Market Power and Misrepresentation

1. Market Power and Misrepresentation MICROECONOMICS Principles and Analysis Frank Cowell September 2006

2. Introduction • Presentation concerns trading behaviour • Context is an exchange economy • usual focus is on simple price-taking • but we will examine non-competitive behaviour • Use a standard modelling framework • Endow traders with different degrees of power • captured in the trading rules • Extend this to a simple model of manipulation and design • Begin with a simple analysis of nonlinear prices

3. Overview... Market Power and Misrepresentation Market power Nonlinear price systems Exchange and monopoly Misinformation

4. The setting • Consider an exchange economy • Suppose one agent has extended monopoly power • Can charge a fee for the right to access good 1 • 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

5. The model • Two goods (1,2) and two traders (Alf, Bill) • Given resource distribution • endowments of two goods are such that Bill owns all good 1 • Alf: [R1a, R2a] = [0, R2a] • Bill: [R1b, R2b] = [R1, R2b] • R2 :=R2a + R2b • Trading outcomes described by allocation • vector of consumptions • Alf: [x1a, x2a] • Bill: [x1b, x2b] • Use good 2 as numéraire • price of good 1 is p := p1/p2 • Assume materials balance condition satisfied with equality • x1a + x1b =R1 • x2a + x2b =R2 • permits use of the Edgeworth box diagram

6. Market power • Suppose Bill has the power to set • the price p • and the entry fee F • Then Bill can fix a budget constraint for Alf anywhere in the diagram… • … subject to one important condition • We return to this in a moment • It has to do with the trading rules • Bill’s control over the budget constraint: • p fixesthe slope; • F fixes the position • In effect Bill has the power to set a non-linear price system • the pair (p, F) • examine how this works:

7. b x1 a x2 b x2 a x1 The “two-part” tariff • The endowment point • Fixed charge • [R] • Price per unit F p 0a

8. b x1 a x2 b x2 0a a x1 Changing the budget constraint... • Varying F • Varying p • [R]

9. Key condition • Bill nearly has total control over Alf • However, one thing remains in Alf’s power: • Alf does not have to consume good 1 • Can just consume his endowment [R1a, R2a] • This condition effectively constrains Bill’s action • Draw Alf’s indifference curve through the endowment point • 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

10. b x1 a x2 b x2 a x1 Exploitation solution • A’s indifference curves • Endowment point • [R] • A’s reservation indifference curve F • B’s constraint set • B’s indifference curves • The solution • Entry fee and price • [xa] p 0a

11. b x1 a x2 b x2 a x1 Solution works in general case • Basic model as before • B’s indifference curves • [R] • Solution as before F • [xa] p 0a

12. Full market power: the result • Bill has maximal power in market for good 1 • can use a nonlinear pricing scheme • sets price ratio and entry fee to market for good 1 • Outcome is full exploitation • trading partner is forced to reserve indifference curve • solution allocation [xa] is on indifference curve through [R] • But it is efficient • 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

13. Overview... Market Power and Misrepresentation Market power Power play in the Edgeworth box Exchange and monopoly Misinformation

14. Using the idea of market power • We have characterised market power in a simplified case • Bill a had built-in monopolistic advantage • also endowed with complete market power • Now use this model • apply this to a number of trading stories • again in a simplified world • Address some key questions • How related to competitive outcomes? • Under what circumstances will we get an efficient outcome?

15. Trading: alternative stories • A case with simplified property distribution • Bill has all of commodity 1 • Alf has all of commodity 2 • Review the standard equilibrium concepts • the core • competitive equilibrium • Examine two polar cases • 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 • Alf can act as a simple monopolist

16. b x1 a x2 b x2 a x1 Trading and competition • A’s indifference curves [R] 0b • B’s indifference curves • The contract curve • Endowment point • Trades acceptable to A&B • The core • CE and prices • [x*] p* 0a

17. b x1 a x2 b x2 a x1 Bill has total market power • Competitive equilibrium [R] 0b • B’s opportunity set given market power • B’s optimal allocation • A nonlinear schedule to implement it • [x*] • [xa] 0a

18. b x1 a x2 b x2 a x1 Alf has total market power • A’s opportunity set given market power [R] 0b • A’s optimal allocation • A nonlinear schedule to implement it [xb] • [x*] 0a

19. Simple monopoly • The three stories have a common element • characterise three points in the core • all stories have efficient outcomes • Now consider a story with less than complete market power • Alf can simply set the price • Bill acts as price taker • Rework the diagram • first map out Alf’s attainable allocations • then characterise optimum… • …conditional on this restricted-power model

20. b x1 Alf can set prices • B’s preferences 0b [R] • Endowment a x2 • A tries out alternative prices • B’s reaction function • A’s attainable set b x2 0a a x1

21. b x1 Monopoly trading • A’s preferences 0b [R] • Efficient allocations (contract curve) a x2 • A’s monopolistic optimum • [xb] • MRS and prices at optimum ^ • [x] • Competitive equilibrium • A’s total market power solution p ^ • [x*] b x2 0a a x1

22. Summary of market power model • 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 • price = Alf’s MRS • price ≠ Bill’s MRS

23. Overview... Market Power and Misrepresentation Market power Applying the simple monopoly model Exchange and monopoly Misinformation

24. Misrepresentation • The standard exchange model tells a simple story • But relies on strong informational assumption • Each trader has full information about the other’s preferences • What happens if we drop this? • Use the same model as the market power example • Take the case where Alf owns good 2 • Bill owns good 1 • Start from case of perfect information • Then suppose that Alf misrepresents preferences • Bill continues to reveals full information

25. b x1 a x2 • [x] ^ b x2 a x1 Misrepresentation and distortion • A’s true ICs [R] 0b • B’s true ICs • The contract curve • Endowment point & core • CE allocation and prices • A’s false IC • Induced equilibrium with A’s misrepresentation p ^ • [x*] p* 0a

26. Misrepresentation: outcome • The equilibrium has been seen before • version with Alf’s misrepresented preferences… • …same that for a simple monopolist • Opportunity to masquerade induces a distortion • trader with informational advantage forces price in his favour • in this case: price ratio = MRSa≠ MRSb • Bilateral trading is manipulable • by revealing false preferences… • …Alf secures higher utility for himself • What if both can misrepresent? • outcome is still likely to be inefficient…

27. b x1 a x2 ~ • [x] • [x] ^ p ^ b x2 a x1 Misrepresentation and distortion (2) • True indifference curves [R] 0b • The contract curve & core • CE allocation and prices • A’s false ICs • Equilibrium if only A misrepresents • B’s false IC • Possible outcome if both misrepresent • [x*] p* 0a

28. Application • Consider a model of international trade • Alfaland exports good 2 • Billestan exports good 1 • Price ratio is terms of trade • 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 • Alfaland demands payment F for access to market for good 2 • …or vice versa for Billestan and good 1