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Econ 200 Practice Midterm Solution

# Econ 200 Practice Midterm Solution - Answer Key Midterm...

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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 π = π 1 + π 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 π 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 + π 2 ( q 1 ) Here p 1 ( q 1 ) = 20 - q 1 + p 2 = 3 2 (20 - q 1 ) (this is the consumer’s willingness to pay in period 1) FOC : 30 - 3 q 1 - 20 - q 1 2 = 0 q 1 = 8 and q 2 = 6 π = 180 2. a. Solve this game using backwards induction. Given q A , B solves max q B 1 - q A + q B 1000 - 0 . 28 q B The f.o.c. is 0 . 72 - q A 1000 - 2 q B 1000 = 0 , 1

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so q B = 720 - q A 2 . Anticipating this, A solves max q A 1 - q A 1000 - 720 - q A 2000 - 0 . 28 q A The f.o.c. is 0 . 72 - 2 q A 1000 - 720 - 2 q A 2000 = 0 , so q A = 360 , q B = 180 . Therefore P = 1 - 540 1000 = . 46 , π A = 360( . 46 - . 28) = 64 . 80 , π B = π A 2 = 32 . 40 .
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Econ 200 Practice Midterm Solution - Answer Key Midterm...

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