Question

24. The production function is f(L,K)=4L”? K12, where L is the number of units of labour and K is the number of units of capital used. If the cost of labour is $36 per unit and the cost of capital is $4 per unit, then the minimum cost of producing 12 units of output will be a. $144. $72. c. $240. d. $24. e. $120

Answer 1

The Answer is (b) $72

Please refer to the cost minimization problem the firm will face, i.e., minimize input cost subject to the production function.

LIK Men (36L + 4k] sit. 4 K 2 = 12 The Lagrangian is L=36L+4K + x[12-422 4²2] Foclan - 361 (4) 1 K ² - 36 = 2(2) [/24/2 2x = 4-(4) LRK 4 = x(2) 1/2 2 at - 12-4² x 2 = 0 - 44² k 12 = 12 From and 36 = XL [ K2 [dividing (1) by (2)] XXL K2 9 = - 9 L=k or L = k Using in ③ we get: 4. 1/2 (92) 12 = 12 » 4.12 3 12 = 12 - 12 L=12 TL = 1 I- From and , x=9L => 1K=91 6 . With L=1 and K=9, the total cost would be: c=362 +4K = (36x1) +(6x4) = 72 Hence, the minimum cost of producing 12 units of output will be $72.