aps6 - Econ201 Spring 2010 Beomsoo Kim Problem Set #6...

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Econ201 Spring 2010 Beomsoo Kim 1/4 Problem Set #6 Solution 20. Solution: (a)Total revenue= P(Q)*Q, P dP Q dQ / / = ε ===> Marginal revenue= ) 1 1 ( ) / / 1 1 ( ) 1 ( = + = × + = + = P P dP Q dQ P P Q dQ dP P P Q dQ dP dQ dTR (b) Profit maximization: MR=MC ===> ) 3 1 1 ( 12 ) 1 1 ( = = P P ===> P=18 21. Solution: Demand: P(Q)=100-Q Cost: C(Q)=20Q (a) Total revenue= P(Q)*Q= (100-Q)*Q MR= dQ dTR = 100-2Q MC=20 AB is demand curve, and AC is marginal revenue curve. (b) Profit maximization: MR=MC ===> 100-2Q=20 ===> Q*=40 P*=100-Q = 100-40 = 60 (c) Profit at profit maximization level of P and Q= P*Q*-C(Q*) = 60*40-20*40 = 1600 (d) For perfect competition, profit maximization ===> MR=MC, MR=P, MC=20 ===> P’=20, Q’= 100-P’= 100-20 = 80 (e) Total surplus for monopoly = M+N Total surplus for perfect competition = M+N+D Deadweight loss = Area (D) = 0.5*(60-20)*(80-40) = 800
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Econ201 Spring 2010 Beomsoo Kim 2/4 22. Solution: (a) Under first degree discrimination, Bob can set a different price for each unit sold,
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aps6 - Econ201 Spring 2010 Beomsoo Kim Problem Set #6...

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