If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $5, then the cost minimizing combination of K and L capable of producing 2 units of output is
A) L = 0.35 and K = 0.35.
B) L = 1 and K = 0.50.
C) L = 0.50 and K = 1.
D) L = 1 and K = 1.
E) L = 1 and K = 0.50

Question

Quizplus · Accepted Answer

To minimize cost, we need to use the inputs in such a way that the marginal cost of production is equal for both inputs.

The marginal cost of producing 1 unit of output with respect to K is 4L, and the marginal cost of producing 1 unit of output with respect to L is 4K. We can set these two marginal costs equal to each other:

4L = 4K
L = K

Now we can use the production function to find the optimal values of K and L:

2 = 4LK
2 = 4K^2
K = 0.5

Therefore, L = K = 0.5, which corresponds to choice B.

If Output Is Produced According to Q = 4LK, the Price