Chapter 5

1. You have been hired to replace the manager of a firm that uses only two inputs, capital

and labor, to produce output. The firm can hire as much labor as it wants at a wage

of $5 per hour and can rent as much capital as it wants at a price of $50 per hour. After

you look at the company books, you learn that the company has been using capital and

labor in amounts that imply a marginal product of labor of 50 and a marginal

product of capital of 100. Use the cost minimizing input rule to explain what action you should take.

2.The manager of a meat packing plant can use either butchers (labor) or meat saws (capital) to prepare packages of sirloin steak. Based on estimates provided by an efficiency expert, the firm’s production function for sirloin steak is given by:

Q = K + L

a. Graph the isoquant corresponding to 5 units of output.

b. What is the marginal product of capital and labor? Does the answer depend on how

much labor and capital are used?

c. If the price of labor is $2 per hour, and the rental price of capital is $3 per hour,

how much capital and labor should be used to minimize the cost of production of the 5 units of output?

3.The manager of a national retailing outlet recently hired an economist to estimate the firm’s production function. Based on the economist’s report, the manager now knows that the firm’s production function is given by Q = K^1/2 L^1/2 and that capital is fixed at 1 unit.

a. Calculate the average product of labor when 9 units of labor are utilized.

b. Calculate the marginal product of labor when 9 units of labor are utilized.

4.An accountant for a car rental company was recently asked to report the firm’s costs of producing various levels of output. The accountant knows that the most recent estimate available of the firm’s cost function is C (Q) = 100 + 10Q +Q^2, where costs are measured in thousands of dollars and output is measured in thousands of hours rented.

a. What is the average fixed cost of producing 2 units of output?

b. What is the average variable cost of producing 2 units of output?

c. What is the average total cost of producing 2 units of output?

d. What is the marginal cost of producing 2 units of output?

5. You are the manager of the firm that sells output at a price of $40 per unit. You are

interested in hiring a new worker who will increase your firms output by 2,000 units

per year. Several other firms are also interested in hiring this worker.

a. What is the most you should be willing to pay this worker to come to your firm?