Question

3. A firm’s production function is Q=min(K, 3L ). Input prices a re as follows: w=$ 2 and r=$1.

On the optimal choice diagram below, draw the isoquant for Q=12. Calculate the optimal choice of K and L for this level of output as well as the total cost.

Then, draw in (with a dotted line) the isocost line consistent with your Total Cost value.

It won't let me copy the graph template but it is a simple graph with K as the vertical axis and L as the horizontal axis.

Answer 1

The production function is Q=min(K, 3L) with w=$ 2 and r=$1.

For Q=12, the optimal choice of K and L must have K = 3L. This suggests that we have

12 = min(K, 3L) where 12 = K and 12 = 3L or L = 4. Hence optimal input mix is K = 12, L = 4. Cost function is C = wL + rK or C = 2L + K. Using Q = K and Q = 3L we have L = Q/3 and K = Q. Cost function becomes C = 2Q/3 + Q or C = 5Q/3

For Q = 12, C = 5*12/3 = $20