1. Households max utility subject to their budjet constraints 2. Firms max profit subject to production function 3. Profit is distributed to households according to shareholdings 4. Supply = demand for each good

Micro Flashcards by Gary Wu

Posner

(2003)

Cartels can cause price increase of between 30% (sugar) and 100% (rubber), causing social costs (as a percentage of industry sales) of 35% (sugar) to 75% (rubber).

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Likelihood of collusion factors (8)

8, 5 with models.
discount rate
# Firms 
Sales frequency
Ease of detecting cheating
Cost asymmetry
Multimarket contact
Leniency Programmes
Coordination difficulties

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Connor

(2003)

Median number of cartel participants is 5. 77% have less than 6.
Supports the Bertrand # firms argument.

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Cabral

(2000)

Danish authorities gathered and published concrete prices. Average prices rose by 15-20% in less than a year, with lower variance.
Supports the ease of detection argument.

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Rees

(1993)

Two firms, British Salt and ICI Weston Point.
British Salt had greater market share and lower costs.
Homogenous good, no prospects of entry.
17 price changes in ten years (1974-1984). Weston Point (the smaller firm) led with price increases from 81-84.

Rees finds that collusive outcomes sustianed: punishment significant enough and threat of punishment credible. Interestingly, smaller firm is price leadrer.

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Measuring market power

Lerner Index

L = (Price - MC)/Price
What is L for monopoly? For Cournot? Perfect competition?

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Measuring market concentration

Herfindahl Index

H is the sum of squared market shares. WHAT IS THE EQUATION?
What is H for monopoly? For oligopoly? Perfect competition?

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CRRA formulae

= CRRA * Y

with two other equivalent forms.

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CARA formula

A(y) = - U’’ (y) / U’ (y)

REMEMBER THE NEGATIVE

For small gambles, r(y) is approx. by 1/2A(y)variance

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Baye and Morgan

(1999)

In the absence of a finite choke price, i.e. firms can raise prices indefinitely, there is a Bertrand-Nash equilibrium with P>C and positive profits.

I.e. Can have Bertrand with positive profits. Other possibility for this is Bertrand with diffrentiation.

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Nash Equilibrium

Set of strategies such taht each player’s strategy is a best response to the other player’s.

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Certainty Equivalent

U bar = U ( Ycertainty)

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4 Conditions for GCE

Households max utility subject to their budjet constraints
Firms max profit subject to production function
Profit is distributed to households according to shareholdings
Supply = demand for each good

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First Theorem

GCE is Pareto efficient.

Proof: At equilirium, MRS = price ratio for both consumers and firms.

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Second Theorem

Assume preferences and production sets are convex (!). Then an Pareto efficient allocation can be achieved as a GCE with appropriate initial endowments.

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5 Duopoly assumptions

Two firms
One shot
HOMOGENOUS GOODS
Linear inverse market demand. Q = Q1 + Q2
Cost functions with CONSTANT MC and no fixed costs

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Bertrand with Diffrentiation equations

q1 = a - bP1 + g P2
q2 = a - bP2 + g P1

Preference ordering assumptions

Complete

Transitive

Adoption Game

asdf

Matching Pennies

asdf

Prisoner’s dilemma

ads

Bertrand with Diffrentiation assumptions

b > 0
g > 0
b > g
a > c(b-g)

Define Subgame perfect

A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game.

Minmax Punishment

Worst one player can do to the other, given that the other player responds optimally.

Folk theorem

Any reasonable payoff pair which gives each player at least their minmax payoff can be supported as a Nash equilibrium of a infinitely repeated game if discount rate is sufficiently close to one (firms are patient).

Lerner Index Equation

L = (Price - MC)/Price

Herfindahl Index equation

Sigma [ (Si)^2 ] Si = qi / Q Si is simply market share

Starting point for all infinite collusion games.

Profit from deviating =< Discount rate adjusted profit from not deviating

Maths Definition of Nash Equilibrium

Notes

Define a market

US Department of Justice Guidelines 1992: A market is the minimal set of products (over product and geographical space) over which a hypothetical monopolist would find it profitable to raise price (from the non-cooperative level)

Cellophane Fallacy

any profit-maximizing firm will set its prices at a level where demand for its product is elastic. Therefore, when a monopolist sets its prices at a monopoly level it may happen that two products appear to be close substitutes whereas at competitive prices they are not. In other words, it may happen that using the SSNIP test one defines the relevant market too broadly, including products which are not substitutes.

Introduction of SSNIP test into DOJ Guidelines

1982

European Comission official adoption of SSNIP

1997

Define market power

Ability of a firm to raise prices above marginal cost

UK Merger Policy

UK: merger disallowed if it would lead to a ‘substantial lessening of competition’ (Enterprise Act 2002)

Arrow's impossibility therem

UPID Unrestricted domain: works for all possible individual preferences. Pareto Principle Independence of irrelevant alternatives non-Dictatorship

Incentive Compatability

What is the math equation? This is needed for A. Choose effort levels and wage such that the agent wants to choose effort that maximises profit

SSNIP Test Steps

Take one good, say A, find price elasticity for it. If it is inelastic (<1), it is a market. If not, take A + B, where B is the good with highest cross-price elasticity with A. Repeat test. If <1, then this is the market. Repeat.

Diversion ratio

Farell and Shapiro Assume n>3 and firms select prices non-cooperatively Firm A will increase its price in a merger with B if B’s pre-merger margin* Diversion RatioAB > Fall in MCA where diversion ratio is fraction of A's sales lost that go to B.

Risk Premium

The maximum amount of money that a risk-averse person would pay to avoid taking a risk. Mathematically, E ( Y ) - certainty equavialent

Pareto Efficient

An outcome is pareto efficient if there is no other feasible outcome Parto superior to it.

Pareto Superior

B is pareto superior to A if no one finds B worse than A and at least one person finds B strictly better