Answer Key - Problem Set 4

# Answer Key - Problem Set 4 - Econ 102 Prof Akbulut Answer...

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Econ 102 Prof. Akbulut Answer Key - Problem Set 4 (10 points) 1. (3 pts.) Nicholson Ch. 7, Problem 7.2 q = kl - 0.8 k 2 -0.2 l 2 a) When k=10 q = 10 l - 80 -0.2 l 2 This is the total product curve. At it’s maximum, MP l = 0. MP l = dq/dl = 10 – 0.4 l = 0 max. of the total product curve is at l = 25. d 2 q/dl 2 = -0.4 The total product curve is concave. AP l = q/l = 10 – 80/ l - 0.2 l AP l = 0 where l = 10, and where l = 40. AP l is at it’s maximum when d AP l / dl = 0. d AP l / dl = 80/ l 2 - 0.2 = 0 max. of AP l curve is at l = 20. When l = 20, q = 40 (40 widgets are produced) AP l MP l Quantity ( q ) 45 25 Labor Input ( l ) Labor Input ( l ) TP l 10 10 20 25 40 MP l AP l

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b) MP l = 10 – 0.4 l MP l = 0 at l = 25 See above graph. c) When k=20 q = 20 l - 320 -0.2 l 2 AP l = q/l = 20 – 320/ l - 0.2 l AP l is at it’s maximum when d AP l / dl = 320/ l 2 - 0.2 = 0 So the maximum of the average productivity of labor curve is at l = 40. When l = 40, q = 160. MP l = 20 – 0.4 l MP l = 0 at l = 50 d) Doubling of k and l here multiplies output by 4. Hence the function exhibits increasing returns to scale.
2. (4 pts.) For each production functions below, show if it has increasing, constant or decreasing returns to scale, and for parts (a) – (c) calculate the RTS(of

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## This note was uploaded on 04/07/2008 for the course ECON 102 taught by Professor Akbulut during the Spring '08 term at Claremont.

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Answer Key - Problem Set 4 - Econ 102 Prof Akbulut Answer...

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