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.
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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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