# Frank Cowell: Microeconomics Market Power and Misrepresentation MICROECONOMICS Principles and Analysis Frank Cowell September 2006.

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Frank Cowell: Microeconomics Market Power and Misrepresentation MICROECONOMICS Principles and Analysis Frank Cowell September 2006

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

Frank Cowell: Microeconomics Overview... Market power Exchange and monopoly Misinformation Market Power and Misrepresentation Nonlinear price systems

Frank Cowell: Microeconomics The setting Consider an exchange economy Consider an exchange economy Suppose one agent has extended monopoly power Suppose one agent has extended monopoly power Can charge a fee for the right to access good 1 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 Assume that any other trader acts as a price taker Analyse this within the context of the Edgeworth box Analyse this within the context of the Edgeworth box

Frank Cowell: Microeconomics The model Two goods (1,2) and two traders (Alf, Bill) Two goods (1,2) and two traders (Alf, Bill) Given resource distribution Given resource distribution  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 Trading outcomes described by allocation Trading outcomes described by allocation  vector of consumptions  Alf: [x 1 a, x 2 a ]  Bill: [x 1 b, x 2 b ] Use good 2 as numéraire Use good 2 as numéraire  price of good 1 is p := p 1 /p 2 Assume materials balance condition satisfied with equality Assume materials balance condition satisfied with equality  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 Suppose Bill has the power to set 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… Then Bill can fix a budget constraint for Alf anywhere in the diagram… … subject to one important condition … 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: Bill’s control over the budget constraint:  p fixes the slope;  F fixes the position In effect Bill has the power to set a non-linear price system In effect Bill has the power to set a non-linear price system  the pair (p, F)  examine how this works:

Frank Cowell: Microeconomics x1x1 a x2x2 b x1x1 b x2x2 a 0a0a The “two-part” tariff   The endowment point   Price per unit F   Fixed charge p l l [R]

Frank Cowell: Microeconomics x1x1 a x2x2 b x1x1 b x2x2 a 0a0a Changing the budget constraint...   Varying F   Varying p l l [R]

Frank Cowell: Microeconomics Key condition Bill nearly has total control over Alf Bill nearly has total control over Alf However, one thing remains in Alf’s power: However, one thing remains in Alf’s power:  Alf does not have to consume good 1  Can just consume his endowment [R 1 a, R 2 a ] This condition effectively constrains Bill’s action This condition effectively constrains Bill’s action Draw Alf’s indifference curve through the endowment point 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 This is the boundary of Bill’s attainable set Begin with case where Bill considers goods perfect substitutes Begin with case where Bill considers goods perfect substitutes

Frank Cowell: Microeconomics Exploitation solution   A’s indifference curves   Endowment point   B’s constraint set   B’s indifference curves   The solution   Entry fee and price F p   A’s reservation indifference curve x1x1 a x2x2 b x1x1 b x2x2 a 0a0a l l [R] ll [xa]ll [xa]

Frank Cowell: Microeconomics Solution works in general case F p   Basic model as before   B’s indifference curves   Solution as before x1x1 b x1x1 a x2x2 a x2x2 b 0a0a l l [R] ll [xa]ll [xa]

Frank Cowell: Microeconomics Full market power: the result Bill has maximal power in market for good 1 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 Outcome is full exploitation  trading partner is forced to reserve indifference curve  is on indifference curve through  solution allocation [x a ] is on indifference curve through [R] But it is efficient But it is efficient   at [x a ] MRS is is the same for both traders…   … so it is on the contract curve Solution applies for general form of Bill’s preferences Solution applies for general form of Bill’s preferences

Frank Cowell: Microeconomics Overview... Market power Exchange and monopoly Misinformation Market Power and Misrepresentation Power play in the Edgeworth box

Frank Cowell: Microeconomics Using the idea of market power We have characterised market power in a simplified case 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 Now use this model  apply this to a number of trading stories  again in a simplified world Address some key questions Address some key questions  How related to competitive outcomes?  Under what circumstances will we get an efficient outcome?

Frank Cowell: Microeconomics Trading: alternative stories A case with simplified property distribution A case with simplified property distribution  Bill has all of commodity 1  Alf has all of commodity 2 Review the standard equilibrium concepts Review the standard equilibrium concepts  the core  competitive equilibrium Examine two polar cases 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 Then consider limited market power  Alf can act as a simple monopolist

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] ll ll p* Trading and competition   A’s indifference curves   B’s indifference curves   The contract curve   Endowment point   Trades acceptable to A&B   The core   CE and prices l l [x*]

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] ll ll l l [x*] ll [xa]ll [xa] Bill has total market power   Competitive equilibrium   B’s opportunity set given market power   B’s optimal allocation   A nonlinear schedule to implement it

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 a x2x2 b l l [x*] ll ll [xb] [xb] Alf has total market power   A’s opportunity set given market power   A’s optimal allocation   A nonlinear schedule to implement it x1x1 b x2x2 a [R] ll ll

Frank Cowell: Microeconomics Simple monopoly The three stories have a common element 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 Now consider a story with less than complete market power  Alf can simply set the price  Bill acts as price taker Rework the diagram Rework the diagram  first map out Alf’s attainable allocations  then characterise optimum…  …conditional on this restricted-power model

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] ll ll ll ll ll ll ll ll ll ll Alf can set prices   B’s reaction function   Endowment   A tries out alternative prices   A’s attainable set   B’s preferences ll ll

Frank Cowell: Microeconomics p 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] ll ll ^ ^ Monopoly trading   Competitive equilibrium   A’s monopolistic optimum   A’s total market power solution   A’s preferences l l [x] ll [xb]ll [xb] l l [x*]   Efficient allocations (contract curve)   MRS and prices at optimum

Frank Cowell: Microeconomics Summary of market power model Suppose Alf has market power Suppose Alf has market power Gets higher utility than in CE Gets higher utility than in CE Gets higher utility if has total market power than as simple monopolist Gets higher utility if has total market power than as simple monopolist CE and total market power are efficient CE and total market power are efficient Simple monopoly is inefficient Simple monopoly is inefficient  price = Alf’s MRS  price ≠ Bill’s MRS

Frank Cowell: Microeconomics Overview... Market power Exchange and monopoly Misinformation Market Power and Misrepresentation Applying the simple monopoly model

Frank Cowell: Microeconomics Misrepresentation The standard exchange model tells a simple story The standard exchange model tells a simple story But relies on strong informational assumption 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 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 Start from case of perfect information Then suppose that Alf misrepresents preferences Then suppose that Alf misrepresents preferences  Bill continues to reveals full information

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] p ^ ^ l l [x] p* Misrepresentation and distortion   A’s true ICs   B’s true ICs   The contract curve   Endowment point & core   CE allocation and prices   A’s false IC   Induced equilibrium with A’s misrepresentation ll ll l l [x*]

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

Frank Cowell: Microeconomics 0b0b 0a0a x1x1 b x1x1 a x2x2 a x2x2 b [R] p ^ p* Misrepresentation and distortion (2)   True indifference curves   The contract curve & core   CE allocation and prices   A’s false ICs   Equilibrium if only A misrepresents ll ll l l [x*] ^ l l [x]   B’s false IC   Possible outcome if both misrepresent l l [x] ~

Frank Cowell: Microeconomics Application Consider a model of international trade Consider a model of international trade  Alfaland exports good 2  Billestan exports good 1 Price ratio is terms of trade 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 Same outcomes could arise if each country can misrepresent preferences of its citizens Could design an efficient outcome if use nonlinear prices 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

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