05-Oligopoly

# 05-Oligopoly - Oligopoly Econ 425 Summer I 2008 Intro In...

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Oligopoly Econ 425, Summer I 2008

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2 Intro b In oligopoly models, a firm must consider rival firms’ behavior to determine its own best strategy. b The interrelationship between firms is the key issue studied in oligopoly. b In that sense, oligopoly models can be viewed as (noncooperative) games of strategies or actions. b Oligopolistic games have three common elements: - two (or more) firms; - each firm maximizes its profit (payoff); - each firm is aware that other firms’ actions can affect its profit.
3 Intro (2) b Three best-known game-theoretic oligopoly models: - Cournot - Bertrand - Stackelberg b Oligopoly models may differ in: - type of actions; - order of actions; - length of game.

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4 Cournot model b Assumptions: - firms set quantities; - single period; - homogenous goods; - same cost of production; - no capacity constraints; - no entry.
5 Cournot model (2) Example : Consider two sellers of spring water, firm A and firm B. - Industry output is Q = q A + q B ; - Linear market demand is Q = 1,000 – 1,000p; - Both firms have a constant marginal cost of 28 cents; - Firms make their quantity decision simultaneously. b What strategy should firm A use to choose its output level? - We will see that the answer depends on firm A’s belief about firm B’s behavior.

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6 Cournot model (3) Graphically Firm A faces a residual demand curve and behaves as a monopoly over those consumers whose demands are not met by firm B. Q \$ Market Demand, Q 1 260 mc Residual MR 1,000 Residual demand 800 200 0.28 q A = Q - q B Q = 1,000 – 1,000p q B = 200 0.54
7 Cournot model (4) Mathematically We can derive firm A’s best-response function (or reaction function), q A = R A ( q B ). i.e. firm A’s optimal response given its beliefs about firm B’s action ( q B ). How? , where By symmetry, A A q q q Q p A 28 . 0 ) ( max Q Q p 001 . 0 1 ) ( = 2 360 B A q q = 2 360 A B q q =

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8 Cournot model (5) b The point of intersection of the best-response functions is the Cournot equilibrium. Why? b
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05-Oligopoly - Oligopoly Econ 425 Summer I 2008 Intro In...

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