Answer to Question #101215 in Microeconomics for Yohannes

Question

What is the long run cost function if the production function is q=L+K?

Answer 1

It is well known that in the long-term, the total costs of L and K will be minimized, provided that the marginal product of labor divided by the marginal product of capital (k) is equal to the price per unit of labor costs divided by the price per unit of capital investment.

In the form of formulas, it looks like:

MPL / MPK = w / r

Respectively:

MPL = 1

IPC = 1

1/1 = w / r

w = r

Based on the long-term cost structure of the company:

TC = wL + rK

we can replace w with r, the cost function LR will be:

TC = wL + wK

TC = w (L + K)

And since q = L + K, we get:

TC = w (L + K)

TC = w * q

Answer:

TC = w * q