Transcript p(y) - Economics of Regulation ECON-d-421

Economie Publique II
February-May 2010
Prof. A. Estache
Lecture 2
Regulating Monopolies Under
information symmetry
1
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
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
3
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
4
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:
n
 
C  q    C qi
i 1
n
i
q
 q
i 1
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
7
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, productspecific 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)
A monopoly can be temporary… (common in
congestion related problems where demand drives
the nature of the market!)
D
D1
D1
D
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:
 C  a q , b q   C  q , q  i  1,
 a 1  b 1 a  0 b  0
i 1
i
i
i
i 2
i i
1
i
2
n
i
Thus, each of i firms produce ai % of output q1 and bi % of
the output q2.
From a policy viewpoint what does this mean?
• If the cost function is subadditive => the technology
implies a natural monopoly: only allow 1 firm!
 C a q ,b q   C q , q 
i
i 1
i
2
1
2
• 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.
 C a q ,b q   C q , q 
i
i 1
i
2
1
2
• => from a policy viewpoint, essential to see how you want
to structure your industry (i.e. when you need to clear a
merger request!)
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?
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
13
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
14
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)
min C  w 0 x*
t
N
s.t. s x s  x* ,
s 1
N
 y
s 1
s
s
 y0
N
*


K
,


0
,
x
0
 s
s
s 1
• NOTE: Economies of Scale is a special case of size efficiency modeling.
K 1
15
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).
min C  w 0 x*
t
N
s.t. s1  s 2 x s  x*
s 1
N
A
A
y

y

 s1 s 0 ,
s 1
N
 s1  1,
s 1
N
B
B
y

y

 s2 s 0
s 1
N
*
0
x
,
0


,

,
1


 s2
s2
s1
s 1
Note: A: voice, B: i-mode service
16
Then we look for data for the empirical
analysis (based on case study of Tokyo)
Variables
Inputs
Outputs
Inputs Price
Description
L (Labor)
The number of employee (person)
K (Capital)
Capital Cost/ wK (million yen)
Vs
The number of subscribers of cellular
phone (thousand)
Ds
The number of subscribers of i-mode
service (thousand), since 1997
wL (Labor)
Labor Cost / L (million yen/person)
wK (Capital)
 s  def (r  dep)
i
i
i
17
Result(1): The shrinking role of Economies of Scale in
telecoms..that’s why deregulation makes sense in that
sector!
DoCoMo Tohoku (northern part)
DoCoMo (Tokyo)
Cost efficiency
SCE
• 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
18
expansion of market size?)
Result(2): …but the sustained role of economies of scope
in telecoms…so still some role for a regulator!
DoCoMo (Tokyo)
DoCoMo Tohoku
K
Economies of scope
(Size efficiency)-1
• K=1 in Tohoku and K=4 in Tokyo. (The
metropolitan area is not size efficient.) Strong
economies of scope exists.
19
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!
20
The efficiency of competition
$/output unit
p(y)
CS
p(ye)
The efficient output level
ye satisfies p(y) = MC(y).
Total gains-to-trade is
maximized.
MC(y)
PS
ye
y
The Inefficiency of Monopoly
$/output unit
p(y)
p(y*)
MC(y)
y
y*
MR(y)
The Inefficiency of Monopoly
$/output unit
p(y)
p(y*)
CS
PS
MC(y*+1) < p(y*+1) so both
seller and buyer could gain
if the (y*+1)th unit of output
was produced. Hence the
MC(y) market
is Pareto inefficient.
y
y*
MR(y)
The Inefficiency of Monopoly
$/output unit
Deadweight loss measures
the gains-to-trade not
achieved by the market.
p(y)
p(y*)
MC(y)
DWL
y
y*
MR(y)
The Inefficiency of Monopoly
The monopolist produces
$/output unit
less than the efficient
quantity, making the
p(y)
market price exceed the
efficient market
p(y*)
MC(y)
price.
e
DWL
p(y )
y*
y
ye
MR(y)
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
( y)  p( y)y  c( y).
(with the usual notation for prices and costs)
• Start by asking what output level y*
maximizes profit?
• Then derive the price
Profit-Maximization
( y)  p( y)y  c( y).
At the profit-maximizing output level y*
d( y) d
dc( y)

0
p( y)y 
dy
dy
dy
so, for y = y*, MR - MC =0 => MR=MC
or:
d
dc( y)
.
p( y)y 
dy
dy
Some more manipulation
d
dp( y)
MR( y)  p( y)y  p( y)  y
dy
dy
y dp( y) 

 p( y) 1 
.

p
(
y
)
dy


Since own-price elasticity of demand is
p( y) dy

y dp( y) =>
1

MR( y)  p( y) 1   .
 
=>when is a monopoly happy …and when not?
Look at the drivers of its MR
1

MR( y)  p( y) 1   .


SO the MR is positive IF demand curve is:
-elastic (ε <-1)
And
MR 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?
1

MR( y)  p( y) 1   .


For a profit-maximum: MR = MC
Now, suppose the monopolist’s MC
is constant, at $k/output unit.
1

MR( y*)  p( y*) 1    k


which leads to
p( y*) 
k
1
1

.
So…:
…means that:
p( y*) 
k
1
1

.
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 rise
3. 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?
Consider MR( y)  p( y) 1  1  .

 
And note again that at optimum, MR = MC
So 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?)
1 (retail
energy?)
10
REGULATE!
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!
Dollars
Unregulated monopoly
$60
A
C
$29
$15
Efficient
production
(requires
subsidy!!!)
F
MR
50,000
B
LRATC
MC
D
100,000
85,000
Number of
Households
Served
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!
So how to come up with fair regulation of the
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
B
LRATC
MC
D
100,000
85,000
Number of
Households
Served
38
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 twopart 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!!!
So how to come up with fair regulation of the
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
LRATC
MC
B
D
100,000
85,000
Number of
Households
Served
40
So how to come up with fair regulation of the
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
41
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; lobbying
42
…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.
2.
Obviously…the regulators objectives (usually spelled out in a
sector law)
The cost of paying for subsidies if needed (and if realistic given
the country’s fiscal capacity)
–
3.
4.
5.
6.
7.
…or the fiscal revenue to be generated by the monopoly
The range of policy instruments available to the regulators
(including subsidies) (and these are typically also spelled out in a
sector law)
The regulatory bargaining power with the operators (more subtle
to identify…but technically convenient to discuss in the modeling
exercise)
The information needed and the asymmetry of its access between
regulators and operators (useful to simulate various assumptions
at this level)
The degree of benevolence of the regulator (can’t be naïve about
this, simply look at how regulatory agencies are set up and
staffed)
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
•
•
–
1 is moral hazard (hidden action problems)
•
•
on operating costs
on consumer preferences
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 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
• 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)=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
For next week…how do we deal with the real
problem for a regulator: 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 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!