econ100_winter2010_lecture19_topost

Q2 will have an entire set of q1 s as a function of

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(q2) Will have an entire set of q1 * ’s, as a function of q2 If q2 increases, optimal amount for q1 to produce FALLS
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How does q1 * vary with q2? D-firm1 MR-firm1 q1 * (q2) q2
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How does q1 * vary with q2? D-firm1 MR-firm1 q1 * (q2’) q1 * (q2) q2’ q2
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As rival’s output increases, firm 1’s optimal output falls q1 q2 q1*(q2)
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Reaction Function Reaction function gives the optimal level of output (or price) for 1 firm, given the output (or price) of a second firm. Given a demand curve, we can find both firm’s reaction functions
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Reaction Functions for Cournot Duopolists q1*(q2) q2*(q1) E
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What is true at point E? At point E, we have q1 * (q2) = q1 * (q2 * ) Firm 1 is producing profit maximizing output, given what firm 2 is doing AND Firm 2 is producing profit maximizing output, given what firm 1 is doing
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Each firm is doing its best, conditional on what the other firm is doing Is an equilibrium, because once actions (q1,q2) are revealed, neither firm would like to change output level Nash Equilibrium
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Example: Find equilibrium price and output for Cournot Duopolists Market Demand: P = 240-12Q MC1 = MC2 = 120 Find q1*, q2*, P* (First step is to find REACTION FUNCTIONS)
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What is Firm 1’s (conditional) demand function? Next, find MR for FIRM 1
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What is Firm 1’s (conditional) demand function? P = 240 12 (Q 1 + Q 2 ) (where Q 2 is not chosen by firm 1) Next, find MR for FIRM 1 TR1 = PQ 1 = (240-12Q 1 -12Q 2 )Q 1 = 240Q 1 12Q 1 2 -12Q 1 Q 2 MR1 = 240 12Q 2 - 24Q 1
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