1. monopoly market power and market failures

Prof. Carlo Cambinicarlo.cambini@polito.it

Monopoly, Market Power and Market Failures

Review of Perfect Competition

Large number of buyers and sellersHomogenous productPerfect informationFirm is a price takerSolution

P = (L)MC = (LR)ACNormal profits or zero economic profits in the long run

Review of Perfect Competition

Microeconomics: a review

Individual demand: consumer behavior

Under the local nonsatiation assumption, the optimalconsumer demanded bundle of goods (i = 1, .., n) is given bythe following problem:

where p is the vector of market prices and m the income levelof the consumer.v(p, m) is the maximum utility achievable at given prices and income and is called indirect utility function. The optimal x(p, m) is therefore the consumer’s demand function.

xumpvx

)(max),(

The Lagrangian for the Utility maximization problemcan be written as:

The FOC is given by:

And it can be re-elaborated as:

)()( mpxxuL −−= λ

nipxxu

,...1for 0)(==−

∂∂ λ

i ,...1,for *)(

⎟⎟⎠

⎞⎜⎜⎝

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

The indirect utility, i.e. the maximum utility asa function of p and m has the followingproperties:

It is non increasing in p, that is if p’ ≥ p, thenv(p’, m) ≤ v(p, m). Similarly, v(.,.) is non decreasing in m.It is continuous and quasi-convex

The quasi-linear utility function

Partial equilibrium analysis: analyse the market functioning of a “good” that has a relatively low weighton the global economy.Hence, we can introduce two simplifying assumptions:

1. the impact of a change in consumers’ income on the expenditure of the “good” is limited (no income effect);2. the substitution effect on the other goods is small too.

The prices of the rest of goods can then be consideredas fixed and we can be assume them as a numeraire, normalised to 1.We can then simplify our utility function in the followingway (yi is the “rest of goods”, i.e. the numeraire):

yxuyxU += )(),(

The quasi-linear utility function

u(xi) is a continuous, increasing, twice-differentiable, and convex function.The optimization problem becomes:

This leads to the following optimal condition:

mypxtsyxuyxU

..)(),(

=−=∂∂

=−∂

∂∂

pxuxxu

=′=∂

∂ )()(

Surplus: a review

Consumer surplus is the total benefit or value that consumers receive beyond what they pay for the good

Producer surplus is the total benefit or revenue that producers receive beyond what it costs to produce a good

Consumer and Producer Surplus

Between 0 and Q0producers receive

a net gain from selling each product--

producer surplus.

ConsumerSurplus

Quantity

Between 0 and Q0 consumer A receives

a net gain from buying the product--

consumer surplus.ProducerSurplus

Marginal effects of a price/quantitychanges on Consumer Surplus

Consumer surplus, as a function of price, is given by:

Hence, it results:

Intutition: the demand has a negative slope, the minusis needed to have a positve quantity

∫∞

dppqpVCS

)()( pqdp

pdV−=

Marginal effects of a price/quantitychanges on Consumer Surplus

Consumer surplus, as a function of quantity, is given by:

Hence, it results:

0)( where

dqqpS(q)

qqpqSCS

)()( qpdq

Perfect competition and Welfare

Welfare economicsWhat are the welfare properties of the perfectcompetitive equalibrium?The representative consumer approach: suppose that the market demand, x(p), is generated bymaximizing the utility of a single representativeconsumer who has a quasi linear utility function u(x)+y, where x is the good under examination and y “everything else”.Under this utility function, we know that:Hence, the direct demand function x(p) is simply the inverse of the above conditionNote that in case of a quasi-linear utility the demandfunction is independent of income!!

pxu =′ )(

Welfare economicsConsider now a representative firm having a costfunction c(x), with c’ > 0, c’’ > 0 and c(0) = 0.In a perfect competitive market, the profit maximizing(inverse) supply function of a representative firm isgiven by p = c’(x).Hence, the equilibrium level of output of the x-good issimply the solution to the equation:

This is the level of output at which the marginalwillingness to pay for the x-good just equals its marginalcost of production.

)()( xcxu ′=′

Welfare analysisWhat is the optimal amount of output that maximizes the representative consumer’s utility?Let w be the consumer’s initial endowment of the y-good. The consumer’s problem is:

Intuition: the welfare maximizing problem is simply to maximizetotal utility consuming x-good and y-goods. Since x units of the x-good means giving up – in a competitive market - c(x) units of the y-good, our social objective function becomes:

The Foc is given by (as before):

The competitive market results in exactly the same level of production and consumption as does maximizing utility directly.

)(max,

xcwyts

)()(max,

xcwxuyx

)()( xcxu ′=′

Welfare analysis

Another way to look at the same problem.Let CS(x) = u(x) - px be the consumer’s surplus and PS(x) = px – c(x) be the producer’s surplus.The total surplus, or welfare, is:

We can conclude saying that the competitive equilibriumlevel of output maximizes total surplus!

[ ])()(

)()(max

xcxuxcpxpxxu

xPSxCSWx

−==−+−=

Welfare analysis: a generalization

Suppose there are i = 1,, n consumers and j = 1,…,m firms. Each consumer has a quasi-linear utility functionui(xi)+yi and each (perfectly competitive) firm has a costfunction cj(xj).An allocation describes how much each consumer consumers of x-good and the y-good, (xi, yi), i = 1,, n, and how much the firm produces of the x-good, zj, j = 1,…,m .The initial endowment of each consumer is taken to besome given amount of the y-good and 0 of the x-good.The sum of utilities is given by:

∑ ∑= =

iiii yxu

The total amount of the y-good is the sum of initial endowments, minus the amount used up in production:

Observing that the total amount of the x-goodproduced must equal the total amountconsumed, we have

∑∑∑===

ii zcwy

∑∑

∑∑∑

zcwxuji

)()(max

Let λ the Lagrangian multiplier on the constraint, we have

where p* = λ since the market is perfectlycompetitive!Hence, market equilibrium necessarilymaximizes welfare for a given pattern of initialendowments (wi).

)(')('

Consumer Equilibrium in a Competitive Market

First Theorem of Welfare EconomicsIf everyone trades in a competitive marketplace, all mutually beneficial trades will be completed and the resulting equilibrium allocation of resources will be economically efficientWelfare economics involves the normative evaluation of markets and economic policy

Pareto OptimalityAn outcome is Pareto optimal if it is not possibleto make one person better off without makingone another worse offIf this is possbile, we face a potential Paretoimprovement (PPI)The adoption of the PPI criterion means that wecan focus on what happens to total surplus.Hence an outcome that maximizes total surplus is Pareto optimal.

Difficult for efficient allocation with many consumers and producers unless all markets are perfectly competitiveEfficient outcomes can also be achieved by centralized systemCompetitive outcome preferred since consumers and producers can better assess their preferences and supplies

Equity and Efficiency

Although there are many efficient allocations, some may be more fair than othersThe difficult question is, what is the most equitable allocation?We can show that there is no reason to believe that efficient allocation from competitive markets will give an equitable allocation

Equity and Perfect Competition

Must a society that wants to be more equitable necessarily operate in an inefficient world?

Second Theorem of Welfare EconomicsIf individual preferences are convex, then

every efficient allocation is a competitive equilibrium for some initial allocation of

Equity and Perfect Competition

Any equilibrium that is equitable can be achieved by redistributing resources and may be efficientTypical ways to redistribute goods, however, are costly

Taxes lead to bad incentivesFirms devote fewer resources to production in order to avoid taxesEncourage individuals to work less

Market Failures

Why Markets Fail

Market PowerThose with market power choose the price and quantityLess output is sold than in competitive marketsInefficiencyCan have market power as producers or as inputs

Why Markets Fail

ExternalitiesMarket prices do not always reflect the activities of either producers or consumersConsumption or production has indirect effect on other consumption or production not reflected in market pricesMay be impossible to get insurance because suppliers of insurance lack information

Why Markets Fail

Public GoodsNonexclusive, nonrival goods that can be made available cheaply but which, once available, are difficult to prevent others from consumingCompany thinking about researching a new technology if can’t get patent

Once it’s made pubic, others can duplicate it

Why Markets Fail

Incomplete InformationConsumers must have accurate information about market prices or production quality for markets to operate efficientlyLack of information can change supply

Buy products with no valueDon’t buy enough of products with value

Some markets may never develop

Market Failures

Economic motivationsExistence of market power (monopoly, natural monopoly, collusive oligopoly) Externality (positive or negative)Market incompleteness (asymmetric information)

Social motivations:Redistributive concerns (urban to rural areas; rich to poor citizens)Merit goods (essential services should be provided to everybody at affordable prices)

⇒ need of State policy in the form of ex ante (regulation) or ex post (antitrust) interventions

Monopoly

Monopoly1. One seller - many buyers2. One product (no good substitutes)3. Barriers to entry4. Price Maker

Monopolist’s Output Decision

1. Profits maximized at the output level where MR = MC

2. Cost functions are the same

MRMCorMRMCQCQRQ

=−==ΔΔ−ΔΔ=ΔΔ

−=0///

)()()(π

Lostprofit

Quantity

$ perunit ofoutput

D = AR

Monopolist’s Output Decision

1. Profits maximized at the output level where MR = MC

2. Cost functions are the same

⎟⎟⎠

⎞⎜⎜⎝

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ

⎟⎠⎞

⎜⎝⎛+=

DEPPMR

QPQPMR

Equilibrium Pricing

MC MR wheremaximized is

MCE PP

=⎥⎦⎤

⎢⎣⎡+

Elasticity of Demand and Price Markup

Quantity

The more elastic isdemand, the less the

markup.

Quantity

P*P*-MC

Measuring Monopoly PowerCould measure monopoly power by the extent to which price is greater than MC for each firmLerner’s Index of Monopoly Power

L = (P - MC)/PThe larger the value of L (between 0 and 1) the greater the monopoly power

L is expressed in terms of Ed

L = (P - MC)/P = 1/Ed

Ed is elasticity of demand for a firm, not the market

Monopoly Power

Pure monopoly is rareHowever, a market with several firms, each facing a downward sloping demand curve, will produce so that price exceeds marginal costFirms often product similar goods that have some differences, thereby differentiating themselves from other firms

Sources of Monopoly Power

Why do some firms have considerable monopoly power, and others have little or none?Monopoly power is determined by ability to set price higher than marginal costA firm’s monopoly power, therefore, is determined by the firm’s elasticity of demand

Sources of Monopoly Power

The less elastic the demand curve, the more monopoly power a firm hasThe firm’s elasticity of demand is determined by:1) Elasticity of market demand2) Number of firms in market: entry barriers and entry deterrence3) Strategic behaviour by incumbent4) New Technology

Elasticity of Market Demand

With one firm, their demand curve is market demand curve

Degree of monopoly power is determined completely by elasticity of market demand (ex. OPEC)The presence of alternative suppliers or substitute products reduces market power (supply and demand side substitution)

With more firms, individual demand may differ from market demand

Demand for a firm’s product is more elastic than the market elasticity

Demand elasticity in telecoms under a Monopoly: evidence from Italy

Dependent Variable Price Income SIP (1988) National calls –0,12 0,5-0,9 Cappuccio (1990)

Revenues from calls (annual base 1973)

–0,11 0,52

Gambardella (1991)

Revenues from calls (annual base 1964)

–0,35 0,25

Ravazzi (1991) Membership –0,1 0,3 Mosconi (1994) e Colombino (1998)

Urban calls National calls International calls

–0,19 –0,25 –0,52

Demand elasticity in telecoms under Monopoly: evidence from US

Bodnar et al. (1988)

Taylor e Kridel (1990)

Dimension

(000 Price

Elasticity

Economic Position

Price Elasticity

of inhabitants) > 500 –0,007 Poor and rural –0,071 100 – 500 –0,006 Poor and urban –0,077 30 – 100 –0,010 Poor black rural –0,089 < 30 –0,013 Rich white urban –0,026 Rurale –0,014 State Price Income

Age Elasticity Elasticity < 26 –0,024 Arkansas –0,059 – 26 – 44 –0,009 Kansas –0,023 – 45 – 64 –0,007 Missouri –0,031 – > 64 –0,008 Oklahoma –0,034 –

Income ($ 000)

Texas –0,037 –

< 12 –0,026 Average –0,037 0,042 12 – 20 –0,012 20 – 28 –0,006 28 – 38 –0,002 > 38 –0,0005

Number of Firms

The monopoly power of a firm falls as the number of firms increases; all else equal

More important are the number of firms with significant market shareMarket is highly concentrated if only a few firms account for most of the sales

Firms would like to create barriers to entry to keep new firms out of market

Patent, copyrights, licenses, economies of scale

Number of FirmsEntry barriers are of interest from two perspectives: (i) corporate strategy and (ii) public policy.Incumbents want to protect not only their market shares but also their profitsA key objective of corporate strategy is profitable entry deterrence.Profitable entry deterrence occurs when incumbent firms are able to earn monopoly profits without attracting entryProfitable entry deterrence depends on the interaction between structural entry barriers and incumbent’s behaviourPublic policy should aim at eliminating entry barriers and detect entry deterrence

Government Restrictions on Entry

Governments create entry barriers whenthey grant exclusive rights to produce toincumbent preventing additional entryForms of exclusive franchises:

Natural Monopoly;Source of revenues (from State ownedcompanies);Redistribute rents among citizens;Intellectual Property Rights (IPRs)

Structural Barriers to Entry

Structural characteristics that protect market power without attracting entry, such as:

Economies of scaleSunk expenditures of the entrantAbsolute cost advantage: incumbent may face lowercosts or a better access to existing facilities (i.e. the use of the network in the telecoms industry)Sunk expenditures by consumers and productdifferentiation:

If a consumer faces a large cost for switching to a new product, he could decide not to switch ⇒switching costs and creation of brand loyalty. Finally, consumer might not view the offerings of other firms as substitute.

Strategic behavior by Incumbents

Incumbents may behave in order to enhance barriers to entry to rivals.Potential strategies:

Aggressive postentry behavior: commit to be aggressive; ex. Investment in sunk capacityRaising rivals’ cost: raising cost of a potential entry or reducing the profitability of entryReducing rivals’ revenues: again reduce the profitability of entry increasing the consumers switching costs and so the market demand for the entrant

New Technology

Technological change can generate new products and services, and the introduction of these products reduces the market power of producers of established products.Nintendo in ’80 was a monopolist, but the monopoly ended after the entry by Sega … and later on by Sony (Playstation) and Microsoft (X Box)

The Social Costs of Monopoly Power

Monopoly power results in higher prices and lower quantitiesHowever, does monopoly power make consumers and producers in the aggregate better or worse off?From a social point of view, the effects of the monopolistic inefficiency can be appreciated if we look at the Marshall’s surplus

Monopoly Dead Weight Loss

The DWL area measures the surplus that could have been created with a competitive market, but goes loss due to level of the price which is fixed by the monopolist

The deadweight loss decreases with ED when the elasticity is large, but it vanishes when the demand is perfectly rigid, because in this case moving prices simply correspond to a surplus transfer between firms and consumers

The determinants of Deadweightloss

Assume constant marginal cost. The deadweight loss associated with a monopolypricing is approximately equal to:

DWL = 1/2dPdQ

It can rewritten as:

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

dPdPdPdQDWL

Since marginal cost is constant, dP = Pm-c, it results

Harnerger’s loss: the inefficiency of a monopoly isgreater the larger the elasticity of demand, the largerthe Lerner Index and the larger the industry(measured by industry revenues) … however L isinversely related to Ed

21 LQPEDWL mm

Since for a monopolisitc firm L = 1/Ed

Loss in the US long distance telecomsmarket: entrants of RBOC into the long distance market (mid 1990s) decreases the welfare loss by $2.78 billion

21 2 π

=⎟⎟⎠

⎞⎜⎜⎝

⎛ −== m

d PcPQPLQPEDWL

The Multi-plant Firm

For some firms, production takes place in more than one plant, each with different costsFirm must determine how to distribute production between both plants

1. Production should be split so that the MC in the plants is the same

2. Output is chosen where MR=MC. Profit is therefore maximized when MR=MC at each plant.

We can show this algebraically:Q1 and C1 is output and cost of production for Plant 1Q2 and C2 is output and cost of production for Plant 2QT = Q1 + Q2 is total outputProfit is then:

π = PQT – C1(Q1) – C2(Q2)

Firm should increase output from each plant until the additional profit from last unit produced at Plant 1 equals 0

MCMRMCMR

ΔΔπ

We can show the same for Plant 2Therefore, we can see that the firm should choose to produce where

MR = MC1 = MC2We can show this graphically

MR = MCT gives total outputThis point shows the MR for each firmWhere MR crosses MC1 and MC2 shows the output for each firm

Production with Two Plants

Quantity

D = AR

MC1 MC2

Q1 Q2 QT

Durable Goods Monopoly

A durable good is a good which providesa stream of sustained consumptionservices: it can be used more than once. Two complicating factors:

Monopoly creates it own competition! The existence of a second-hand market limits monopoly market powerThe price consumers are willing to pay todaydepends on the expectations about the price of the good tomorrow

Durable Goods Monopoly

Assume that the good last forever and so that it does not depreciate over time. Example: land

Competitive supply: the supply curve isfixed; supply and demand determine the equilibrium price for a lifetimeconsumption. Alternatively, the price can be transformed in ayearly rental price.

Durable good in perfect competition

Durable good in monopoly

The monopolist sets the marginal revenuesequal to the marginal cost (= 0) and determinethe first year consumption and price (Q1 and P1)In the second period, the monopolist faces a residual demand given by Qc – Q1 whereconsumers have a willingness to pay larger thanmarginal costs but lower than P1.In order to sell additional units of the good and use its stock, the monopolists cannot do betterthan reducing the price … up to the competitive price!

Durable good in monopoly

Durable goods: the Coaseconjecture

The monopolist has therefore the incentive to practice intertemporal price discrimination: it increases its profit decreasing prices over time.Initially, monopolist only supplies thoseconsumers having a high willingness topay.Then, the monopolist increases its profit by moving down the demand curve

Durable goods and strategic actions

Strategic consumers:Incentives to delay purchasing if they anticipate that the monopolist will lower prices in the future

Cost of waiting depends on the discount rate, i.e. on the actual cost of consumption tomorrow: the larger it is, the greater the preference of consumers for a dollar today asopposed to a dollar tomorrow.Assume that the adjusting period is very small and the discount rate equal to 0 (the discount factor is equal to 1): a durable goods monopolist has no monopoly power ifthe time between price adjustment is vanishingly small ⇒the Coase Conjecture

Durable goods and strategic actions

Strategies to mitigate the Coase Conjecture:Firms might convince consumers that prices do not decrese over time though

Leasing, since the good is returned to the firmInvestment in reputation not to increase supply (ex Disney movies)Limit capacityNew customers, i.e. expected increase in the demandPlanned obsolescence, decreasing the durability of itsgood, and so enhacing the demand tomorrow keepingthe price high!

Durable goods and Pacmaneconomics

Is it true that the monopoly always loose itsmarket power? No, it is the contrary, monopolycomes perfect since the firm can now extract allsurplus from consumers!Monopolistic firm only needs to move down the demand selling to consumers sequentially in order of their reservation prices : this is the Pacman StrategyThis results is more likely when the number of buyer is finite and the willigness to pay of consumers highly differs.

Durable goods: Coase vs. Pacman

Study by Von der Fehr and Kuhn (1996):When the number of buyers is very large and there are small differences in willingness topay, then Coase outcome is more likelywhen the number of buyer is finite and the willigness to pay of consumers highly differs, Pacman discriminatory outcome emerges.

Natural Monopoly and Government Intervention

The Social Costs of MonopolySocial cost of monopoly is likely to exceed the deadweight lossNo allocative efficiency, no incentive to minimize cost ⇒X-inefficiencyHicks’s statement: “The best of all monopoly profit is a quite life!!”Rent Seeking

Firms may spend to gain monopoly powerLobbyingAdvertisingBuilding excess capacity

Dynamic efficiency? Shumpeter vs. Arrow approach on the effect of the market structure on investment

The Social Costs of Monopoly

Government can regulate monopoly power through price regulation

Recall that in competitive markets, price regulation creates a deadweight lossPrice regulation can eliminate deadweight loss with a monopoly

Regulation vs. Competition policy

CP attempts to avoid situation where market power can be exploited; regulation deals with the situation.Prices/profits/quality are not usually explicitly controlled with CPRegulation specifies precise details of what firm can and cannot do (ex ante intervention); CP issues “guidelines” and uses precedent (ex post intervention)Typically have sector-specific regulators, and a generalist competition policy authority

Marginal revenue curvewhen price is regulatedto be no higher that P1.

If left alone, a monopolistproduces Qm and charges Pm.If price is lowered to P3 output

decreases and a shortage exists. For output levels above Q1 ,

the original average andmarginal revenue curves apply.

If price is lowered to PC outputincreases to its maximum QC and

there is no deadweight loss.

Price Regulation$/Q

Quantity

P2 = PC

Q3 Q’3

Any price below P4 resultsin the firm incurring a loss.

The Social Costs of Monopoly Power

Natural MonopolyA firm that can produce the entire output of an industry at a cost lower than what it would be if there were several firmsUsually arises when there are large economies of scaleWe can show that splitting the market into two firms results in higher AC for each firm than when only one firm was producing

Quantity

Setting the price at Prgiving profits as large as possible without going

out of business

If the price were regulate to be Pc,the firm would lose money

and go out of business. Can’t cover average costs

Unregulated, the monopolistwould produce Qm and

charge Pm.

Regulating the Price of a Natural Monopoly

Some definitions on Natural Monopoly

Single product contest: presence of economy of scale, i.e. ATC should bealways decreasingIs this definition sufficient also in a multiproduct setting? NOT AT ALL!!In a multiproduct setting, given a vector of quantities i = 1,.., n, the cost function C(.) should be sub additive, i.e.

Some definitions on Natural Monopoly

Sufficient conditions to have a naturalmonopoly in a multiproduct setting are:

Presence of economies of scope:C(q1,0) + C(0,q2) > C(q1,q2)

Average incremental costs should be decreasing(Baumol, Panzar and Willig, 1982)

where IC1(q1,q2)= C(q1,q2) - C(0,q2)C(0,q2) is the so called stand alone cost of product 2AIC = IC1(q1,q2)/q1

Questions that need to be addressed:

Whether (and how) to privatise?

Whether to break up monopoly (or allow mergers)? Structural regulation (vertical or horizontal separation)

Which parts of the industry to regulate?

Example: Telecommunications

Local telephony

Long distance telephony

International telephony

Internet

Mobile telephony

Natural monopoly

Example: Electricity market

Production and Import

National Transmission (high voltage)

Local transmission (low voltage

Final market

Natural Monopolies

Example: Gas industry

Production and Import

National transmission

Local transmission

Retail market

Natural monopolies

Reserve in stock

Conduct regulation: price control

First best pricing: price equal to marginalcost (as in a perfect competitive environment)

Public transfer to cover firm’s loss

Demo: consumers have a quasi-linear utility function Uh = Rh + Sh(p), such that

∂Uh/∂p = ∂Sh(p)/ ∂p (no revenueeffect)

In a monoproduct setting:Maxp W = S(p) – T + πwhere π = pq(p) + T - C(q) – FThus, W = S(p) + pq(p) - C(q) – FDeriving w.r.t. p, we get: p = C’(q)

In absence of any kind of transfer fromregulator to the firm, what could happen?The regulator should set prices in order tolet the firm reach its break even

Second best solution: price = ACThe average cost pricing rule

Conduct regulation: price controlFirm’s profit are zero, but there is always a deadweigh loss (squared area in figure)

Conduct regulation: price controlMultiproduct setting: practical methods, fullydistributed costs (FDC)Suppose to have a cost function:

Price equal marginal cost leads to losses. How to cover them?A rule to share the fixed cost F should bedefined by the regulator.

Conduct regulation: price controlFully distributed costs (FDC): price shouldcover not only direct (marginal) cost, but alsoa share of the fixed costs, i.e.

where fi is the so called cost driver:

⎪⎪⎪⎪

Method)Cost able(Attribuit if )(

Method)Output (Relative if )(

Method) Revenues (Gross if )(

Conduct regulation: price control/6It is easy to show that all the three methodsabove described leads to define a “equalmark up rule”.In fact:

Is this efficient?

Conduct regulation: price controlThe answer is NO!

A+B = Extra-revenues to cover fixed costC+D = deadweight loss!!

p’p’

A BC DA B

How to minimize deadweight loss?Mark up on prices should be different according tothe different demand structure of the goods:

Even if A’+B’ = A + B, C’+D’< C+D

A’ C’

Immagine that no public transfer could be used and εij = 0Regulator should set prices such that:Maxpi S(pi) + π s.t. π ≥ 0Denoting with λ the lagrangian multiplier of the constraint we have:L = S(pi) + (1+ λ)π = S(pi) + (1+ λ)(Σpiqi – C(qi))

What is λ? It can be interpreted as the shadow price of public funds.

Optimal second best solutions: Ramsey-Boiteaux Pricing rule

i.e. the price-cost margin (in percentage of price) should be inversely related to the price elasticity of demand:

cpLηλ

λ 11+

∂∂η −=

In general, we have:

If demands are interdependent (i.e. εij ≠ 0) .. Superelasticities (Laffont and Tirole, 1993)

Cross subsidization

In many Utilities, the price in some servicesare set lower than their marginal cost mainlyfor distributional concerns.Example: in Telecoms, USO implies thatprice for urban calls and the fixee fee have been set for long time below marginal cost, while long distance calls (national and international) have been set above costs in order to recoup the losses on other services.

Cross subsidization

Problem: cross subsitization could bestrategically used by the incumbentoperator in order to prevent entry in the market or to induce exit of new entrants.Potential anticompetitive behaviour: incumbent could set price above cost in the monopolistic segment of the market (i.e. Local telephony), in order to reduce its price in the more competitive ones (Long distance or Internet)

Cross subsidization

How to avoid or detect cross subsidization?

Faulhaber’s Test (1975).Two services (p1and p2).

I^ test on incremental cost:p1q1≥IC1(q1,q2)= C(q1,q2) - C(0,q2)p2q2≥IC2(q1,q2)= C(q1,q2) - C(q1,0)

Cross subsidization

II^ test on incremental cost:

p1q1 ≤ C(q1,0)p2q2 ≤ C(0,q2)

If the two tests have success, then retail tariffs are subsidy free. Otherwise, Incumbent could have set its tariffs anticompetitively, and so more scrutiny isneeded (from Competition or Regulatory Authority)

1. monopoly market power and market failures

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