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Market Power and Misrepresentation

MICROECONOMICSPrinciples and Analysis Frank Cowell

July 2015

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Note: the detail in slides marked “ * ” can only be seen if you run the slideshow

Slide2Introduction

Presentation concerns trading behaviourContext is an exchange economyusual focus is on simple price-takingbut we will examine non-competitive behaviourUse a standard modelling frameworkEndow traders with different degrees of powercaptured in the trading rulesExtend this to a simple model of manipulation and designBegin with a simple analysis of nonlinear prices

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Slide3Overview

Market power

Exchange and monopoly

Misinformation

Market Power and Misrepresentation

Nonlinear price systems

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Slide4The setting

Consider an exchange economySuppose one agent has extended monopoly powerCan charge a fee for the right to access good 1this can only work for goods where resale is difficultotherwise consumers can undermine the fee by bulk-buying and selling on the commodity to otherssometimes public utilities fit this paradigmAssume that any other trader acts as a price takerAnalyse this within the context of the Edgeworth box

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Slide5The model

Two goods (1,2) and two traders (Alf, Bill)Given resource distributionendowments of two goods are such that Bill owns all good 1Alf: [R1a, R2a] = [0, R2a] Bill: [R1b, R2b] = [R1, R2b] R2 := R2a + R2bTrading outcomes described by allocationvector of consumptionsAlf: [x1a, x2a]Bill: [x1b, x2b] Use good 2 as numéraireprice of good 1 is p := p1/p2Assume materials balance condition satisfied with equalityx1a + x1b = R1x2a + x2b = R2permits use of the Edgeworth box diagram

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Slide6Market power

Suppose Bill has the power to set the price pand the entry fee FThen Bill can fix a budget constraint for Alf anywhere in the diagramsubject to one important conditionthis has to do with the trading rulessee belowBill’s control over the budget constraint: p fixes the slope;F fixes the positionIn effect Bill has the power to set a non-linear price systemthe pair (p, F)examine how this works:

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Slide7x

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The “two-part” tariff

The endowment point

Price per unit

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Fixed charge

p

[

R]

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0

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Slide8x

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*Changing

the budget

constraint

Varying

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Varying

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[R]

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Slide9Key condition

Bill nearly has total control over AlfHowever, one thing remains in Alf’s power:Alf does not have to consume good 1can just consume his endowment [R1a, R2a]This condition effectively constrains Bill’s actionDraw Alf’s indifference curve through the endowment pointAlf’s reservation indifference curvecannot be forced to trade at an allocation with lower level of utilityThis is the boundary of Bill’s attainable setBegin with case where Bill considers goods perfect substitutes

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Slide10Exploitation 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 indiff curve

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[R]

[

x

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]

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Slide11Solution works in general case

F

p

Basic model as before

b

’s indifference curves

Solution as before

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1

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[R]

[

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Slide12Full market power: the result

Bill has maximal power in market for good 1can use a nonlinear pricing schemesets price ratio and entry fee to market for good 1 Outcome is full exploitationtrading partner is forced to reserve indifference curve solution allocation [xa] is on indifference curve through [R] But it is efficientat [xa] MRS is is the same for both traders…… so it is on the contract curveSolution applies for general form of Bill’s preferences

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Slide13Overview

Market power

Exchange and monopoly

Misinformation

Market Power and Misrepresentation

Power play in the Edgeworth box

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Slide14Using the idea of market power

We’ve characterised market power in a simplified caseBill a had built-in monopolistic advantagealso endowed with complete market powerNow use this model apply this to a number of trading storiesagain in a simplified worldAddress some key questionsHow related to competitive outcomes?Under what circumstances will we get an efficient outcome?

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Slide15Trading: alternative stories

A case with simplified property distributionBill has all of commodity 1Alf has all of commodity 2Review the standard equilibrium conceptsthe corecompetitive equilibriumExamine two polar casesBill has complete market power (can choose point in A’s acceptance set)Alf has complete market powerThen consider limited market powerAlf can act as a simple monopolist

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Slide160

b

0

a

x

1

b

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1

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2

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[R]

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

[

x*]

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Slide170

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0

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[R]

[x*]

[

x

a

]

Bill has total market power

Competitive equilibrium

b

’s opportunity set given market power

b’

s optimal allocation

A nonlinear schedule to implement it

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Slide180

b

0a

x

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[x*]

[

x

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]

Alf has total market power

a

’s opportunity set given market power

a’

s optimal allocation

A nonlinear schedule to implement it

x

1

b

x

2

a

[R]

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Slide19Simple monopoly

The three stories have a common elementcharacterise three points in the coreall stories have efficient outcomesNow a story with less than complete market powerAlf can simply set the price Bill acts as price takerRework the diagramfirst map out Alf’s attainable allocationsthen characterise optimumconditional on this restricted-power model

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Slide200

b

0

a

x

1

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x1

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x2

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x2

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[R]

Alf can set prices

b’

s reaction function

Endowment

a

tries out alternative prices

a

’s attainable set

b

’s preferences

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Slide21p

0

b

0

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x

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x2

a

x2

b

[R]

^

^

Monopoly trading

Competitive equilibrium

a

’s monopolistic optimum

a’

s total market power solution

a

’s preferences

[

x]

[

x

b

]

[x*]

Efficient allocations (contract curve)

MRS and prices at optimum

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Slide22Summary of market power model

Suppose Alf has market powerGets higher utility than in CEGets higher utility if has total market power than as simple monopolistCE and total market power are efficientSimple monopoly is inefficientprice = Alf’s MRSprice ≠ Bill’s MRS

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Slide23Overview

Market power

Exchange and monopoly

Misinformation

Market Power and Misrepresentation

Applying the simple monopoly model

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Slide24Misrepresentation

The standard exchange model tells a simple storyBut relies on strong informational assumptioneach trader has full information about the other’s preferencesWhat happens if we drop this?Use the same model as the market power exampletake the case where Alf owns good 2Bill owns good 1Start from case of perfect information Then suppose that Alf misrepresents preferencesBill continues to reveals full information

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Slide250b

0a

x

1

b

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[R]

p

^

^

[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

[x*]

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Slide26Misrepresentation: outcome

The equilibrium has been seen before version with Alf’s misrepresented preferencessame that for a simple monopolist Opportunity to masquerade induces a distortiontrader with informational advantage forces price in his favourin this case: price ratio = MRSa ≠ MRSb Bilateral trading is manipulableby revealing false preferencesAlf secures higher utility for himselfWhat if both can misrepresent? outcome is still likely to be inefficient…

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Slide270

b

0a

x

1

b

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x

2

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[R]

p

^

p*

Misrepresentation and distortion (2)

True indifference curves

The contract curve & core

CE allocation and prices

a

’s false ICs

Outcome if

a

misrepresents

[x*]

^

[x]

b’

s false IC

Outcome if both misrepresent

~

[x]

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Slide28Application

Consider a model of international tradeAlfaland exports good 2Billestan exports good 1Price ratio is terms of tradesuppose one country can impose a tariffget inefficient (monopoly) outcomesuppose other country retaliates with its own tariffoutcome may still be inefficientSame outcomes could arise if each country can misrepresent preferences of its citizensCould design an efficient outcome if use nonlinear pricesAlfaland demands payment F for access to market for good 2or vice versa for Billestan and good 1

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