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Answers to Selected Questions in Practice Problem Set 3 ECON 11 Summer Session C 2010 Microeconomic Theory Yong Yang 1. [Production and cost] (a) L = 1 (b) q = L yields L = q 2 . (c) The cost is 100 L , so the cost function is 100 q 2 . (d) MC = 200 q and AC = 100 q . A figure is omitted. (e) The cost is wL = 300 L - L 2 . Since L = q 2 , the cost function is C ( q ) = 300 q 2 - q 4 . (f) MC = 600 q - 4 q 3 and AC = 300 q - q 3 . (g) MC = AC gives 300 q = 3 q 3 , so q = 10. (h) A figure is omitted. Both MC and AC are cubic functions, and MC lies above AC for q < 10, but below for q > 10. Make sure that AC reaches its maximum at q = 10. 2. [Optimal choice of inputs] (a) MP L = K 2 L , and MP K = L 2 K . (b) MRTS = MP L /MP K = K/L . (c) Let K/L = 4 / 9 and solve with 30 = LK , then L = 45 and K = 20. (d) The cost is P L L + P K K = 360. P L L is 180, so half of the total cost was distributed to the labor, and the same for capital. (e) Let K/L = 9 / 9 and solve with 30 = LK , then L = 30 and K = 30. (f) The cost is 540, and both the labor share and the capital share are half of the total cost. (g) The statement is true. For Cobb-Douglas production function, the labor share is always fixed no matter what the input price ratio is and what amount is produced. (h) For P L = P K = 4, we have L = K = 30, and the labor share is half of the total cost. P L = 9 and P K = 4 yields L = 20 and K = 45, and the labor share is half of the total cost.

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