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DSME6651 Economics Analytics

Homework #2

1. Wendy gets utility from reading books (B) and watching movies (M). Her utility function is given by . The price for a book is 80 and a movie ticket costs 120. Wendy’s income is 4,800. What is Wendy’s utility-maximizing consumption bundle of books and movies?

2. A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $10 per hour and capital is rented at $15 per hour. If the marginal product of labor is 70 units of output per hour and the marginal product of capital is 120 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital used in its production process?

3. A multiproduct firm’s cost function was recently estimated as

a. Are there economies of scope in producing product 1 and product 2?

b. Are there cost complementarities in producing products 1 and 2?

c. Suppose the division decide to sell the rights to produce product 2. How would the change the firm’s marginal cost of producing product 1?

4. You are a manager at Glass Inc.—a mirror and window supplier. Recently, you conducted a study of the production process for your single-side encapsulated window. The results from the study are summarized in the table below and are based on the 8 units of capital currently available at your plant. Workers are paid $65 per unit of labor, per unit capital costs are $20, and your encapsulated windows sell for $12 each. Given this information, optimize your human resource and production decisions. Do you anticipate earning a profit or a loss in the short run?

5. A firm sells its product in a perfectly competitive market where other firms charge a price of $75 per unit. The firm’s total costs are .

a. How much output should the firm produce in the short run?

b. What price should the firm charge in the short run?

c. What are the firm’s short-run profits?