# F09H2ak - Econ 467 Maria Muniagurria Answer Key Homework...

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Econ 467 Maria Muniagurria Answer Key Homework 2 (I) Consider two identical firms (Firm 1 and Firm 2) that produce an homogenous product. The demand for their product is : P= 200 -Q, where Q= q 1 + q 2 . Each firm has a cost function: C(q i ) = 20 q i ( i.e. the Mc i is 20 and there are no fixed costs) (1) Calculate the Stakelberg equilibrium assuming that Firm 1 is the Leader and Firm 2 the Follower (i.e. calculate the SPNE assuming that Firm 1 moves first). (a) Step 1: calculate the reaction function for firm 2. Done in another problem: (*) q 2 = (180 - q 1 ) / 2 . (b) Step 2 : calculate the profit maximizing q 1 assuming that firm 2 will behave according to its reaction function. Choose q 1 to maximize Π 1 (q 1 , q 2 ) assuming q 2 is given in equation (*): Π 1 (q 1 ) = [200 - q 1 - ( (180 - q 1 ) / 2 )] q 1 - 20 q 1 = [180- q 1 - ( (180 - q 1 ) / 2 )] q 1 . Setting the first derivative equal to zero : d Π 1 ( ) / d q 1 = (180 /2 ) - 2q 1 + q 1 = 0 then : q 1 = 90, q 2 = 45, p= 65 ,

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F09H2ak - Econ 467 Maria Muniagurria Answer Key Homework...

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