# 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.