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CHAPTER 27 OLIGOPOLY
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27.1 Choosing a Strategy Oligopoly: There are a number of competitors in the market, but not so many as to regard each of them as having a negligible effect on price. Duopoly: Two firms only.
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27.1 Choosing a Strategy Sequential game: Players take actions in a given order. Quantity leader: The firm who chooses its quantity first. Quantity follower: The firm who chooses its quantity following the leader.
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27.2 Quantity Leadership The follower chooses its output, given the output of the leader. F.O.C. Reaction curve: the optimal y2 as a function of y1.
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27.2 Quantity Leadership Linear demand:
Zero marginal cost for simplicity. The profit function of firm 2: Isoprofit: the locus of (y1, y2) that yield a constant level of profit. Reaction curve:
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27.2 Quantity Leadership Higher profits for inner isoprofits.
The reaction curve attains the maximal profit for a given y1. The reaction curve passes though the top of the isoprofits.
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27.2 Quantity Leadership The leader chooses y1 in recognition of the follower’s reactions. Profit function: F.O.C.:
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27.2 Quantity Leadership The leader knows that the system will settle on firm 2’s reaction curve. The leader choose the lowest isoprofit on firm 2’s reaction curve.
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27.3 Price Leadership The leader has set a price p;
The follower take this price as given and set its output S(p): The demand faced by the leader is the residual demand R(p)=D(p)-S(p); The leader’s problem:
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27.3 Price Leadership
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27.3 Price Leadership Follower’s cost function: c2(y)=y2/2
Follower’s supply curve: y2=p Linear market demand: D(p)=a-bp Residual demand: R(p)=a-(b+1)p The leader’s problem: The leader’s output:
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27.5 Simultaneous Quantity Setting
Each firm forms a belief about the other firm’s output; Each firm chooses its profit-maximizing output according to this belief; Nash equilibrium: the belief is consistent with the outcome and no firm has incentives for further adjustment.
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27.5 Simultaneous Quantity Setting
Firm 1 expects that firm 2 produces y2e units; Firm 2 expects that firm 1 produces y1e units; Firm 1’s problem: Firm 1’s output: y1=f1(y2e); Firm 2’s problem: Firm 2’s output: y2=f2(y1e).
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27.5 Simultaneous Quantity Setting
The equilibrium satisfies y1*=f1(y2*) and y2*=f2(y1*). The equilibrium is given by the intersection of the two reaction curves.
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27.6 An Example of Cournot Equilibrium
Linear market demand: p(y)=a-by; Zero marginal cost; The reaction curves: Equilibrium conditions: y1=y1e, y2=y2e Equilibrium outputs:
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27.7 Adjustment to Equilibrium
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27.8 Many Firms in Cournot equilibrium
Suppose that there are n firms; Total industry output: Y=y1+…+yn; Firm i’s F.O.C.:
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27.8 Many Firms in Cournot equilibrium
Firm i’s market share: si=yi/Y With a large number of firms, each firm’s market share is negligible, and the Cournot equilibrium is effectively the same as pure competition.
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27.9 Simultaneous Price Setting
Firms set their prices and let the market determine the quantity sold; Assuming constant marginal cost c; Prices can never be lower than c; If ph>c, the low bidder can always increase its profits by charging a slightly lower price; Both firms charging p=c is the unique equilibrium.
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27.10 Collusion Cartel: Firms set prices and outputs so as to maximize total industry profits. Cartel’s problem: F.O.C.:
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27.10 Collusion Marginal profits of firm 1:
Each firm has incentives to deviate from the cartel solution. Cartel is unstable in the short run. Punishment mechanism is needed to maintain the cartel in the long run.
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27.10 Collusion
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27.11 Punishment Strategies
Punishment strategy Coorperation stage: produce the Cartel quantity until a deviation is observed; Punishment stage: produce the Cournot quantity for ever. The firm being punished will choose the Cournot quantity in response.
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27.11 Punishment Strategies
Present value of cartel behavior: Present value of cheating: Cheating won’t happen if
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