a merger request!)

1 2 1 2, ,i iiC a q b q C q q

1 2 1 2, ,i iiC a q b q C q q

Economies of scale are important but so are economies of scope!

– Economies of Scope?• Should we allow monopolies to produce two related

products together or should we force an unbundling?

• Once more: look at the costs

– The formal definition• C (q1,q2) < C (q1,0) + C (0,q2)

– Under Economies of Scope, it is cheaper to produce two goods together.

• Generation of electricity + transmission?• Freight + passenger train transport?

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Let’s look at an example

• Imagine you want to test the extent to which there may be a natural monopoly in cellular phone market as a result of the evolution of the sector (market and technology),

• So you are concerned with:– the change of whole market size and market

share of each competitors, which may affects natural monopoly status.

– innovations which may alter the cost structure of this industry

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The Problem really boils down to one of cost analysis…

• To test if you have a natural monopoly…you need to assess the cost structure of that industry

• Assessment is generally done by estimating

econometrically or approximating through non linear programming techniques a cost function for the sector

• Note: in practice not easy to distinguish statistical errors and inefficiency when you estimate...– But there are techniques to do this…and huge volume of

methodological and empirical research on this

• Here is how you get to approximate your cost function

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So First we want to measure the Size Efficiency

• Size Efficiency: Whether one company should produce all services or K companies should do from the efficiency point of view? With “x” as the input quantities and “w” as the input prices and “C” as total costs and with “y” the range of product we want to deliver (with weights on x and y)

• NOTE: Economies of Scale is a special case of size efficiency modeling.

0x

yyxx

xw

*

1

10

1

*

*0

,0,

,..

min

s

N

ss

N

sss

N

sss

t

K

ts

C

1K

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Next we want to measure Economies of Scope

• Economies of Scope (Orthogonal Cost Subadditivity)– is also a special case of size efficiency modeling (K=2, orthogonally constrained).

0x

xx

xw

*21

12

11

102

101

1

*21

*0

,0,,1,1

,

..

min

ss

N

ss

N

ss

N

s

BBss

N

s

AAss

N

ssss

t

yyyy

ts

C

Note: A: voice, B: i-mode service

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Then we look for data for the empirical analysis (based on case study of Tokyo)

Variables Description

Inputs L (Labor) The number of employee (person)

K (Capital) Capital Cost/ wK (million yen)

Outputs Vs The number of subscribers of cellular phone (thousand)

Ds The number of subscribers of i-mode service (thousand), since 1997

Inputs Price

wL (Labor) Labor Cost / L (million yen/person)

wK (Capital) i

ii deprdefs )(

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Result(1): The shrinking role of Economies of Scale in telecoms..that’s why deregulation makes sense in that

sector!

• SCE is less than zero in the metropolitan area (ex. Tokyo). It means diseconomies of scale….technological revolution matters!

• SCE falls around 1995 at almost of all units (due to rapid expansion of market size?)

DoCoMo Tohoku (northern part) DoCoMo (Tokyo)

SCE

Cost efficiency

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Result(2): …but the sustained role of economies of scope in telecoms…so still some role for a regulator!

• K=1 in Tohoku and K=4 in Tokyo. (The metropolitan area is not size efficient.) Strong economies of scope exists.

DoCoMo Tohoku DoCoMo (Tokyo)

Economies of scope

(Size efficiency)-1

K

Now that we know that monopolies exist…

so really…what’s the social problem we need to worry about?

• To answer this question:

–Compare the welfare gains from trade under competition vs. under a monopoly!

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The efficiency of competition $/output unit

y

MC(y)

p(y)

ye

p(ye)

The efficient output levelye satisfies p(y) = MC(y).Total gains-to-trade ismaximized.

CS

PS

The Inefficiency of Monopoly$/output unit

y

MC(y)

p(y)

MR(y)

y*

p(y*)

The Inefficiency of Monopoly$/output unit

y

MC(y)

p(y)

MR(y)

y*

p(y*)CS

PS

MC(y*+1) < p(y*+1) so bothseller and buyer could gainif the (y*+1)th unit of outputwas produced. Hence the market is Pareto inefficient.

The Inefficiency of Monopoly$/output unit

y

MC(y)

p(y)

MR(y)

y*

p(y*)

DWL

Deadweight loss measuresthe gains-to-trade notachieved by the market.

The Inefficiency of Monopoly

$/output unit

y

MC(y)

p(y)

MR(y)

y*

p(y*)

ye

p(ye) DWL

The monopolist produces less than the efficient quantity, making the market price exceed the efficient market price.

How much does this DWL matter to society?• If small DWL=>don’t worry too much • Empirical estimates suggest that DWL varies from

0.1 and 14% of GDP…depending on method of estimation!

• But if it is reasonably big …or if it is perceived to be big (as in the case of public services)….then you need to regulate

• To regulate, you need to understand the optimal strategy for a monopolist

• The more its optimal strategy leads pricing to differ from marginal cost pricing…the more you need to worry !

• => look at how a monopoly picks it pricing• Easiest way to do so is analytically

Useful to keep in mind how we do the simple math to figure out how a monopolist will

chose prices and quantities?

• Suppose that the monopolist seeks to maximize its economic profit

(with the usual notation for prices and costs)

• Start by asking what output level y* maximizes profit?

• Then derive the price

( ) ( ) ( ).y p y y c y

Profit-Maximization

( ) ( ) ( ).y p y y c y At the profit-maximizing output level y*

d ydy

ddy

p y ydc y

dy( )

( )( ) 0

so, for y = y*, MR - MC =0 => MR=MC or:

ddy

p y ydc y

dy( )

( ).

Some more manipulation

MR yd

dyp y y p y y

dp ydy

p yy

p ydp y

dy

( ) ( ) ( )( )

( )( )

( ).

1

Since own-price elasticity of demand is

p yy

dydp y

( )( ) => MR y p y( ) ( ) .

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=>when is a monopoly happy …and when not?

Look at the drivers of its MR

MR y p y( ) ( ) .

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SO the MR is positive IF demand curve is:-elastic (ε <-1)AndMR is negative IF demand curve is :-inelastic( -1<ε <0)

NOTE: 1. This elasticity depends not only on the particular demand curve but also on where on that demand curve stands (could decrease as price becomes lower)NOTE 2: Because the demand curve is downward sloping, the monopoly must lower its prices to sell more unuts=> the MR is always<price! (>< for a competitive firm MR is always=p)

=>How do you get to the monopolist optimal pricing?

MR y p y( ) ( ) .

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For a profit-maximum: MR = MC

Now, suppose the monopolist’s MC is constant, at $k/output unit.

MR y p y k( *) ( *)

1

1

which leads to p yk

( *) .1

1

So…:p yk

( *) .1

1

…means that:1. We need to track what happens to the supply of y* by the monopolist as a function of the demand elasticity

2. as rises towards -1 the monopolist alters its output level to make the market price of its product rise3. a profit-maximizing monopolist always selects an output level for which market demand is own-price elastic.4. Most of what we will do later in using applied regulation techniques will build around these 3 variables:

•What is k (costs), •what is the demand side (ε) and •how does the monopoly play with P and y to maximize profits given this costs and the demand elasticity!!

NOTE: how do prices relate to market power in an industry?

MR y p y( ) ( ) .

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Consider

And note again that at optimum, MR = MCSo substitute and rearrange… and you find:

(P-MC)/P= -1/ε•Which tells us; (i) the price-cost margin as a share of price…and (ii) that this margin ONLY depends on ε!!!•This is also known as the Lerner Index of market power•The monopoly’s price is close to its MC when high ε•Its margins is however low when ε is low!•P increasingly exceeds MC as the demand become less elastic!•For instance if ε=-100=>P=1.01MC but if ε=-2, P=2MC•=> Key variable to focus on to know about troubles is ε

Look at some numbers…

Demand elasticity

(ε)

Markup Optimal governmt strategy

0,1 (retail water?)

10 REGULATE!

1 (retail energy?)

1 REGULATE!

4 (transport?) .25 ?

10 (internet phone)

.1 Don’t worry too much…

…=> Regulating a Natural Monopoly boils down to understanding that: • A natural monopoly cannot be forced to use

marginal cost pricing.– Doing so makes the firm exit, destroying both the

market and any gains-to-trade.

• How far the monopoly will go distancing itself from MC pricing depends on ε– If close to |1|: Huge markup => huge DWL– If much higher than |1|: Small markup => small DWL

• So challenge is to pick regulatory schemes to induce the natural monopolist to produce the efficient output level without exiting.

To be efficient…MC works for efficiency but financially … does not work without a

subsidy!

B$15

$29

A

C

MC

$60

LRATC

50,000

DMR

85,000

100,000 Number of Household

s Served

Dollars

Unregulated monopoly

F

Efficient production (requires subsidy!!!)

So what can you allow a monopoly to do?

• IF Huge economies of scale (AC is always declining) natural monopoly⇒

• To have a financially viable natural monopoly need a policy to ensure service ⇒is provided at reasonable cost to users and reasonable profit to provider!

• MOST OF THIS IS ABOUT PRICING TO ENSURE COST RECOVERY AND A FAIR RETURN ON ASSETS!

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So how to come up with fair regulation of the pricing by a Natural Monopoly???

B$15

$29

A

C

MC

$60

LRATC

50,000

DMR

85,000

100,000 Number of Household

s Served

Dollars

Unregulated monopoly

"Fair rate of return" productionWhich allows cost

recovery

F

What kind of pricing policies would allow a monopoly to recover its costs and get a fair

return on its assets?(i) MC pricing WILL NOT do it!

– ⇒ unable to earn a normal ROR ⇒ Govt NEEDS TO give a subsidy

(ii) Allow monopoly to recover documented costs (=>cost-plus or rate of return regulation since the + is a markup over

allowed cost to allow for a return on assets allocated to the monopolist’s production)

• Could allow AC pricing earn a normal ⇒ ROR (Franchise bidding• Could allow provided to charge at its highest cost ( peak load

pricing)• Could allow nonlinear pricing: two-part tariff, discriminatory two-

part tariff, multipart tariff• Could consider Ramsey pricing (look at the elasticity of demand of

the various users…)

(iii) Impose a maximize average price and let the monopoly deal with the costs (i.e. set a price cap)

– (vii) …or could nationalize….Public ownership of natural monopoly(iii) Could nationalize…

MORE ON ALL THIS LATER IN THE COURSE!!!

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So how to come up with fair regulation of the pricing by a Natural Monopoly???

B$15

$29

A

C

MC

$60

LRATC

50,000

DMR

85,000

100,000 Number of Household

s Served

Dollars

Unregulated monopoly

"Fair rate of return" productionWhich allows cost

recovery

F

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So how to come up with fair regulation of the pricing by a Natural Monopoly???

B$15

$29

A

C

MC

$60

LRATC

50,000

DMR

85,000

100,000 Number of Household

s Served

Dollars

Unregulated monopoly

"Fair rate of return" productionWhich allows cost

recovery

F

•Set this return on assets?*Set an average price generating this return* Allow for a more complex pricing Structure•Simply set a maximum price (price cap)? •Give the operator a •Subsidy/transfer

What are the goals of regulation to keep in mind while trying to chose between these

different instruments?• Allocative efficiency

– price (of inputs and outputs…) reflect costs

– optimal product variety and quality

• Productive efficiency– Create an incentive to ensure that costs are minimized

– dynamic as well as static

• Equity/Fairness– minimize excess profit

– Make sure the tariff structure is fair to all users

• Financial viability…that is…fairness to the operator!– Reasonable return in relation to cost of capital!

• Minimize Regulatory burden– informational requirements; monitoring

– regulatory costs; lobbying42

…Looks like a regulator needs to achieve too many objectives … so what’s the best way to think them

through?

• Best way is to follow a synthetic model that allows one to address all these issues one by one

• …this is what the Armstrong-Sappington paper does

• So let’s focus on how they set up the regulation problem formally

So what exactly does optimal regulation theory need to focus on ?• The key relevant factors are:

1. Obviously…the regulators objectives (usually spelled out in a sector law)

2. The cost of paying for subsidies if needed (and if realistic given the country’s fiscal capacity)

– …or the fiscal revenue to be generated by the monopoly 3. The range of policy instruments available to the regulators

(including subsidies) (and these are typically also spelled out in a sector law)

4. The regulatory bargaining power with the operators (more subtle to identify…but technically convenient to discuss in the modeling exercise)

5. The information needed and the asymmetry of its access between regulators and operators (useful to simulate various assumptions at this level)

6. The degree of benevolence of the regulator (can’t be naïve about this, simply look at how regulatory agencies are set up and staffed)

7. The regulator’ability to committee to long term policies (legal issue)

(1) The regulator’s goals • Assume the regulator is benevolent• Assume that the regulator will focus on: (i) efficiency

(DWL), (ii) equity (how to share the DWL between the users and the operators) and (iii) financial viability of the operation (how much to get the taxpayer to contribute if needed)

• => Formally, to get to core of the DWL story: the regulator wants to maximize a weighted sum of– consumer/taxpayers surplus (S) (CS + subsidies or – taxes and

their associated distortions)– the rent of the operator (R) (net profits in the real world…including

transfers by the government to firms)

W = S + αR – with α, the weight given by the regulator to the rent of

the operator (it is =1 if the regulator only cares about efficiency)

– with 0 ≤ α ≤1– NOTE: If α =1: NO distributional preferences!

(2) The costs of raising funds to pay for subsidize matters to the regulators too…• Λ is the cost of raising funds from the taxpayers (=social

cost of public funds)• Λ≥ 0 because taxes distort production and consumption

activities => create DWL• If Λ = 0, marginal cost pricing is the familiar story from

traditional textbooks– Most real world models in fact assume no distortions from taxes!!!

• If Λ > 0, marginal cost pricing becomes much more complex because added costs due to added distortions in the system!

• What drives Λ? driven by institutions and macro conditions– About 0.3 in developed countries, >1 in LDCs

• Taxpayers welfare drops with taxes paid at a rate of 1 + Λ • In the literature:

– Baron and Myerson (1982) assume Λ=0 but a sets α<1– Laffont and Tirole (1986) assume Λ >0 but sets α=1

(3) The range of policy instruments available to the regulators (including subsidies)

• Can the gvt afford subsidies and make direct payments

– (common assumption in the literature)?

• Can the regulators set tariffs?• Can the regulator influence tariff

structure?• Cant the regulator influence quality?• Can the regulators impose cost

benchmarking?

(4) The regulatory bargaining power with the operators

• The usual assumption is that the regulator has all the necessary bargaining power

– Not always realistic but useful to come up with a benchmark against which the alternative of no bargaining can be assessed

– It turns out that it is not too costly to assume this in terms of the realism of the model used to assess optimal regulatory policy

• Usually modeled as its ability to offer a regulatory policy that the operators can decide to accept or reject

– If the operator rejects it…the interaction is over!

(5) The information needed and the asymmetry of its access between regulators and operators

• The usual assumption is that the operators know more about demand and costs (technology, quality, efforts, …) than the regulators

• => information asymmetry • Three types of informational problems

– 2 are adverse selection (hidden information problems) analyzed here

• on operating costs

• on consumer preferences

– 1 is moral hazard (hidden action problems)• On level of effort by managers to cut operating costs

• Crucial issue…since optimal regulatory policy varies significantly depending on the nature and level of this information asymmetry!

(6) The degree of benevolence of the regulator

• What if the regulator could be “captured” by the industry it is regulating?

• What if regulatory and operators could collude to get taxpayers and users to pay more than needed?

• This is about explicit and implicit corruption in a sector

(7) The regulator’s ability to commit to long term policies

• How do repeated interactions change the optimal regulatory policy when recognize that regulatory decisions is not a one time shot??

• Same story as in game theory…when you play once your optimal strategy will not be the same as when you need to face the same other players several times!

So what is optimal regulation under PERFECT INFORMATION?• => assume the regulator is omniscient!• Need to do this since it gives us a

benchmark against which to compare all the cases in which information asymmetry prevail

• Only way to get a sense of the cost of asymmetry

• …and the benefit of reducing it through the proper incentive mechanisms, from the most complex one to the simple imposition of regulatory accounting guidelines to increase the transparency of accounts!

Optimal regulation under perfect information:

• Consider – n products with prices p=(p1, p2, ….., pn)– v(n), the aggregate consumer surplus– π(p), the operators’ profit with a price vector of p– T any transfer paid by consumers (taxpayers) to

operators as part of the price paid for the services– S = v(p) - (1+Λ)T and R = π(p) +T– A non negativity constraint with respect to the rent R:

R≥0– Note: π(p) may be negative but must be recovered by T

– =>W= S + αR = v(p) – (1+Λ)T + α (π(p) +T)

• The main assumption in this benchmark is that the regulatory knows the two functions v(n) and π(p) perfectly

2 cases• We need to distinguish between 2

cases:

1. The government can make or get a transfer (i.e. a subsidy to the firm or a payment from the firm)

2. The government cannot afford a transfer

Case 1: Transfer are feasible• Since α ≤1 and Λ≥0, it is optimal to extract all firm

profit and use it to reduce the tax burden, that is, society is worse off when a T is needed to support the operator– The α plays not role here!– $1 of lower tax makes the taxpayer better off by $(1+Λ)

• This happens if dW/dT = -(1+ Λ) + α <0 Want T as small as possible, given the constraint

that Rent may not be negative R=0 π(p) = -T since R = π(p) + T Now replace T by - π(p) So total welfare with prices p is

W = v(p) – (1+Λ)T + α (π(p) +T) = v(p) + (1+Λ) π(p)

What happens if there is no cost to raise public funds?

• If Λ=0 (as usually assumed)P maximizes v+π = total surplusUnder full information when transfers are

possible, no rents are left to the firm and …marginal cost pricing is the optimal regulatory

rule accounting for the fact that the firm will still break even thanks to the transfers

• This is the full information outcome we always worked with in standard microeconomics !

What happens is there is a cost to raise public funds?

• If Λ>0 , then prices are above MC (on average)• We get into the markup story (to allow the firm to

pay for taxes) such as the Lerner pricing we discussed earlier

• In the single product case with π(p)=(p-c)*(q(c), optimal price derive from – dW/dp = v’(p) + (1+Λ) π’(p)=0 dW/dp = -q(p) + ((1+Λ)*(q(p))+ ((p-c)*q’(p))=0 (p-c)p = (Λ/(1+Λ)* (1/η)– => at optimum, we chose p to maximize this expression Where c is MC and η is the elasticity of demand – Price-cost margin is higher when Λ is higher and η lower– You’ll see later that this is like Ramsey-Boiteux pricing but here

Λ is not the shadow price of the firm’s budget constraint but the MC of raising gvt revenue and then distributing this revenue to the firms to cover its costs

Case 2: perfect information BUT unfeasible transfers (1)

• In this case, no possibility of transfers• => the operator must be financially autonomous• But if increasing returns to scale, MC pricing leads to

financial losses• => need to add a constraint to the previous social welfare

function:max v(p) + π(p)

s.t. π(p) ≥ 0(and here Λ and α now play no role)

• So denote λ ≥ 0, the Lagrange multiplier associated with the profit constraint, then choose p to maximize v(p) + π(p)+ (1+ λ ) π(p)

=> the 2 problems take the same form, the only difference is that in the former case Λ is exogeneous, while here λ is endogenously chosen to make the operator break even

Perfect information and unfeasible transfers (2)

max W=v(p) + π(p)s.t. π(p) ≥ 0

=> Set dW/dp = v’(p) + (1+λ) π’(p)=0dW/dp = -q(p) + ((1+ λ)*(q(p))+ ((p-c)*q’(p))=0

At optimum: Chose p so as to maximize

(p-c)p = (λ /(1+ λ )* (1/η)

Where c is MC and η is the elasticity of demand

By the way: why Ramsey-Boiteux?

• Ramsey (1927) looked at how to max consumer surplus while relying on proportional taxes to raise a target level of revenue

• Boiteux (1956) looked at how to max consumer surplus while marking prices up above marginal cost to recover fixed costs

Claimed ATCClaimed ATC

For next week…how do we deal with the real problem for a regulator: Asymmetric Information!

MRMR

MCMC

Fig 12.3

$

Q

DD

PPMPMP

True ATCTrue ATC

QQMPMP

A profit motive exists for a A profit motive exists for a natural monopoly to mislead a natural monopoly to mislead a regulator over ATC!!!!regulator over ATC!!!!

QQATCPATCP

PPATCPATCP

What next week will boil down to:

• Find a regulatory mechanism that takes into account the social costs adverse selection and moral hazard subject to the participation constraint of the firm and the budget constraint of the government

• End up balancing the costs associated with adverse selection and moral hazard

• Ultimately…it is all about taking regulatory action to reduce information asymmetries!