Question

1. A plant's production function is Q = (L4/2 + K1/2)2. The price of labor is $10 per unit, and the price of capital is $30 per unit. In the short-run, capital is fixed at 9 units. The plant has a production quota of 1600 units of output that it must meet. a. Calculate the short-run minimum cost of producing 1600 units of output. (5 points) b. Assuming that the plant still meets its production quota, how much will it cost in the long- run? (7 points) c. Use isoquant(s) and isocost(s) to graphically illustrate your answers to (a) and (b). Use this graph to compare your long-run and short-run input levels as well as your long-run and short- run costs. (10 points)

Answer 1

Walo r = 30 K=9 0 O=(22+kk) 2 0=1600 0=1600= (2+ q 2 2 400 = 1h in yo=ch. you ik + 3 2=32² = 1369 Cost = 13690+270=43960 13960 In toy rin MKTS=w VE 28 Lh+k'a) kth * = 4 [2=9k] put into L 16005 Celk + kk)? 40=3K²+k akk 40=4kh (K=100] 4K2900] TC = 9ooot loo(30) = 12000 You C900, 100) -1600 1369 900 1200