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Unformatted text preview: Answer Key: Midterm Exam 1. a. Just charge the monopoly rental rate at each period Max p (20 p ) FOC : 20 = 2 p p = 10 = 1 + 2 = 2(10(20 10)) = 200 b. The inability to commit in period 1 will make the monopolist maximize period 2 profits given the residual demand in period 2. This residual demand in period 2 is given by q 2 = 20 p 2 q 1 and the monopolist solves Max p 2 p 2 (20 p 2 q 1 ) FOC : 20 2 p 2 q 1 p 2 = 20 q 1 2 2 ( q 1 ) = (20 q 1 ) 2 4 We find q 1 by maximizing the total profits over the two periods (anticipating optimal behavior in period 2) Max q 1 p 1 ( q 1 ) q 1 + 2 ( q 1 ) Here p 1 ( q 1 ) = 20 q 1 + p 2 = 3 2 (20 q 1 ) (this is the consumers willingness to pay in period 1) FOC : 30 3 q 1 20 q 1 2 = 0 q 1 = 8 and q 2 = 6 = 180 2. a. Solve this game using backwards induction. Given q A ,B solves max q B 1 q A + q B 1000 . 28 q B The f.o.c. is . 72 q A 1000 2 q B 1000 = 0 , 1 so q B = 720 q A 2 ....
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.
 Spring '08
 PHILIPHAILE
 Monopoly

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