Micro Flashcards
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).
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
Connor
(2003)
Median number of cartel participants is 5. 77% have less than 6.
Supports the Bertrand # firms argument.
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.
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.
Measuring market power
Lerner Index
L = (Price - MC)/Price
What is L for monopoly? For Cournot? Perfect competition?
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?
CRRA formulae
= CRRA * Y
with two other equivalent forms.
CARA formula
A(y) = - U’’ (y) / U’ (y)
REMEMBER THE NEGATIVE
For small gambles, r(y) is approx. by 1/2A(y)variance
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.
Nash Equilibrium
Set of strategies such taht each player’s strategy is a best response to the other player’s.
Certainty Equivalent
U bar = U ( Ycertainty)
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
First Theorem
GCE is Pareto efficient.
Proof: At equilirium, MRS = price ratio for both consumers and firms.
Second Theorem
Assume preferences and production sets are convex (!). Then an Pareto efficient allocation can be achieved as a GCE with appropriate initial endowments.
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
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
