Frank Cowell Microeconomics September 2006 Market Power and
Frank Cowell: Microeconomics September 2006 Market Power and Misrepresentation MICROECONOMICS Principles and Analysis Frank Cowell
Frank Cowell: Microeconomics Introduction n n Presentation concerns trading behaviour Context is an exchange economy u u n n Use a standard modelling framework Endow traders with different degrees of power u n n usual focus is on simple price-taking but we will examine non-competitive behaviour captured in the trading rules Extend this to a simple model of manipulation and design Begin with a simple analysis of nonlinear prices
Overview. . . Frank Cowell: Microeconomics Market Power and Misrepresentation Market power Nonlinear price systems Exchange and monopoly Misinformation
Frank Cowell: Microeconomics The setting n n n Consider an exchange economy Suppose one agent has extended monopoly power Can charge a fee for the right to access good 1 u u u n n this can only work for goods where resale is difficult otherwise consumers can undermine the fee by bulk-buying and selling on the commodity to others sometimes public utilities fit this paradigm Assume that any other trader acts as a price taker Analyse this within the context of the Edgeworth box
Frank Cowell: Microeconomics The model n n Two goods (1, 2) and two traders (Alf, Bill) Given resource distribution u u n Trading outcomes described by allocation u u u n vector of consumptions Alf: [x 1 a, x 2 a] Bill: [x 1 b, x 2 b] Use good 2 as numéraire u n endowments of two goods are such that Bill owns all good 1 Alf: [R 1 a, R 2 a] = [0, R 2 a] Bill: [R 1 b, R 2 b] = [R 1, R 2 b] R 2 : = R 2 a + R 2 b price of good 1 is p : = p 1/p 2 Assume materials balance condition satisfied with equality u u u x 1 a + x 1 b = R 1 x 2 a + x 2 b = R 2 permits use of the Edgeworth box diagram
Frank Cowell: Microeconomics Market power n Suppose Bill has the power to set u u n n Then Bill can fix a budget constraint for Alf anywhere in the diagram… … subject to one important condition u u n We return to this in a moment It has to do with the trading rules Bill’s control over the budget constraint: u u n the price p and the entry fee F p fixes the slope; F fixes the position In effect Bill has the power to set a non-linear price system u u the pair (p, F) examine how this works:
The “two-part” tariff Frank Cowell: Microeconomics b x 1 a §The endowment point §Fixed charge x 2 l [R] §Price per unit F p b x 2 0 a a x 1
Changing the budget constraint. . . Frank Cowell: Microeconomics b x 1 a x 2 l [R] §Varying F §Varying p b x 2 0 a a x 1
Key condition Frank Cowell: Microeconomics n n Bill nearly has total control over Alf However, one thing remains in Alf’s power: u u n n This condition effectively constrains Bill’s action Draw Alf’s indifference curve through the endowment point u u n n Alf does not have to consume good 1 Can just consume his endowment [R 1 a , R 2 a ] Alf’s reservation indifference curve Cannot be forced to trade at an allocation with lower level of utility This is the boundary of Bill’s attainable set Begin with case where Bill considers goods perfect substitutes
Exploitation solution Frank Cowell: Microeconomics b x 1 a §A’s indifference curves §Endowment point x 2 l [R] §A’s reservation indifference curve §B’s constraint set §B’s indifference curves §The solution §Entry fee and price F l [xa] p b x 2 0 a a x 1
Solution works in general case Frank Cowell: Microeconomics b x 1 a §Basic model as before §B’s indifference curves §Solution as before x 2 l [R] F l [xa] p b x 2 0 a a x 1
Full market power: the result Frank Cowell: Microeconomics n Bill has maximal power in market for good 1 u u n Outcome is full exploitation u u n trading partner is forced to reserve indifference curve solution allocation [xa] is on indifference curve through [R] But it is efficient u u n can use a nonlinear pricing scheme sets price ratio and entry fee to market for good 1 at [xa] MRS is is the same for both traders… … so it is on the contract curve Solution applies for general form of Bill’s preferences
Overview. . . Frank Cowell: Microeconomics Market Power and Misrepresentation Market power Power play in the Edgeworth box Exchange and monopoly Misinformation
Using the idea of market power Frank Cowell: Microeconomics n We have characterised market power in a simplified case u u n Now use this model u u n Bill a had built-in monopolistic advantage also endowed with complete market power apply this to a number of trading stories again in a simplified world Address some key questions u u How related to competitive outcomes? Under what circumstances will we get an efficient outcome?
Frank Cowell: Microeconomics Trading: alternative stories n A case with simplified property distribution u u n Review the standard equilibrium concepts u u n the core competitive equilibrium Examine two polar cases u u n Bill has all of commodity 1 Alf has all of commodity 2 Bill has complete market power (i. e. can choose point in A’s acceptance set) Alf has complete market power Then consider limited market power u Alf can act as a simple monopolist
Trading and competition Frank Cowell: Microeconomics b [R] x 1 §A’s indifference curves b 0 l §B’s indifference curves a x 2 §The contract curve §Endowment point §Trades acceptable to A&B §The core §CE and prices l [x*] p* b x 2 0 a a x 1
Bill has total market power Frank Cowell: Microeconomics b [R] x 1 §Competitive equilibrium b 0 l §B’s opportunity set given market power a x 2 §B’s optimal allocation §A nonlinear schedule to implement it l [x*] l [xa] b x 2 0 a a x 1
Alf has total market power Frank Cowell: Microeconomics b [R] x 1 §A’s opportunity set given 0 b market power l a x 2 §A’s optimal allocation l [xb] §A nonlinear schedule to implement it l [x*] b x 2 0 a a x 1
Simple monopoly Frank Cowell: Microeconomics n The three stories have a common element u u n Now consider a story with less than complete market power u u n characterise three points in the core all stories have efficient outcomes Alf can simply set the price Bill acts as price taker Rework the diagram u u u first map out Alf’s attainable allocations then characterise optimum… …conditional on this restricted-power model
Alf can set prices Frank Cowell: Microeconomics b [R] x 1 0 b § B’s preferences § Endowment § A tries out alternative prices §B’s reaction function §A’s attainable set l a x 2 l l b x 2 l 0 a a x 1
Monopoly trading Frank Cowell: Microeconomics b [R] x 1 0 b § A’s preferences l a x 2 l [xb] ^ l [x] ^p § Efficient allocations (contract curve) § A’s monopolistic optimum § MRS and prices at optimum §Competitive equilibrium §A’s total market power solution l [x*] b x 2 0 a a x 1
Summary of market power model Frank Cowell: Microeconomics n n n Suppose Alf has market power Gets higher utility than in CE Gets higher utility if has total market power than as simple monopolist CE and total market power are efficient Simple monopoly is inefficient u u price = Alf’s MRS price ≠ Bill’s MRS
Overview. . . Frank Cowell: Microeconomics Market Power and Misrepresentation Market power Applying the simple monopoly model Exchange and monopoly Misinformation
Frank Cowell: Microeconomics Misrepresentation n n The standard exchange model tells a simple story But relies on strong informational assumption u u n Use the same model as the market power example u u n n Each trader has full information about the other’s preferences What happens if we drop this? Take the case where Alf owns good 2 Bill owns good 1 Start from case of perfect information Then suppose that Alf misrepresents preferences u Bill continues to reveals full information
Misrepresentation and distortion Frank Cowell: Microeconomics b [R] x 1 §A’s trueb. ICs 0 l §B’s true ICs a x 2 §The contract curve §Endowment point & core §CE allocation and prices ^ l [x] §A’s false IC ^ p l §Induced equilibrium with A’s misrepresentation [x*] p* b x 2 0 a a x 1
Misrepresentation: outcome Frank Cowell: Microeconomics n The equilibrium has been seen before u u n Opportunity to masquerade induces a distortion u u n trader with informational advantage forces price in his favour in this case: price ratio = MRSa ≠ MRSb Bilateral trading is manipulable u u n version with Alf’s misrepresented preferences… …same that for a simple monopolist by revealing false preferences… …Alf secures higher utility for himself What if both can misrepresent? u outcome is still likely to be inefficient…
Misrepresentation and distortion (2) Frank Cowell: Microeconomics b [R] x 1 §True indifference curves 0 b §The contract curve & core l a x 2 §CE allocation and prices l §A’s false ICs §Equilibrium if only A misrepresents ~ ^ [x] l [x] §B’s false IC p^ l §Possible outcome if both misrepresent [x*] p* b x 2 0 a a x 1
Application Frank Cowell: Microeconomics n Consider a model of international trade u u n Price ratio is terms of trade u u n n Alfaland exports good 2 Billestan exports good 1 if one country can impose a tariff …get inefficient (monopoly) outcome if other country retaliates with its own tariff …outcome may still be inefficient Same outcomes could arise if each country can misrepresent preferences of its citizens Could design an efficient outcome if use nonlinear prices u u Alfaland demands payment F for access to market for good 2 …or vice versa for Billestan and good 1
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