1. Assume that a firm uses two inputs: capital and skilled labor. a. Use an isoquant-isocost diagram to show how the firm will change its use of skilled labor if there is a decrease in the wage rate

1. Assume that a firm uses two inputs: capital and skilled labor. 

a. Use an isoquant-isocost diagram to show how the firm will change its use of skilled labor if there is a decrease in the wage rate paid to skilled labor.

b. On the same diagram, decompose the total change in skilled labor into substitution and scale effects. Please carefully indicate the total effect, the substitution effect, and the scale effect.

2. Existing empirical evidence indicates that the capital and unskilled labor are gross substitutes.

a. Based on the information that capital and unskilled labor are gross substitutes, show how the demand curve for capital changes when there is a decrease in the wage paid to unskilled labor.

b. Based on the information that capital and unskilled labor are gross substitutes, use an isoquant-isocost diagram to show the substitution and scale effects of a decrease in the wage paid to unskilled labor on the firm’s optimal use of capital. Please put capital on the vertical axis and unskilled labor on the horizontal axis.

3. Suppose labor and capital are perfect substitutes in production. Suppose that the production function describing this relationship is Q = 2E + 6K. Given this production function, the technology indicates that 1 unit of capital can do the work of 3 workers (you should be able to show this). The firm wants to produce 100 units of output. Suppose that the price of capital is $750, and the price of labor is $300. How much capital will the firm use? How much labor will the firm use? I suggest that you draw a graph to help yourself along.

4. Consider a firm for which production depends on two normal inputs capital and labor, with prices r and w, respectively. Initially the firm faces market prices of w = 6 and r = 4. Then both of these prices fall to w = 4 and r = 2. No diagram is necessary for this problem.

a. In which direction will the substitution effect change the firm’s employment of labor? Why?

b. In which direction will the scale effect change the firm’s employment of labor? Why?

c. Can we say conclusively whether the firm will use more or less labor? Why or why not? 

5. Consider the situations described below. For each situation described, state and explain one Hicks-Marshall Law of derived demand that best applies. 

a. University professors resist a university policy that allows graduate students to teach undergraduate classes.

b. The demand for unskilled labor in a labor-intensive industry is more elastic than the demand for labor in a capital-intensive industry.

c. The demand for labor for workers making insulin is more inelastic than the demand for labor for workers making aspirin.

d. You are analyzing the elasticity of demand for airlines pilots and learn that U.S laws are changed so that foreign airlines are allowed to fly domestic routes