Question 2: Suppose a firm has the following production function: Q(L, K) = min

Question

Question 2: Suppose a firm has the following production function: Q(L, K) = min { K, 4L) Recall that the isocost line is as follows: C=wL + rK 1. What is the (long-run) optimal choice of L and K for a given Q, w, and r? In other words,provide a formula for the optimal choice of labor L"(w, r, Q) and capital K*(w,r, ) as a function of the parameters Q, w, and r 2. Given Q 16, w = 4, and r = 1 , what are the optimal levels of labor and capital, L* and K * ? What is the cost of producing Q = 16 at these input prices? 3. Suppose now that you are in the short run, Q = 16, w-4, r-1, and the capital level is fixed at K = 20, what is the optimal level of labor in the short run? What is the cost of producing Q = 16 in the short run at these input prices? Would it be possible to meet Q = 16 if K = 4 in the short run?

Explanation / Answer

2) K*(w,r,Q)=Q

L*(w,r,Q)=1/4Q

K*(4,1,16)=16

L*(4,1,16)=1/4*16=4

Q(L)=min(20,4L)

Q(L)=4L

Q(L)=min(4,4L)

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