Economie Publique II
February-May 2010
Lecture 3
Regulating Monopolies under
information asymmetry
Prof. A. Estache
1
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( y*) 
…means that:
k
1
1

.
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
Since
1

MR( y)  p( y) 1   .


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!
So how to come up with fair regulation of
pricing by a Natural Monopoly???
Dollars
Unregulated monopoly
$60
A
C
$29
$15
"Fair rate of
return" production
Which allows cost
recovery
F
MR
50,000
•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
LRATC
MC
B
D
100,000
85,000
Number of
Households
Served
7
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 ArmstrongSappington 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
Yes
No
Cost to
raising
public
funds
Yes
No
Irrelevant Λ
but
Ramsey pricing
(MC”>MC
With strong role
for η)
MC’ (>MC) + T (<T’) N.A.
With strong role for
η in driving markup
MC + T
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)=0
dW/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
Now …
how do we deal with Asymmetric Information!
$
A profit motive exists for a
natural monopoly to mislead a
regulator over ATC!!!!
PMP
Claimed ATC
PATCP
True ATC
MC
MR
QMP
D
QATCP
Q
Fig 12.3
•
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
No
Yes
P?
P?
Moral
hazard
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 Adjustment
Rate 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?
 Pure Rate of Return
» frequent discretionary
reviews
» current prices based on
previous year’s costs
» relatively low risk for
investors
 Pure Price Cap
» infrequent mandatory
reviews
» future prices based
on cost projections
» relatively higher risk
for investors
• …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
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 Rent
incentives Extraction
Fixed Price
Cost plus
100%
0%
0%
100%
Performance 0<y<100% 0<y<100%
based
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
BM 82
LS 89
LT 86
LS 88
MC
FC
N
N
Y
Y
Y
N
N
Y
Demand Effort
Y
Y
Y
N
N
47
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!
52
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 LaffontTirole 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
56
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!