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Economie Publique IIFebruary-May 2010

Lecture 3Regulating Monopolies under

information asymmetry

Prof. A. Estache

How did the seminar on procurement relate to what we are studying in class?

• The seminar was about deciding:– Who should provide public services– How to organize the provisions of these public services– How to do so at the lowest possible costs for taxpayers

and users• Accounting for the facts that:

– Even when you have natural monopolies you can try to introduce competition (an operator may be forced to BID for the right to enjoy the monopoly!)

– Governments are not always very good at delivery things– Governments face significant information gaps on both

the supply (cost, quality) and the demand side when they design these markets to procure the public services they need to deliver

Now back to theory… a brief reminder

• What are we worried about in this class?– How best to deliver services that are essential

to society • Accounting for the fact that the cost structures of

these services make it difficult to rely on the simplest forms of competition…

– Existence of deadweight loss (DWL)• Rent earned by a monopoly (over and above normal profit) as

a waste for society

– Size of that DWL• Big or small?• Need to do something about it or not?

– Distribution of DWL• Taxpayers vs. users

To address these concerns we need to remember that …

p yk

( *) .1 1

…means that:Most of what we do in applied regulation build on 3 aspects:

•k, reflecting the costs which we take as given!• driven by technology, various dimensions of quality and effort levels

•demand side (ε) • driven by preferences but also budget constraints which drive the

ability to pay of the users

•how the monopoly plays with P and y to maximize profits given these costs and the demand elasticity!!

Remember also that now we know how prices relate to market power in an industry

MR y p y( ) ( ) .

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Since

And since MR=MC…we can derive:

(P-MC)/P= -1/ε

= the Lerner Index of market power•The monopoly’s profit margin is high when high (demand elasticity) ε and low in the opposite case!•=> Key variable to focus on to know about potential troubles in terms of DWL is ε (DEMAND!!!)

• More variables when you start accounting for the information asymmetry problems…

…so… Regulating a Natural Monopoly boils down to understanding that:

• A natural monopoly cannot be forced to rely on marginal cost pricing alone– Doing so makes the firm lose money, so it exits,

destroys 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.

• But nothing to say about the cost side of the business..and yet, we know it matters as much as the demand side!

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So how to come up with fair regulation of 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

In other words, what should optimal regulation theory focus on ?

The key relevant factors are:

1. The specific regulatory objectives

2. The economic and financial costs of paying for

subsidies

1. Hmmm… what’s the difference btw econ and financial costs??

3. Range of policy instruments available

4. Bargaining power of regulators

5. Information needs and asymmetry

6. “Purity” of the regulator

7. Regulator’s long terms commitment ability

Now…• Let’s become a bit more formal

about all this discussion of optimal regulation…

• That’s when the Armstrong-Sappington paper kicks in…

Remember the notation of the key variables • v(n), the aggregate consumer surplus associated with the consumption of the “n”

products made available to society by producers• η is the elasticity of demand• S, the total welfare surplus of the consumers accounting for the fact that they are hurt

by taxes if taxes are needed to finance the monopoly • π(p), the operators’ profit with a price vector associated with the range of products

provided of p

• R, the total rent associated with any monopoly power the operator may have on the sector, accounting for the fact that the government may subsidize its activities

• p=(p1, p2, ….., pn) the set of prices associated with these n products

• T any transfer paid by consumers (taxpayers) to operators as part of the price paid for the services

• 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, no tax driven distortions!– If Λ > 0, MC pricing becomes much more complex because added costs due to

added distortions in the system!

• W, the total welfare of society, given the preferences of consumers, the profit of monopolists and the costs and benefits to taxpayers of the regulatory instruments in place

• α, the weight given by the regulator to R (it is =1 if the regulator only cares about efficiency and there NO distributional preferences; if = 0, the gvt cares as much about consumers as about producers

How does one set up a model to identify the optimal regulation?

• Consider – 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)

• Main question: Do the designers of the optimal regulatory regime have full or partial access to the information needed to design this regime?

• Main assumption in benchmark: the regulator knows the two functions v(n) and π(p) perfectly => relatively simple to design optimal regulation

First, we have full information but we need to consider 2 cases

• We need to distinguish between 2 cases:

1. The government can make or get a transfer• That is (1): a subsidy to the firm • That is (2): a transfer can be negative,

so a subsidy may become a tax!

2. The government cannot afford a transfer

More generally, under full information we will see that

Transfer feasible

Cost to raising public funds

Yes No

No MC + T Irrelevant Λ

but

Ramsey pricing (MC”>MC

With strong role for η)

Yes MC’ (>MC) + T (<T’)

With strong role for η in driving markup

N.A.

Case 1: Transfer are feasible but costly (Λ>0)

• This is the most general case• We start from W= S + αR = v(p) – (1+Λ)T + α (π(p) +T)• Since α ≤1 and Λ≥0, it is optimal to extract all firm profit

and use it to reduce the tax burden since society is worse off when a T is needed to support the operator

• This happens if dW/dT = -(1+ Λ) + α <0 Want T as small as possible but need to accept the

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

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

– The α plays not role here at the optimum– $1 of lower tax makes the taxpayer better off by $(1+Λ)

So what is W when transfers are feasible?

• Total welfare at optimum with prices p is

W = v(p) + (1+Λ) π(p)

Note:– The α plays not role here because you

don’t force a corner solution!

– $1 of lower tax makes the taxpayer better off by $(1+Λ)

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

• If Λ=0 (as often assumed in basic micro textbooks)

Still need to find p that maximizes W=v+π = total surplus

Under 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/subsidies

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

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

• If Λ>0 , then optimal 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 derived 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

• We see that – 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– (no taxes or subsidies)

• => 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 exogenous, 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

Now …how do we deal with 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 the rest of this class boils down to:

• Set up the regulation problem as an agency problem (principal vs agent)

• Find a regulatory mechanism 1. that takes into account the social costs

– adverse selection– and moral hazard

2. subject to the participation constraint of the firm and

3. subject to 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!

More generally, under imperfect information

we will need too be able to fill in this matrix

Imperfect information due to

Cost to raising public funds

Adverse selection

Moral hazard

No P? P?Yes P? P?

What’ s special about the modern theory of regulation?

• There a clear concern for pushing the monopolist provider to perform in terms of:

1. Delivering the services• Not very different from early tradition of regulation focusing

on trying to push for more quantity to meet demand

2. …but more importantly to do so at so at the lowest possible cost and hence price!

• So the big deal is to tell the operator: I don’t believe your costs…I will tell you what I am willing to believe and allow you to recover!

• This is when price cap regimes start to replace cost-plus regime or old fashion rate of return regulation

• But what is the difference between of cost-plus or rate of return regulation and a price cap

A first look at price caps vs cost-plus regulation

• So prices for network industry services can be set according to:– Cost-based estimates for industry– Prices revealed through competition for the market

• NOTE: – The same rules are used to reset prices since regulated

prices are not set forever!– Regulated prices need to be adjusted over time to take

into account changes in costs due to:• E.g., changes in wages or exchange rates• Technological or efficiency gains in industry

1st Methods of Price AdjustmentRate of Return Regulation

• Under rate of return regulation, prices are adjusted to permit investors to achieve a specified rate of return on investments– Provides security to investors, thereby also lowering

the cost of capital– Firms have weak incentives to increase efficiency since

they do not benefit from lowering costs– Because returns are based on value of capital

investments, firms may have incentive to over-invest in capital

– Examples: traditional form of regulation for public and private utilities around the world

2nd Methods of Price Adjustment: Price Cap Regulation

• Under a price cap, maximum prices for a basket of services are fixed for 3-5 years with a formula (RPI-X) reflecting future inflation and expected efficiency gains– Firms have strong incentives to improve efficiency,

since they retain the benefits of lower than expected costs

– Risks for investors are higher than under rate of return, resulting in a higher cost of capital

– Difficult to make correct predictions about future conditions in between price reviews

– examples: started by Littlechild in the UK and now copied everywhere

Rate of Return vs. Price Cap?

• …In practice, as we will see later in the course, rate of return and price cap schemes can be similar– Regulators effectively decide on an allowable rate of return

at time of price cap review– If reviews are frequent (e.g., interim price reviews in UK

utilities), they can approximate rate of return

Pure Price Cap» infrequent mandatory

reviews» future prices based

on cost projections» relatively higher risk

for investors

Pure Rate of Return» frequent discretionary

reviews» current prices based on

previous year’s costs» relatively low risk for

investors

A 3rd complementary methods of price

adjustment: Yardstick” Regulation• Under yardstick regulation, regulators

compare firms’ performance with that of similar firms to arrive at a cost standard– Comparison may be with similar firms in different

geographical regions (e.g., UK) or with a model “efficient” firm (e.g., Chile)

– Can reduce subjectivity of evaluations by regulators– Can be difficult to identify valid comparators and can

be complex to implement– example: electricity in Holland, Water in the UK, port

terminals in Argentina

So how does incentive theory fit into all this?

• Basically, it tells you when it is a good idea to replace cost-plus (or rate of return) regulation with price cap regulation and vice versa…accounting for the type of information asymmetry that you (the regulator) faces

• The built in assumption is that price caps will usually be better when you want a monopoly to deliver at the lowest possible cost and to push the monopoly to do so for the long run

Starting point for incentive based regulation

• Recognize that regulatory has less than perfect information about:– Cost reduction opportunities of operator – Behavior of operator– Demand for the regulated services

• => strategic advantage to the regulated firm!...very different from the full information story!

• Advantage even stronger if regulated firm can capture the regulator!

• The only good news for the regulator is that regulation is a repeated game…– so regulator can learn – Operator needs to be careful not to build a bad

reputation!

Assume first our regulator is a benevolent regulator (no private agenda)• For a benevolent regulator: the optimization

is:– Find a regulatory mechanism that takes the

social cost of adverse selection (and moral hazard) into account subject to this participation constraint

– Balance costs of reducing costs, with risks of pushing too hard

– The costs vs the risks is what drives the choice between fixed prices and flexible price contracts

• Fixed price is price cap• Flexible price is cost-plus or rate of return

What if the main information problem is adverse selection?

• A firm’s costs may be high or low based on:– inherent attributes of its technical production

opportunities,– exogenous input cost changes over time (summer vs

winter) or space (rural vs urban)• This is not much, but it is at least some

information the regulator can use• His knowledge takes the form of a set of probabilities assigned

to the various possible costs => end up working with a lower and an upper bound within which the regulator knows the true costs lies…and the name of the game is to try to close the gap between the upper and the lower bound as much as possible

• But regulator faces a participation constraint for the firm– If the firms finds regulation is too harsh, it pulls out!– The operator knows it and hence has an incentive to act

strategically

What if the main information problem is moral hazard?

• A firm’s costs also depends on the level of managerial efforts to lower the costs!– Poor efforts = X-inefficiency!

• Problem is that regulator cannot observe effort directly

• => even if regulator can observe costs ex-post, it cannot simply reimburse costs (cost-plus regulation) assuming that the firm really tried its best

• …but again…if the regulator hits too hard…the risk that the participation constraint becomes binding!

• => firm again has an incentive to act strategically!

Price cap (or fixed prices) again• Set a fixed price EX-ANTE that the regulated

firm will be allowed to charge

• What’s special about it?– Prices are not influenced by managerial effort

even if costs are– => any additional profit from cost reducing

efforts goes to operator– => high powered incentives to max effort!– => solve moral hazard risk– BUT: full cost of adverse selection: if need a

high cost firm, will have to accept high price and for low cost firms, high unshared rent…

What if regulator awards a cost-plus contract instead?

• The operator is compensated for all the costs of production that it incurs

• Some assumptions built in..– Firm will reveal whether it is a high or low

cost firm

– =>There is no rent as excess profit

– => No adverse selection problem

– BUT moral hazard problem and associated costs are fully realized!

How are these 2 regulatory options usually modeled?

• The firm has a revenue requirement, RR, to cover its costs C

• RR can be based :– on a pre-set fixed component a, as well as – a component b contingent on a firm’s realized costs (b

is the realized cost sharing parameter)

– => RR = a + (1-b) C• For a price cap: RR = a since b=1 and a=C*, the

regulators’ assessment of efficient costs• For cost of service: RR = C since a=b=0• For a hybrid or performance based mechanism:

– O<b<1 and 0<a<C*

How’s the jargon on this?This is about rent extraction vs. incentives…

Managerial incentives

Rent Extraction

Fixed Price 100% 0%

Cost plus 0% 100%

Performance based

0<y<100% 0<y<100%

So how does one pick between cost-plus and price cap? (1)

• If moral hazard (effort) is the main problem and adverse selection is not a big deal– Price cap

• If adverse selection is the main problem and moral hazard is not a big deal– Cost plus

• But in real life…probably optimum is often in the middle:– Profit sharing mechanisms or sliding scale regulatory

mechanisms• Price allowed is partially responsive to realized costs and

partially fixed ex-ante

So how does one pick between cost-plus and price cap? (2)

• Ideally, come up with a menu of contracts– Make it profitable for a firms with low cost to

choose a high powered incentive scheme (price cap) and a high cost firm, a low powered incentive (cost plus)

– If the low cost firm behaves as a high cost one, it lose the rent

– If the market only has high cost firms, then participation constraint is not binding for these firms

– => contracts with different a’s and b’s!!!

Back to the formal model under asymmetric information

• The benevolent regulator’s objective is the same as before

–Max W= S + αR

– Assume also:• α≤1 => we assume that the firms’s profits are

less valued than consumer welfare

• Λ=0 => no social cost of public funds

Let’s focus first on regulation under adverse selection

• We don’t know the type of the firm (low or high cost?)

• Different ways of modeling this:– Baron-Myerson (1982)– Lewis-Sappington (1989)– Laffont-Tirole (1986)– Lewis-Sappington (1988)– Armstrong-Sappington (2008)

Baron-Myerson (1982)• Exogenous marginal cost c Є {cL, c H}

unobserved by the regulator

• The probability of the firm being a low cost is Ø

• The fixed cost F of the operator are common knowledge

• Consumer demand Q(p) and consumer surplus v(p) are also common knowledge

• Focus on a trade off between allocative efficiency and rent minimization

Lewis-Sappington (1989)

• Focuses on different sources of adverse selection

• Exogenous marginal and fixed costs unobserved by regulators

• Cost function– C(Q) = cL Q + F L or C(Q) = cH Q + F H

– Negative relation between marginal and fixed costs: cL < cL F H >F H

– Consumer demand is common knowledge

Laffont-Tirole (1986)• Again different sources of adverse selection but also

leaves room for moral hazard• Endogenous marginal costs, observed by regulator• Regulator does not know trade-off between fixed and

marginal costs• Fixed cost (or effort) are not observable• Low cost firms can achieve marginal cost c by incurring a

high fixed cost FL(c)

• High cost firms can achieve marginal cost c by incurring a high fixed cost FH(c) >FL(c)

• The probability of the firm being a low cost is Ø• Consumer demand is common knowledge• Again trade-off between efficiency (productive) and rent

minimization

Lewis-Sappington (1988)

• Cost function C(Q) is common knowledge

• Consumer demand is exogenous but unobserved by regulator

• Demand is QL(p) or QH(p) > QL(p)

• The probability of low demand is Ø

What we know (Y) and what we don’t know in these models?

Costs Demand Effort

MC FC

BM 82 N Y YLS 89 N N YLT 86 Y N Y NLS 88 Y Y N

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A unified treatment of regulation under adverse selection (Armstrong-Sappington (2008) (1)

• Firm’s private information is binary– State i=L or H (low or high)

• Exogenous probability of state L is Ø

• Firms profits in state i with price p is πi(p)

• Contract for firm i is price pi and Transfer Ti

• Firm’s equilibrium rent in state i is Ri = πi(p) + Ti

• Define difference Δπ(p) in firm’s profits in state H compared to stage L, given (regulated) price:

Δπ(p) ≡ πH(p) - πL(p)

In the case of Baron-Myerson,

=(p-cH )q(p) – (p-cL )q(p) = (cL – cH) q(p)

A unified treatment of regulation under adverse selection (Armstrong-Sappington (2008) (2)

• Consumer surplus in state i with price p is vi(p)

• Net consumer surplus is vi(pi)-Ti

• With social cost of public funds, this would become as before vi (pi ) + (1+Λ) Ti

• The welfare in state i is thus

W = [vi (pi ) - Ti ]+ αRi , i= L or H

• A better expression is W = wi (pi ) – (1- α)Ri

where wi (p)= vi (p ) – πi (p) • The expected welfare is W=ØWL + (1-Ø)WH

• With 2 participation constraints:Ri, Ri ≥0 • If full info: p maximizes W and R=0

Adding asymmetry adds incentive constraints to the participation constraints!!

• We need 2 incentive compatibility constraints (ICC):1. Low cost firms must not have the incentive to pretend

they are high costs– RL = πL(pL) + Ti ≥ Ri = πH(pH) + TH = RH - Δπ(pH) 2. High cost firms must not have the incentive to pretend

they are Low costs– RH≥ RL + Δπ(pL)

• Adding these inequalities implies Δπ(pH) ≥ Δπ(pL) and so it must be the case that pH ≥ pL

• => full information outcome is only possible if the ICC are met

• Problem is that with the B-M or L-T assumptions and models…this is NEVER possible!

• => marginal cost pricing won’t do it!– Low price firms will have high profits, the others, low

ones

Why is it that full information optimum does not work in L-S(1989)?

• The full information outcome requires marginal cost pricing with a transfer to compensate the deficit from marginal cost pricing

• For the ICC to be respected…according to the math…we need– The difference btw high and low cost firms in variable

costs in producing low price output higher than the difference in fixed costs (this is the highest transfer the firm could get as a low cost firm)

• Otherwise, incentive for high cost to pretend to be low costs

– The difference in fixed costs greater than the difference in variable costs in producing high price outputs

• Otherwise profits not sufficient to cover higher fixed costs

Why is it that full information optimum does not work in L-S(1989)?

• In practice, this means– The introduction of info asymmetry leads to a social

inefficiency

– The less performing firms have a higher prices and sell less than at 1st best even if its profits=0

– The good performers get an informational rent which leads to a higher profit simply because it can pretend to be unproductive and claim the same level of generosity by the regulator as the poor performer!

– Price cap: full efficiency but high rent

– Rate of return: zero rent, but no efficiency!

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So how to think about how to distinguish between the different types of firms?

• Need to be able to generate a separating equilibrium rather than a pooling equilibrium

• Pooling: all types receive the same transfer and charge the same price

• Separating: high and low cost firms receive different transfers and charge different prices

• => ok to have different prices for the same service under a separating equilibrium!– Rent is inversely related to price!

What happens in the Laffont-Tirole model? (1)

• Here, the regulator has 3 instruments– Price, marginal cost and transfers– ..but does not know the fixed costs…– However, lower MC implies higher FC

• Formally,– the rent is Ri = Q(pi) (pi-ci) –Fi (ci) + Ti

– The 1st IC constraint is: RL ≥ RH + FH (cH )- FL (cH)– The 2nd for high cost firms is similar

• Welfare in state I is

W = v(pi) + Q(pi) (pi-ci) –Fi (ci) - (1-α) Ri

What happens in the Laffont-Tirole model? (2)

• What’s interesting?– Prices do not affect the IC (given choice of Rs)– Prices max W => p=mc– In the end, in this very popular model of adverse

selection,

–Prices are used to achieve allocative efficiency

–Transfers are used to give incentive for cost reduction

– Note that since MC are observable, it is easy for regulator to chose p=MC

– In this model, rent due to difference in fixed cost

What happens in the Laffont-Tirole model? (3)

• Ultimately, very similar to B-M (1989)– Bad guy does less effort than needed,

good guy behaves =suboptimal socially– Again informational rent for good guy and

no profit for bad guy– Good guy prefers fixed price contrat

(independent of cost)– Bad guy prefers cost-plus contract

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Note: What’s the problem with pooling equilibrium?

• May be too costly to obtain any information• Strong risks of opposition of social and

private incentives• Example:

– Unknown demand and concave cost function• Marginal cost prices are such that pL > pH

• IC requires pL < pH

• => optimum involves pooling: pL = pH

• Similar story would come from known and identical MC but different fixed costs

Pooling in L-S (1988)

• Cost function common and CONCAVE (=> decreasing marginal costs)

• Consumer demand exo but unobserved by regulator

• As a result of concave cost function, this is one case where low demand firm claims that state of demand is high– => high costs firms are happy since get to

be seen in the same way as low cost firms!

What about moral hazard?• Regulator’s problem: how to push for unobserved cost-reducing effort• Modeler’s problem: How do you model effort?

• Firm’s optimization problem given a contract specifying UL and UH to reflect the 2 state: Low cost L (socially desirable) and high cost H

• Ø is the probability that state L is chosen by operator• It cannot be observed by regulator…but the regulator CAN observe if

the firm is in state L or H

• Max Ø UL + (1- Ø ) UH – D(Ø) -> Ø (ICC)

• Firm’s equilibrium effort is D’(Ø) = UL – UH

• ΔU = [UL – UH] is the power of the incentive scheme

• Optimal effort is Ø = Ø*(ΔU )• In the 2 outcome case, the ICC can be replaced by this optimal effort

condition• Again in this case, since U is known, the regulator can directly

determine L and H by choosing p and T• NOTE :by increasing effort, the firm can increase the probability that

the favorable state occurs., BUT, increased effort implies higher costs.

CONCLUDING COMMENTS• Harder to argue for marginal cost pricing

alone in these models• Transfers end up having an incentive role as

well as a financing role and hence become even more interesting

• So…to get the right incentives– Pricing as in full information– But paying to get the good guys to show up and

the bad guys not to show up!

• That’s where all these complex pricing scheme are helpful!