Microeconomics Theory - Production and Cost Function
A firm has the following production function Q and cost function as follows:
Q= KL where Q = quantity, K=capital, L=labor
C= 3L +12K where C= cost
Calculate the cost when the firm produced 36 units.
Hint: In equilibrium, where MPK and MPL are marginal products of capital and labor respectively; and w and r are cost of capital and labor.
The answer is 72.
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1 solution
Given Q=KL . MPK=dQ/dK=L and MPL=dQ/dL=K. In equilibrium, MPK/r=MPL/w. Therefore, L/r=K/w. Rewrite this, L= 4K or K=L/4.Now we can substitute this into the production function and find K and L. KL=36, hence, 36/K=4K. K=3 and L= 12. Also given C= 3L +12K. Therefore, C= 36+36= 7 2