Question

Consider a firm with long-run production function [ Q=f(L, K)=3 dot qrt{L dot K} ] where ( Q ) is output, ( L ) is labor input, and ( K ) is capital input. Input prices are ( w=1 ) and r=4 per unit of labor and capital, respectively. Suppose, capital is fixed at level k=k" in the short-run. Find the firm's total cost function in the short-run?

Answer 1

In the short run, the firm's total cost function is TC = w imes L.

Step-by-step explanation:

In the short run, the firm's production function is Q = f[L] since capital is fixed. This means that the firm's output (Q) depends only on the amount of labor (L) employed. To find the firm's total cost function in the short run, we need to consider the cost of labor. The cost of labor is given by the labor input (L) multiplied by the wage rate (w=1). Therefore, the firm's total cost function in the short run is TC = w imes L.