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CHAPTER 9 & 10 HOMEWORK You should show detailed calculations/processes and explanations. Answer itself is NOT sufficient. 2. The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 - 3(01 + 02) and costs are ci(Q1) = 2601 and C2(Q2) = 3202. Determine the reaction function for each firm. ATR1/AQ1 = 200 - 6Q1 - 3Q2 ATR2/ 4Q2 = 200 - 3Q1 - 6Q2 Setting MR1 = MC Setting MR2 = MC2 200 - 6Q1 - 3Q2 = 26 200 - 3Q1 -6Q2 = 32 6Q1 = 174 - 3Q2 6Q2 =168 -3Q1 Q1= 29 - = Q2 Q2= 28 -= Q1 Firm 1 Reaction Function Firm 2 Reaction Function b. Calculate each firm's equilibrium output. Firm 1 Firm 2: 21= 29 - (28 -401) 22= 28 - )= 18 Q1 = 29 - 14 + 1/4Q 1 Q1 - 1/4Q1 = 15 3Q1/4 = 15 15 x = = 20 The equilibrium output for firm one is 20 and the equilibrium output for firm 2 is 18.c. Calculate the equilibrium market price. P = 200 - 3(Q1 + Q2) P = 200 - 3(20+18) P = 200 - 114 = $86 The equilibrium market price is $86 d. Calculate the profit each firm earns in equilibrium. Firm's 2 Profit Firm's 1 Profit = P * Q1 - TC = P * Q1 -TC = 86 * 18 - 32 * 18 = $972 = 86 * 20 - 26 * 20 = $1200 The profit for firm two is $972 The profit for firm one is $1200