Tài liệu Pricing communication networks P13 pptx

A principal difficulty for the regulator is that he does not have full information about the cost structure and the production capabilities of the firm, nor does he know the actions and

Regulation

The regulator’s job is to supervise a market so that it operates efficiently He acts as a high level controller who, taking continual feedback from the market, imposes rules and incentives that affect it over the long term In the telecoms market the regulator can influence the rate of innovation, the degree of competition, the adoption of standards, and the release

to the market of important national resources, such as the frequency spectrum

The efficiency of an economy can be judged by a number of criteria One criterion is

allocative efficiency This has to do with what goods are produced The idea is that producers

should produce goods that people want and are willing and able to buy Another criterion

is productive efficiency This has to do with how goods are produced The opportunity cost

of producing any given amounts of products should be minimized Resources should be used optimally New technologies and products should be developed as most beneficial

Finally, distributive efficiency is concerned with who things are produced for: goods should

be distributed amongst consumers so that they go to people who value them most

In general, competitive markets tend to produce both allocative and productive efficiency However, in cases of monopoly and oligopoly firms with market power can reduce

effi-ciency We say there is market failure In this case, regulation can provide incentives to the

firms with market power to increase efficiency The incentives can either be direct, by im-posing constraints on the prices they set, or they can be indirect: for example, by increasing the competitiveness of the market There is no single simple remedy to market failure Sometimes competition actually reduces allocative efficiency In the case of a natural monopoly, social welfare is maximized if a single firm has the exclusive right to serve a certain market This is because there are large economies of scope and scale, and because the rapid creation of industry standards leads to efficient manufacturing and also to marketing of complementary products and services We see this in traditional telephony, and other public utilities, such as electric power, rail transportation and banking The job of the regulator is

to ensure that the monopolist operates efficiently and does not exploit his customers Information plays a strategic role in the regulatory context, because regulated firms can obtain greater profits by not disclosing full information about their costs or internal operations A principal difficulty for the regulator is that he does not have full information about the cost structure and the production capabilities of the firm, nor does he know

the actions and effort of the firm This is another example of the problem of asymmetric information, already met in Section 12.4 in the context of interconnection contracts We

illustrate this in Section 13.1, with some theoretical models, and then explain ways in

Pricing Communication Networks: Economics, Technology and Modelling.

Costas Courcoubetis and Richard Weber Copyright  2003 John Wiley & Sons, Ltd.

ISBN: 0-470-85130-9

which the regulator can achieve his goals despite his lacking full information The firm’s information about the future behaviour of the regulator may also be imperfect; this leads

to intriguing gaming issues, especially when decisions must be made about large, hard to recover investments In Section 13.2 we describe some practical methods of regulation Section 13.3 considers when a regulator ought to encourage competition and how he can

do this In Section 13.4 we discuss the history of regulation in the US telecommunications market and describe some trends arising from new technologies

13.1 Information issues in regulation

13.1.1 A Principal-Agent Problem

In this section we present a simple model for the problem of a regulator who is trying to control the operation of a monopolist firm Unless he is provided with the right incentives, the monopolist will simply maximize his profits As we have seen in Section 5.5.1, the social welfare will be reduced because the monopolist will tend to produce at a level that is less than optimal The regulator’s problem is to construct an incentive scheme that induces the firm to produce at the socially optimal level

We can use the principal-agent model with two players to illustrate various problems

in constructing incentives and the importance of the information that the regulator has of

the firm Recall, as in Section 12.4, that the principal wants to induce the agent to take

some action In our context, the principal is the regulator and the agent is the regulated

firm The firm produces output x, which is useful to the society, and receives all of its income as an incentive payment, w.x/, that is paid by the regulator In practice, firms do

not receive payments direct from the regulator, but they receive them indirectly, either through reduced taxation, or through the revenue they obtain by selling at the prices the regulator has allowed To produce the output, the firm can choose among various actions

a 2 A, and these affect its cost and production capabilities.

There are two types of information asymmetry that can occur The first is known as

hidden action asymmetry and occurs when the regulated firm is first offered the incentive contract and is then free to choose his action a The level of output x takes one of the values x1; : : : ; x n , with probabilities p a1; : : : ; p a

n, respectively, where P

i p a i D1 for each

a 2 A The firm’s cost is c x; a/ Think, for example, of a research foundation that makes

a contract with a researcher to study a problem Once the contract is signed the researcher

chooses the level of effort a that he will expend on the problem ‘Nature’ chooses the

difficulty of the problem, which together with the researcher’s effort determines the success

of the research Note that the researcher does not know the difficulty of the problem at the time he chooses his level of effort He only knows the marginal distribution of the various final outcomes as a function of his effort, for instance, the probability that he can solve the problem given that he expends little effort The research foundation cannot with

certainty deduce the action a, but only observe the output level This is in contrast to the full information case, in which the regulator can observe a and make the incentive payment

depend upon it One way that full information can be available is if each output level is associated with a unique action, so that the regulator can deduce the action once he sees the output level

Another possibility is that the regulator does not know the firm’s cost function at the time

he offers the incentive contract We call this hidden information asymmetry Now a denotes the type of the firm, and c.x; a/ is its cost for producing output x At the time the contract

is made, the firm knows its own c.Ð; a/, but as we will see, it can gain by not disclosing

INFORMATION ISSUES IN REGULATION 293

it to the regulator It turns out that information asymmetry is always to the advantage of the firm, who can use it to extract a more favourable contract from the regulator By trying

to ‘squeeze’ more of the profits of the firm from the contract, the regulator can only have negative effects on social efficiency

Let us investigate the problems that the regulator must solve in each case In the case of

hidden action asymmetry the principal knows the cost function c.a/ (where for simplicity

we suppose this cost depends only upon the action taken), but he cannot directly observe a.

The principal’s problem is to design a payment schemew.x/ that induces the socially best action from the agent Let u.x/ be the utility to the society of a production level x The

problem can be solved in two steps First, compute the socially optimal action by finding

the value of a that solves the problem

maximize

a

" n X

i D1

p a i u x i /  c.a/

#

Now find a payment scheme that gives the agent the incentive to take action a rather than

any other action Since there may be many such payment schemes, we might choose the one that minimizes the payment to the agent This is the same as minimizing his profit Let v.w/ be the agent’s utility function for the payment he receives In most practical cases, v

is concave The principal’s problem is

minimize w.Ð/

n

X

i D1

subject to

n

X

i D1

n

X

i D1

p i a v.w.x i //  c.a/

½

n

X

i D1

p i b v.w.x i //  c.b/ ; for all b 2 A n fag

(13.3)

Condition (13.2) is a participation constraint : if it is violated, then the agent has no incentive

to participate Condition (13.3) is the incentive compatibility constraint : it makes a the

agent’s most desirable action The solution of (13.1) provideswa.Ð/, the best control As a

function of the observable output only, it induces the agent to take action a Observe that

at the optimum (13.2) holds with equality; otherwise one could reduce w by a constant amount and still satisfy (13.3) Hence, we must have thatP

i p i a v.w.x i // D c.a/.

In the full information case, in which the principal observes a, a simple punishment policy solves the problem Constraint (13.3) is ensured by taking w D 1 if any action

other than a is taken When a is taken, the optimal payment is w.x i/ D wŁ for all i ,

wherev.wŁ/ D c.a/ Such a payment provides complete insurance to the agent, since he

is recovers the cost of a, no matter what the outcome x i

Unfortunately, such a simple policy will not work if the action cannot be observed

If we use a complete insurance policy the agent will pick the policy with the least cost (as he has a guaranteed revenue) To guarantee (13.3), the payment must depend on the

outcome, that is, w.x i / 6D w.x j /, i 6D j Additionally, we must guarantee (13.2), with

P

i p a i v.w.x i // D c.a/ Since v.w/ is concave in w, the payment vector will need to have

a greater expected value than in the full information case, that is,P

i p i a w.x i/ ½ wŁ Thus, under information asymmetry, the principal must make a greater average payment Notice that other incentive schemes also work Let us assume a simple hidden information

model with u x/ D v.x/ D x The incentive payment

for some constant F, has a nice interpretation Firstly, we can interpret it as a ‘franchise’ contract: the agent keeps the result x and pays back to the principal a fixed amount F,

the ‘franchise fee’ Secondly, the participation and the incentive compatibility conditions imply that the agent solves the problem

maximize

a [x.a/  c.a/  F] ; subject to x.a/  c.a/  F ½ 0 Hence, the agent will choose the socially optimal action aŁif F is small enough to motivate

participation, i.e if

F  x aŁ/  c.aŁ/

If the principal knows x Ð/ and c.Ð/ then he can set F equal to the maximum allowable value, say FŁDx aŁ/c.aŁ/, and so push the profit of the agent to zero However, if these

functions are not known, then the principal cannot take chances, and must choose F less than FŁ This illustrates how hidden information means greater profits for the regulated firm

We say there are informational rents If the goal is to maintain the output that maximizes

social welfare (allocative efficiency), then hidden information increases producer surplus (and decreases distributive efficiency) A possible way to solve the problem of defining a

reasonable F is through auctioning (monopoly franchising), in which the agents bid for the least value of F that they can sustain, hence indirectly revealing information to the

principal

In another simple illustrative example of hidden information, which shows more clearly the trade-off between lower profits for the regulated firm and economic efficiency, the firm

is one amongst a number of possible types, differing in the cost function, c i x/ Again,

the agent’s type is unknown when the contract is signed The regulator knows only the probability distribution of the various agent types In practice, such a model makes sense since it is hard for the regulator to construct the actual cost function of the regulated firm; moreover, it is to the advantage of the agent to hide his cost function from the regulator unless he is very inefficient The possibility that the firm might have a high operating costs forces the regulator to offer him a high compensation Similar examples from other contexts concern contracts between a firm and workers with different efficiencies, and between an auto insurer and drivers of different propensities to accidents Again, an efficient worker benefits from the existence of inefficient workers, since these force the firm to offer him a greater incentive

The principal wants to construct a payment scheme that maximizes economic efficiency under uncertainty about the agent’s type Suppose the principle posts a payment scheme

that is a function of the output x Given his cost c i x/, an agent of type i selects the

optimal level of output Although this is straightforward when there is a single type of

agent, there is a complication when there are multiple types, since an agent of type i could find it profitable to impersonate an agent of type j , and produce the corresponding output

INFORMATION ISSUES IN REGULATION 295

level To avoid this, the optimal payment scheme must allocate greater average profits to the agents that it would do if it could make the payments depend on agent type This again illustrates the power of information in the regulatory framework Any attempt to reduce the profits will result in different output levels, and so reduce economic efficiency

More precisely, suppose an agent can choose any positive level of output x Suppose it

is desired to maximize social welfare In the complete information case, it is optimal to

offer a type i agent a payment of c i xŁ

i / to produce xŁ

i , where x iŁmaximizes x  c i x/, i.e.

c0i xŁ

i/ D 1 Suppose there only two types of agent, of equal probability, and that type 1 is

the more efficient, in the sense that its marginal cost function c01.x/ lies below c0

2.x/ for all

x, as shown in Figure 13.1 We say that the cost functions have the single crossing property , since even if c2.0/ < c1.0/, the functions can cross at most once Then a candidate payment scheme is given by two pairs:.c1.xŁ

1/; xŁ

1/ D A C B; xŁ

1/ and c2.xŁ

2/; xŁ

2/ D A C D; xŁ

2/,

as shown in (a) of Figure 13.1 Note that this is the optimal incentive payment scheme in the full information case, in which the principal knows the agent’s type when he offers a

contract In this case, he offers an agent of type i only one possible contract: make xŁ

i for a payment of c i xŁ

i/Cž, where ž is a small positive amount that gives the agent a small profit This payment could be optimal in the hidden information case if the incentive

compatibility conditions were to hold, i.e if an agent of type i were to choose output level

x iŁafter rationally choosing the contract that maximizes his net benefit Unfortunately, this

does not happen An agent of type 1 is better off to produce x2Łand so receive a net benefit

of D, instead of zero The only way to prevent him from doing this is to add D to the payment for producing x1Ł, and hence provide incentives for socially optimal output One can check that this works, and that each type will now produce at the socially optimal level Note that the inefficient agent obtains zero profit, while the efficient agent is rewarded by

obtaining a profit of D.

The principal cannot reduce the agents’ profits without reducing economic efficiency However, he can reduce the payment made to an agent of type 1, and so increase his own

surplus, if he reduces the payment for output level xŁ

1 from the initial value A C B C D to some value A0CB0CD0, and reduces xŁ

2to xŁŁ

2 , as shown in (b) of Figure 13.1 By reducing distributive inefficiency (through reducing the incentive payment) he also reduces social efficiency, since a type 2 agent does not now produce at the socially optimal level Note that this example is very similar to that given and for second degree price discrimination

in Figure 6.4

B

(a)

1

A

D

B′

(b)

A′

D′ 1

Figure 13.1 A principal-agent problem in regulation In the case of perfect information, shown in

(a), it is optimal to offer A C B to agent 1 to produce xŁ1, and A C D to agent 2 produce x2Ł Each just covers his cost However, if offers cannot be tailored to agents (because their types are

unknown) then agent 1 will choose to produce x2Łand obtain net profit of D Now (b) shows how the principal increases his surplus He reduces the target output level of the high cost agent to x2ŁŁ,

below the socially optimal level xŁso as to decrease D to D0

13.1.2 An Adverse Selection Problem

We have seen above how the principal may experience an adverse selection problem because

he lacks the information to discriminate amongst types of agents and make them distinct of-fers Adverse selection occurs when some type of agent finds it profitable to choose the offer that was intended for another type of agent We have seen that when the goal of the principal

is to make agents choose actions that maximize social welfare, the effect of adverse selection

is to force the principal to make a larger payment than he would if he had full information

A consequence of adverse selection is that there may be no prices that a regulator can prescribe to a firm such that the firm can recover its cost More generally, adverse selection can destroy a market, as we see in the following example

Example 13.1 (A market for used cars) Consider a market for used cars, in which the

principal (the buyer of a car) can check the quality of the car only after he has purchased it from the agent (the seller) Suppose that cars have qualities uniformly distributed on [0; 1],

and that a seller of a car of quality x is willing to sell only if the offered price s exceeds x,

which is perhaps an amount he owes on a loan and must repay A buyer of a car of quality

x values it at u x/ D 3x=2.

Since the buyer cannot observe the quality of a car before making an offer, he must make the same offer for every car His problem is to maximize his net benefit He does this

by choosing his offer s to maximize E x [u.x/  s j x  s], where the expectation over the random variable x is conditioned by the participation constraint x  s For a given s, the expected quality of a purchased car is s=2, and so the buyer must choose s to maximize 3s =4  s, giving s D 0 Thus no cars are sold.

Note that, if the quality of a car is in the interval [2s=3; s], then both buyer and seller can

benefit from a transaction If the quality of a car is in the interval [0; 2s=3] then a transaction

profits the seller, but not the buyer The average quality of a car is s=2, which is less than

the lowest acceptable level of 2s=3 for which the buyer would wish to participate This

adverse selection phenomenon causes market breakdown Although there are social welfare gains to be made by matching some pairs of buyers and sellers, the lack of information makes such interaction impossible Of course, if the distribution of the quality were such

that the average quality were greater than 2s=3, then the market would not break down,

and there would be a positive value of s that it would be optimal for a buyer to bid.

The problem is that the buyer is unable to distinguish between high and low quality cars

If he were able to obtain information about the quality of a car he could adjust his bid appropriately Hence, it benefits both the seller and the buyer if the quality can be signalled The seller could allow the buyer to take the car for a test drive, or to have the car checked

by a mechanic As a simple illustration, suppose the buyer can check whether the quality

of a car is more or less than 1=2 It is easy to see that such a simple signal of ‘high’ or

‘low’ quality is enough to create a stable market in which both sellers and buyers profit For

instance, offering s D 3=4, but only for cars with x > 1=2 is a policy that gives the buyer

an average profit of 3=16 In fact, the optimal choice of s is s D 1=2 C ž for an arbitrarily small ž Now the buyer has nearly full information as he knows the actual quality of any car he purchases must lie in the interval [1=2; 1=2 C ž]

Similar to the above example, let us consider a model of an ISP who sells Internet connectivity

Example 13.2 (A market for Internet connectivity) Suppose there are n potential customers, requiring x ; : : : ; x units of Internet use, where these are independently and

METHODS OF REGULATION 297 uniformly distributed on the interval [0; 1] Suppose the regulator requires the ISP to charge all customers a flat feew, without taking account of their actual resource usage Then, under certain conditions, there may be no profitable production level for Internet services

Suppose that a customer of type x has a utility for the service u x/ D x, and so does not buy service if his surplus of x w is negative The network exhibits economies of scale,

so that the per unit cost when using total bandwidth b is

².b/ D a b

n=2 C

1  b

n=2



which varies linearly from its maximum value 1 when b D 0 to its minimum value a < 1

when b D n=2 (where n=2 is the maximum average bandwidth consumed by the customers

when all subscribe to the service) If the regulator sets a price w, then only the customers

with x ½ w will subscribe, and they will number n.1  w/ on average The average

bandwidth that any one will consume is 1 C w/=2, and the average total amount of

bandwidth consumed will be b D n.1  w/.1 C w/=2 The average profit per customer

of the firm will be

w 1

2².b/.1 C w/ D w 1

2[1 .1  w2/.1  a/].1 C w/

For w D 0 the profit is a < 0, and for w D 1 (the maximum possible charge) the profit is also 0 Numerical calculation shows that when a is greater than 0.7465, the profit

of the firm increases with w but is always negative Hence, no value of w allows stable operation The reason is adverse selection: given w, only customers with x ½ w subscribe.

But w is targeted at the average customer Adverse selection prevents the average from being favourable This again illustrates that there are major problems with flat rate pricing

13.2 Methods of regulation

The following sections describe various methods of monopoly regulation

13.2.1 Rate of Return Regulation

Under rate of return regulation a firm must set its prices, its level of production and its

inputs, subject to the constraint that its rate of return on its capital is no more than a ‘fair rate of return’ set by the regulator The firm maximizes its profit under this constraint The problem with this type of regulation is that the firm has the incentive to inflate the

base on which the rate of return is calculated (the so-called Averch–Johnson effect ) For

example, it might substitute more expensive capital for labour, even when this does not minimize its production cost In other words, production can be inefficient because of an inefficient choice of inputs However, this might not be bad for the overall efficiency It can be shown that under rate of return regulation the producer produces more output than

he would do if he were unregulated Since it is the monopolist’s reduced level of output (compared with the output under perfect competition) that causes a reduction in social welfare below its maximum, rate of return regulation does improve social welfare

13.2.2 Subsidy Mechanisms

Price subsidies and taxes can be used to control the point at which the economy of monopoly producer and the consumers lies The goals are to maximize overall efficiency and redistribute the profits of the monopolist

The complete information case The easiest case is that of full information, in which the

regulator knows the consumers’ demand curve and the cost function of the firm In this case, a simple policy is to subsidize part of the price set by the firm so that the price seen by the customers are marginal cost prices at the socially optimum production and consumption level of the economy Then the firm is made to pay a lump-sum tax equal to its profits

at this level Clearly, this strategy maximizes social welfare and reduces the monopolist’s

profit to zero More precisely, let p M and p MC be the monopolist price and the marginal

cost price at the levels of output x M and xŁ, that maximize respectively the monopolist

profit and the social welfare Note that p M > p MC Initially, the monopolist chooses price

p M and has profits

p M x Mc x M/ Assume that the monopolist’s cost function has decreasing marginal cost Then the regulator

returns to each user an amount p Mp MCfor every unit purchased, and this makes demand

rise to the desired point xŁ This increase in demand is welcomed by the monopolist who

sees his profits rise even further To see this, observe that as the derivative of c.x/ is decreasing in x,

p M ½ marginal cost at x M ½ c xŁ/  c.x M/

xŁx M

Hence

p M xŁc xŁ/ ½ p M x Mc x M/

Now, the regulator exacts from the monopolist a one-time lump-sum tax equal to his

profits p M xŁc xŁ/ Clearly, the monopolist can only continue producing xŁ, for zero

profit If he chooses any other production level or price (i.e p M) he will suffer a loss

The total surplus subsidy mechanism A problem with the above strategy is that to

compute the right price subsidy one must know the cost function of the monopolist This

is not required with the following simple mechanism The regulator only need know the demand curve only, which is often possible The mechanism generalizes the approach of Section 13.1, using an incentive payment like (13.4), in which

ž the monopolist is allowed to set prices and collect the resulting revenue, and

ž the regulator pays the monopolist the entire consumer surplus in the form of a subsidy

Recall that the consumer surplus at consumption level x, given monopolist price p x/, is

CS.x/ D

Z x

0

p y/ dy  p.x/x and so can be calculated knowing only the demand curve p y/.

The reason that this mechanism induces social optimality is that the monopolist eventually receives all the social welfare (namely, the sum of the producer’s profit and the consumer surplus); thus, his rational choice is to set prices that induce the socially optimum production level

METHODS OF REGULATION 299

The problem is that the consumers have no surplus A remedy would be to auction, as in

(13.4), the maximum amount F that a monopolist would be willing to pay as a lump-sum

to participate in this market Since the cost function is not known, the maximum value of

F is unknown If competing firms have different cost functions, the one with the lowest

cost would win, and make a profit equal to the difference between its cost and the cost of the competitor with the next lowest cost The mechanism that follows remedies some of the above problems

The incremental surplus subsidy mechanism Unlike those previously described, this

mechanism does not work in one step Although it assumes explicit knowledge of the cost function of the firm, it observes the responses of the firm over time to incentives provided by the regulator, and by adapting to the firm’s behaviour eventually settles on the socially optimal operating point, with zero profits for the monopolist It is an improvement

of the average price regulation mechanism that we will briefly mention in Section 13.2.3

In just two rounds, this mechanism achieves output efficiency, zero monopolist profits and

cost minimization This latter is key since it provides the incentives to the firm to operate

as efficiently as possible, without the presence of actual competition

Assume that time is divided in periods, t D 1; 2; : : : , and in each period the demand and the cost are the same At the end of period t, the regulator observes the current and

the previous unit price or quantity sold, the expenditure of the firm in the previous period

E t1(taken from the firm’s accounting records), and infers the previous accounting profits

³t1 D p t1 x t1E t1 As in the previous section, we suppose the regulator can also calculate the consumer surplus Knowing this, the regulator

ž pays the monopolist a subsidy equal to the incremental change in consumer surplus between periods t  1 and t, and

ž takes in tax the previous accounting profit ³t1

To model the fact that the firm might not operate under minimum cost, we suppose that

during period t the accounted expenses of the firm are E t D c t Cwt , where c t is the actual operating cost and wt ½ 0 is a discrepancy between the actual operating cost and the one declared through the accounting records Then the actual profits are O³t D³tCwt

Let W x/ denote the social welfare when the output level is x Given all the above, the producer makes a profit in period t of

³tCý

CS.xt /  CS.x t1/³t1

D³tC

²

[W x t/  O³t ]  [W x t1/  O³t1]

¦

³t1

D³tC

²

[W x t/  ³tCwt /]  [W.x t1/  ³t1Cwt1/]

¦

³t1

DW x t /  W.x t1/  wt Cwt1

Summing over periods t D 2; : : : ; −, we obtain W.x−/  w−W x1/ C w1, and see that for all− ½ 2 the monopolist maximizes his total accumulated profit to time − by choosing x−

to maximize the social welfare W x−/, and truly declaring his actual costs, so that w− D0 Notice that once he does this, his profit in period− is 0, for all − > 2 Maximizing social welfare at time− provides the incentive to operate as efficiently as possible, i.e to choose

the smallest possible function c.x t/

13.2.3 Price Regulation Mechanisms

Price regulation mechanisms are those that directly control the monopolist’s prices The general idea is that the regulator specifies a set of constraints on the firm’s prices (called

price caps), which are defined relative to a reference price vector The firm is free to set any

prices that satisfy these constraints The aim in that (a) the social surplus increases relative

to the reference set of prices, and (b) the firms have incentives to improve production efficiency Various schemes have been devised They differ in respect of the information that they require and the dynamics of the resulting prices movements

A simple scheme, called regulation with fixed weights, requires that prices be chosen

from the set

n

p :P

i p i q i p0/ Pi p i0q i p0/o (13.5)

where p0 is the reference price vector and p is the new price vector Observe that since the customers can always buy the old quantity q.p0/ under the new prices and pay less, the new price vector can only increase consumer surplus The weakness of the scheme

lies in the choice of an appropriate reference price vector p0 and in the ability to estimate

accurately the demand q p0/

An alternative is dynamic price-cap regulation The regulator observes the prices and the corresponding demand during period t  1, and controls the prices for period t to lie

in the set

n

p t :P

i p t i q i t1P

i p i t1 q i t1

o

(13.6)

This simple variant of (13.5) is called tariff-basket regulation and has a number of desirable

properties First, the consumer surplus is nondecreasing, and it can be shown that under reasonable assumptions and constant production costs the prices converge to Ramsey prices Secondly, the decoupling of prices from cost provides the firm with an incentive to increase its productive efficiency However, the lack of connection with cost means that the scheme

is not robust; if the firm can change its costs then there can be divergence from marginal cost and the firm may obtain greater profits One way to further increase the incentive to reduce costs is to multiply the right-hand side of (13.6) by a coefficient .1  X/, where 100X % is the intended percentage increase in production efficiency.

In another dynamic price-cap mechanism, due to Vogelsang and Finsinger, the regulator

assumes knowledge of the quantity q t1 produced in t  1 and of the resulting cost to the firm, c.q t1/ Then he insists that prices be chosen from the set

n

p t :P

i p i t q i t1c q t1/o (13.7)

In the case of firms with increasing economies of scale, and which chooses price myopically (that is, to optimize (13.7) at every step), prices under this scheme converge to Ramsey prices and push the profits of the firm to zero However, the scheme provides an incentive for nonmyopic firms to inflate temporarily their costs of production, since this allows for greater prices in the future This can lead to an undesirable reduction in social welfare Economists have found ways to combine various aspects of the above schemes, to improve them and remedy their shortcomings

A simpler mechanism, which involves less information, is average revenue regulation,

in which prices are chosen from the set

n

p t :P

i p t i q i t1.1  X/ NpPi q i t1o

(13.8)