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 after the wage decrease, the new profit-maximizing level of production increases from Q* = 2 to Q** = 4. Draw the new profit-maximizing isoquant on the same graph and label it “Q**=4.” Illustrate the scale effect graphically. Next, find the new profit-maximizing choice of labor, L*, which will incorporate both the substitution effect and the scale effect. What is the new profit-maximizing choice of capital, K*, which also incorporates both the substitution and scale effects?