solutionproblemset6 - UCLA Economics 11 Fall 2006 Professor...

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UCLA Economics 11 – Fall 2006 Professor Mazzocco Problem Set 6 Answer Key 1) Suppose the production function for widgets is given by: Q=KL - 0.8K 2 – 0.2L 2 a) Suppose K=10, graph the total and average productivity of labor curves. b) At what level of labor input does the average productivity reach a maximum? How many widgets are produced at this point? c) Again, assuming K=10, graph the MPL curve. At what level of labor input does MPL=0? d) Does this production function exhibit constant, increasing or decreasing returns to scale? Answer: a) total productivity: Q=10L-80-0.2L 2 average productivity: APL = 10 – 80/L -0.2L b) Max APL L=20, q=25 c) MPL=10 – 0.4L MPL=0 when L=25 d) Increasing returns to scale 2) Suppose that a production function is given by q=L+K 0.5 , where v is the price of K and w is the price of L. a) Find the marginal productivity of labor and capital. b) Find the most efficient combination of inputs for producing 347 units of output when w=4 and v=1.
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