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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

௹቗ݪ୒Ǿݪ୓ቘ, 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 ݪ୒൩ 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