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tut 10 Solutions

# tut 10 Solutions - Solutions 1 Demand Schedule for Pepsi is...

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Solutions 1. Demand Schedule for Pepsi is given as Q 2 (P 1 ,P 2 ) = 49.52 -5.48P 2 +1.40P 1 Marginal Cost is given as C 2 = 3.96 Follow Steps: I. Begin with the Profit function of Pepsi 2 = P 2 Q 2 C 2 Q 2 = (P 2 C 2 ) Q 2 Sub in known Q 2 (P 1 ,P 2 ) and C 2 2 = (P 2 3.96) (49.52 -5.48P 2 +1.40P 1 ) 2 =71.2208 P 2 5.48 P 2 2 +1.40 P 1 P 2 -5.544 P 1 196.0992 II. Differentiate with respect to P 2 and set the derivative equal to zero. III. Solve for P 2 * (reaction function ) P 2 * = 6.49 +0.1277P 1 2. This is a standard Cournot Model except marginal costs differ. Firm 1’s profit function: ∏ 1 = (a-q 1 -q 2 ) q 1 c 1 q 1 1 =aq 1 -q 1 2 -q 2 q 1 - c 1 q 1 Differentiate with respect to q 1 and set equal to zero: ∂∏ 1 /∂ q 1 =a -2 q 1 q 2 c 1 = 0 Solve for b 1 (q 2 ) i.e. Firm 1’s best response function: b 1 (q 2 ) = ½ (a q 2 c 1 ) By symmetry of the process we can get Firm 2’s best response (just change c 1 to c 2 , and change q 1 to q 2 ): b 2 (q 1 ) = ½ (a q 1 c 2 ) Sub in b 2 (q 1 ) for q 2 in the b 1 (q 2 ) (N.B. Logic of this step, Firm 1’s best approximation of

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tut 10 Solutions - Solutions 1 Demand Schedule for Pepsi is...

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