Frank Cowell: Microeconomics
September
2006
Market Power and Misrepresentation
MICROECONOMICS
Principles and Analysis
Frank Cowell
Frank Cowell: Microeconomics
Introduction
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Presentation concerns trading behaviour
Context is an exchange economy
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Use a standard modelling framework
Endow traders with different degrees of power
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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
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Consider an exchange economy
Suppose one agent has extended monopoly power
Can charge a fee for the right to access good 1
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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
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Two goods (1,2) and two traders (Alf, Bill)
Given resource distribution
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Trading outcomes described by allocation
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vector of consumptions
Alf: [x1a, x2a]
Bill: [x1b, x2b]
Use good 2 as numéraire
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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
price of good 1 is p := p1/p2
Assume materials balance condition satisfied with equality
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x1a + x1b = R1
x2a + x2b = R2
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permits use of the Edgeworth box diagram
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Frank Cowell: Microeconomics
Market power
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Suppose Bill has the power to set
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Then Bill can fix a budget constraint for Alf anywhere in the
diagram…
… subject to one important condition
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We return to this in a moment
It has to do with the trading rules
Bill’s control over the budget constraint:
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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
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the pair (p, F)
examine how this works:
The “two-part” tariff
Frank Cowell: Microeconomics
b
x1
The endowment point
Fixed charge
x2a
 [R]
Price per unit
F
p
x2b
0a
x1a
Changing the budget constraint...
Frank Cowell: Microeconomics
b
x1
x2a
 [R]
Varying F
Varying p
x2b
0a
x1a
Key condition
Frank Cowell: Microeconomics
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Bill nearly has total control over Alf
However, one thing remains in Alf’s power:
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This condition effectively constrains Bill’s action
Draw Alf’s indifference curve through the endowment point
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Alf does not have to consume good 1
Can just consume his endowment [R1a, R2a]
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
x1
A’s indifference curves
Endowment point
x2a
 [R]
A’s reservation
indifference curve
B’s constraint set
B’s indifference curves
The solution
Entry fee and price
F
 [xa]
p
x2b
0a
x1a
Solution works in general case
Frank Cowell: Microeconomics
b
x1
Basic model as before
B’s indifference curves
Solution as before
x2a
 [R]
F
 [xa]
p
x2b
0a
x1a
Full market power: the result
Frank Cowell: Microeconomics
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Bill has maximal power in market for good 1
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Outcome is full exploitation
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trading partner is forced to reserve indifference curve
solution allocation [xa] is on indifference curve through [R]
But it is efficient
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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
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We have characterised market power in a
simplified case
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Now use this model
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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
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How related to competitive outcomes?
Under what circumstances will we get an efficient
outcome?
Frank Cowell: Microeconomics
Trading: alternative stories
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A case with simplified property distribution
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Review the standard equilibrium concepts
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the core
competitive equilibrium
Examine two polar cases
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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
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Alf can act as a simple monopolist
Trading and competition
Frank Cowell: Microeconomics
b
[R] x1
A’s indifference
curves
b
0

B’s indifference curves
x2a
The contract curve
Endowment point
Trades acceptable to A&B
The core
CE and prices
 [x*]
p*
x2b
0a
x1a
Bill has total market power
Frank Cowell: Microeconomics
b
[R] x1
Competitive
equilibrium
b
x2a
B’s opportunity set given
market power
0
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B’s optimal allocation
A nonlinear schedule to
implement it
 [x*]
 [xa]
x2b
0a
x1a
Alf has total market power
Frank Cowell: Microeconomics
b
[R] x1
A’s opportunity
set given
0b
market power
x2a
A’s optimal allocation
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[xb]
A nonlinear schedule to
implement it
 [x*]
x2b
0a
x1a
Simple monopoly
Frank Cowell: Microeconomics

The three stories have a common element
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Now consider a story with less than complete
market power
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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
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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] x1
0b
 B’s preferences
x2a
 Endowment
 A tries out alternative
prices
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B’s reaction function
A’s attainable set
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x2b

0a
x1a
Monopoly trading
Frank Cowell: Microeconomics
b
[R] x1
0b
 A’s preferences

x2a
 [xb]
^
 [x]
^p
 Efficient allocations
(contract curve)
 A’s monopolistic optimum
 MRS and prices at
optimum
Competitive equilibrium
A’s total market power
solution
 [x*]
x2b
0a
x1a
Summary of market power model
Frank Cowell: Microeconomics
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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
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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
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The standard exchange model tells a simple story
But relies on strong informational assumption
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Use the same model as the market power example
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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
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Bill continues to reveals full information
Misrepresentation and distortion
Frank Cowell: Microeconomics
b
[R] x1
A’s truebICs
0
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B’s true ICs
x2a
The contract curve
Endowment point & core
CE allocation and prices
^
 [x]
A’s false IC
^
p

Induced equilibrium with
A’s misrepresentation
[x*]
p*
x2b
0a
x1a
Misrepresentation: outcome
Frank Cowell: Microeconomics
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The equilibrium has been seen before
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Opportunity to masquerade induces a distortion
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trader with informational advantage forces price in his favour
in this case: price ratio = MRSa ≠ MRSb
Bilateral trading is manipulable
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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?
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outcome is still likely to be inefficient…
Misrepresentation and distortion (2)
Frank Cowell: Microeconomics
b
[R] x1
True indifference
curves
b
0
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The contract curve & core
x2a
CE allocation and prices
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A’s false ICs
Equilibrium if only A
misrepresents
~ ^
[x]
 [x]
B’s false IC
p^

Possible outcome if both
misrepresent
[x*]
p*
x2b
0a
x1a
Application
Frank Cowell: Microeconomics

Consider a model of international trade
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Price ratio is terms of trade
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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
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Alfaland demands payment F for access to market for good 2
…or vice versa for Billestan and good 1