Question

1. Suppose a firm wants to minimize the costs associated with producing according to function: q = f(L,K) = [1/3,2/3, where w, the cost of labor, is 8 and r, the cost of capital, is 2. w a. Find the cost minimizing combination of labor and capital for producing 8 goods. How much will they cost to make? b. Illustrate your answer to part a with an isoquant/isocost drawing. c. Find the cost function C(8,2,q) (Note: go through the same process of solving as you did in part a, just don't solve for a specific value of q).

Answer 1

b K Iso cost Cor 24 Isoquant 16 q=8 7 o 2* L 6 w e Cost function t TC= col trk 2 k 82 z) C = 82 t +2 (8L) 2 82 + 16L 24L 12 2/3 Now , K 2² 228 L q= 23 x 2 - L' (8L) 42 4Lz q 3) 242= 6q [e=6q