econ100_winter2010_lecture19_topost

# Firm 1 sets mr mc this gives us firm 1s reaction

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Firm 1 sets MR = MC This gives us Firm 1’s reaction function Similarly, we can find Firm 2’s reaction function

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Firm 1 sets MR = MC 240 12Q 2 - 24Q 1 = 120 This gives us Firm 1’s reaction function Q 1 = 5 - .5Q 2 Similarly, we can find Firm 2’s reaction function Q 2 = 5 - .5Q 1
To find equilibrium outcome, we need q1 * (q2 * ) Q 1 = 5 - .5Q 2 = 5 - .5(5 - .5Q 1 ) Q 1 = 5 2.5 + .25Q 1 Q 1 = 2.5/.75 = 3.33 Similarly, Q 2 = 3.33 Total output = 6.66

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Once we know total Q, and can use demand function to find equilibrium price P = 240 12(6.66) = 240-80 = \$160
Summary: solving Cournot Duopoly problems Start with market demand, and marginal cost functions for both firms Recall that Q = q1 +q2 Set MR = MC for EACH firm, to find reaction functions Solve for intersection of r.f. to find q1*,q2* Substitute (q1*+q2*) into D to find equilibrium price

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How do PC, M & CD compare? Mkt D: P = a-bQ MC = C 1. PC: know that S=D, or, all will set P = MC a-bQ = c, or Q = (a-c)/b 2. Monopoly: will set P = MR MR: a-2bQ = c Q = ½((a-c)/b) 3. Cournot Duop:
How do PC, M & CD compare? Perfect Competition: know that S=D, or, all will set P = MC a-bQ = c, or Q = (a-c)/b
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