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Answers to Selected Questions in Practice Problem Set 4 ECON 11 Summer Session C 2010 Microeconomic Theory Yong Yang 1. [Profit maximization] (a) MC = 20 + 2 Q so solving P = MC gives Q = 15. (b) C = 100 + 300 + 225 = 625 and thus π = PQ - C = 750 - 625 = 125. (c) V C = 20 Q + Q 2 , and AV C = 20 + Q . (d) MC = 20 + 2 Q . A figure is omitted. Make sure that MC lies above AV C everywhere. (e) The firm produces a positive amount as long as P is greater than the minimum of AV C . AV C is minimal at 20 when Q = 0. When P = 30, it produces Q = 5, but if P = 10, it produces nothing. (f) When P = 20 or below, it produces nothing. (g) When P = 40, it produces Q = 10 where C = 400. So π = PQ - C = 400 - 400 = 0. Firms would enter to get a positive profit when P = 50. They would exit if P = 30. There is no entry or exit at P = 40. (h) True. AC is 40 at its minimum with the given cost function, so entry and exit makes the price fixed at 40. 2. [Profit with long run cost] (a) The firm need to input L such that Q = 4 L , so L = 1 4 Q 2 . The short run cost function is C = P L L + P K K = Q 2 + 100. (b) V C = Q 2 , AC = Q + 100 Q , AV C = Q , and MC = 2 Q . (c) ∂AC ∂Q = 1 - 100 Q 2 is 0 when Q = 10. Also MC - AC = Q - 100 Q is 0 when Q = 10. (d) P = MC yields Q = 20. L = 1 4 Q 2 = 100 is required, C = 500, and π = 300. (e) MRTS = K/L , so the firm’s optimal input choice requires K/L = 25 / 4. Solving simultane- ously with Q = LK , the input demands are L = p 25 / 4 Q and K = p 4 / 25 Q . Then the long run cost function is C = P L L + P K K = 20 Q . (f) V C = 20 Q , AC = 20, AV C = 20, and MC = 20. (g) In (d), 20 was Q maximizing the short run profit. To produce 20 units, L = 50 and K = 8 by the input demands from (e). (h) P > MC everywhere, so the firm would produce infinite amount of outputs. This is more than Q = 20 in (d).

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