Question 1 Suppose a firm has the production function Q K04

Question 1. Suppose a firm has the production function Q = K0.4L0.6. The wage rate is given by w and the rental rate of capital is given by r. Find the firm’s demand functions for K and L. Suppose the firm is currently producing Q = 100 units of output. Suppose it receives an order for 150 units of output. What will it do?

Solution

Ans: Given that the wage is w and the rental rate is r. The production function is given by Q=K^0.4 L^0.6

The optimum solution is where MPL/MPK = w/r

Here we have that MPL= 0.6 (K/L)^0.4 and MPK = 0.4 (L/K)^0.6

Thus, Solving this, MPL/MPK = w/r , we get that (K/L) = (2w/3r).

From this we have that K= (2wL)/3r and L=(3rK/2w).

In case the firm receives an order for 150 units it should invest in taking more of that input where the marginal product is more. This will enable it to do the additional production at the most efficient cost setting.