Consider The Production Function

Consider the production function Q = K1/2L1/2, where L is the quantity of the labor input, K is the quantity of the capital input, and Q is the quantity of the output good. Suppose we know that Q* = 2 is the profit-maximizing level of output. The price of labor, W, is 10 and the price of capital, C, is 4.

Suppose that the wage, W, decreases from 10 to 7. Illustrate the substitution effect graphically. Next, find the new profit-maximizing choice of labor, L*, if only a substitution effect occurred (and no scale effect). Finally, what is the new profit-maximizing choice of capital, K*, again assuming that only the substitution effect is present and not the scale effect.