Question

3. Suppose a firm has the production function Q = 50 KL

1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units?

2) Using the solution in part 1), what will the firm’s long-run total cost be?

Answer 1

0 - 50 KL MPL = du/IL MPL = 50K MPK = delak IMPK = 50 L wadio R = 35 (wage rate) (rental ride). at cest minimize point, MPL HPK - w SUL > Soko - k-2 = 1 k = 2L - (1) Put u in production for. 0 = 50KL Q = 50 (2) ا حماده - > L = To (labor demand for) demand - 10 lond, K= 2L 1993 >> K-2 - & K ro (capital demand fn). lo deca

Put ce= 40000 in Lubor and capital demond fr. وهو : او ص140 داو هه =L 40000 - 200 20 lo 200 K To » K= 140000 > x= 20 => 1K = 40] 40 units of capital and zo units of Labor edhe firm should employed in the long run to maimize the cost of producing 40ow units. Un 6. Long dan cest fni c= WL t RK Y c = (w To + (5) To ca Totte [ c = 2.5o. (lung aun cast fon). ona Gun Ce