Lecture9_Oligopoly1

# Lecture9_Oligopoly1 - Lecture 9 Oligopoly Models Click to...

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Click to edit Master subtitle style  11/5/10 Lecture 9 Oligopoly Models Econ 121: Industrial Organization UC Berkeley Fall 2010 Prof. Cristian Santesteban

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11/5/10 Overview Cournot – simultaneous quantity Stackelberg – sequential quantity Bertrand – simultaneous price Dominant Firm – sequential price Product Differentiation
OLIGOPOLY The Cournot Model reaction curve Relationship between a firm’s profit-maximizing output and the amount it thinks its competitor will produce. Cournot equilibrium Equilibrium in the Cournot model in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly. Firm 1’s reaction curve shows how much it will produce as a function of how much it thinks Firm 2 will produce. Firm 2’s reaction curve shows its output as a function of how much it thinks Firm 1 will produce. In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore, neither firm will move from this equilibrium. Reaction Curves and Cournot Equilibrium

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OLIGOPOLY Cournot and The Linear Demand Curve—An Example Two identical firms face the following market demand curve P = 30 – Q Also, MC 1 = MC 2 = 0 Total revenue for firm 1: R 1 = PQ 1 = (30 – Q ) Q 1 then MR1 = ∆ R 1/∆ Q 1 = 30 – 2 Q 1 – Q 2 Setting MR 1 = 0 (the firm’s marginal cost) and solving for Q 1, we find Firm 1’s reaction curve: By the same calculation, Firm 2’s reaction curve: Cournot equilibrium: Total quantity produced: 1 2 1 15- 2 Q Q = 2 2 1 15- 2 Q Q = 1 2 10 Q Q = = 1 2 20 Q Q Q = = =
OLIGOPOLY Collusion and The Linear Demand Curve—An If the two firms collude, then the total profit-maximizing quantity can be obtained as follows: Total revenue for the two firms: R = PQ = (30 – Q ) Q = 30Q Q 2, then MR1 = ∆ R /∆ Q = 30 – 2 Q Setting MR = 0 (the firm’s marginal cost) we find that total profit is maximized at Q = 15. Then, Q 1 + Q 2 = 15 is the collusion curve . If the firms agree to share profits equally, each will produce half of the total output: Q 1 = Q 2 = 7.5 What would the quantities if these firms priced at marginal cost, i.e., the competitive outcome?

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OLIGOPOLY Contrasting Three Cases: The Linear Demand Curve—An The demand curve is P = 30 − Q , and both firms have zero marginal cost. In Cournot equilibrium, each firm produces 10. The collusion curve shows combinations of Q 1 and Q 2 that maximize total profits. If the firms collude and share profits equally, each will produce 7.5. Also shown is the competitive equilibrium, in which price equals marginal cost and profit is zero. Duopoly Example Figure 12.5
11/5/10 Simultaneous Games Firm cannot observe the other firms’ choices It must therefore make its choice subject to a belief of what the other firms’ choices will be Since the game is simultaneous – the other firms cannot respond. Hence, each firm must take the other firms’ choices as given In equilibrium, the beliefs about

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