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Eco 403: Industrial Organization Economics, Fall 2012
Dr. Abdel-Hameed H. Nawar
Oligopoly
Isoprofit Curve
An isoprofit Curve of a firm, ࠅ
௹ݪǾݪቘ, is defined to be the set of all possible combinations of each firm's output levels that give that firm the same level of profit.
How is an isoprofit curve shaped?
Property 1. An isoprofit curve is concave and reaches a maximum on the firm's reaction (best response) curve. Recall that for an ݧ-variable function, the hyperplane that is tangent to the function at a particular point lies above the function if it is concave and lies below the function if it is convex. For a single variable function, i.e. where ݧ ൩ ΐ, Firm 1's and Firm 2's isoprofit functions are largest.
Note that:
Is unilaterally deviation gainful? As we will see for firm 1,
This is symmetric game:
• Collusion profit when the rival deviates ࠅ
Firm 1
Firm 2
Collude Deviate
Clearly, collusion cannot be sustained.
Collusion is not sustainable in one period model since cheater cannot be punished.
Repeated Games
• Firms in some industries do not play one-shot game but rather strategically interact repeatedly. This may affect the equilibrium behavior. In particular, it opens possibilities for collusion in an industry. • Repeated game is a game that is played over and over again. Repetition could be finite or infinite times and time is discrete. • Due to the time-value of money, a 1 dollar earned during the first period is worth more than a dollar in later repetitions. Players must discount future payoffs when they make current decisions.
An infinitely repeated game of Collusion
Present Value
ݫ ൩ interest rate per period
Period 1 Period 2 ... Period T
the time value of the money. The value today of a future payoff is called the present value (PV), which is an increasing function of ߹ • If ߹ future (impatient), • If ߹ (patient).
Trigger Strategy
Collusion could be achieved in an infinitely repeated game by using the following set of strategies:
1. Each firm produces the collusion level of output each
period as long as its rival does the same.
2. If any firm produces a different level of output, then
beginning from the next period and forever its rivals will punish the firm by playing the CN equilibrium.
Collusion is sustainable if the
• PV(collusion) > PV(deviation once & then punished forever); or • PV(punishment) > PV(gains from collusion)
Let PV(collusion) be denoted by ܡܛ
once & then punished forever) be denoted by ܡܛ
Collusion is sustainable if
Thus Thus • If firms care less about the future than the present, then deviation may be attractive. • If firms care about future more, then collusion is sustainable. • Collusion is sustainable if the firm is sufficiently patient (i.e. ߹ Note:
PV(gains from deviation)
PV(punishment)
We can obtain
PV(punishment) > PV(gains from deviation)
which gives the same condition for sustainability:
Numerical Example
Total cost: ݓ݂
Monopoly Case
FOC In case of collusion we assume that each firm makes ΐΑ൴ of
Duopoly Case
Firm 1's profit
FOC
Firm1's
best response curve:
By symmetry,
Solving for ݪ
and ݪ,
By symmetry, ݪ
By symmetry,ࠅ
Homework Exercise
• Draw firm 1's best response curve and the isoprofit curve corresponding to its profit in the Cournot-Nash equilibrium. • Draw firm 2's best response curve and the isoprofit curve corresponding to its profit in the Cournot-Nash equilibrium. Hint: for a given level of profit ࠅു௹,
Collusion
If firm 1 thinks that form 2 will play the collusive level of output, firm 1 has an incentive to deviate taking firm 2's output level as given and then maximizing its profit: Using the reaction function ݪ൩ ΓΑ ൣ The above results can be summarizes in as follows:
Firm 1
Firm 2
Collude Deviate
Collude 1764,1764 1323, 1984.5
Deviate 1984.5, 1323 1568,1568 *
Clearly, (Deviate, Deviate) is the NE in a one period game. In an infinitely repeated game, collusion outcome (Collude, Collude) is sustainable if: and hence if
If the discount factor ߹
sustainable.
CNE, Monopoly and Perfect Competition
The ࢱ-firm linear symmetric CNE
For ݢ ൩ ΐǾΑǾȂݧ, the following hold ቘ௲ decreasing ௲ Increasing Decreasing
What are some of the insights?
As the number of firms in the industry goes up, each individual firm produces less, but total output goes up, the market price decreases and the total surplus increases.
Optimal Entry in a Cournot
We assume:
Decreasing
በ Increasing ௳ቘో Increasing
What are some of the insights?
As the number of firms in the industry goes up, each individual firm produces less, but total output goes up, the market price decreases and the total surplus increases.
Optimal Entry in a Cournot Nash World
As the number of firms in the industry goes up, each individual firm produces less, but total output goes up, the market price decreases and the total surplus increases. Stage 1: Foreseeing a Cournot game, firms decide whether or not to enter at a cost of ݅. Stage 2: the number of entrants (say ݧ) is observed and the firms strategically choose Cournot Nash Equilibrium: Backward Induction: in a multiple stage game, we solve the game backwards from the last stage.
Stage 2: ݧ, the number of entrants
Stage 2: ݄ntry will occur until profit equals entry cost: where ݧ
The social planner's decision problem:
FOC • In the linear symmetric Cournot game , the market provides too much entry. • In general there are two extremes associated with entry.
1. Surplus appropriability: an entrant ignores an
increase in consumer surplus due to entry
2. Business stealing: an entrant ignores declines of
the profits of existing firms caused by entry (negative externality)quotesdbs_dbs16.pdfusesText_22