Quantitative Problems

1.
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A firm that is made up of two divisions, A and B, generates revenues of $1000 from the sale of its output and incurs production costs of $600 every month. The owners of the firm anticipate that they could rent the firm to someone else for at most $300 a month.

(a) Calculate the firm's accounting, normal, supernormal, and economic profits.

Suppose that the current owners receive an offer from another firm to rent division A for $200 per month. If they accept this offer, then they anticipate that division B by itself will generate only $400 in revenues, at a production cost of $100 per month. Incidently, division B alone is worthless to anyone else.

(b) Recalculate the four profit measures. What are the firm's owners predicted to do?
2.
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A steel producer possesses the production function y = 10K 0.25 L0.75, where y is the quantity of steel, in metric tons, K is the firm's capital stock, and L is the number of labor hours it employs (measured in thousands).

(a) Assume the firm's current capital stock is fixed at K = 4096. If the firm employs L = 81 labor units, then how much steel does it produce?

(b) Suppose that the firm receives an order to produce 270 metric tons of steel. If its capital stock is fixed at K = 4096, then how many hours of labor must it employ to satisfy the order?

(c) In the long run, the firm is free to vary both its capital stock and the number of worker hours it employs. Given this, what happens to the firm's output if it doubles the amount of labor and capital it uses? What happens if it quadruples the amount? What does this result suggest in general?
3.
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The last 30 years or so have witnessed startling technology changes (the widespread use of the PC and the emergence of the Internet, being two prime cases in point). Discuss the likely effects of these technology changes on a typical firm's production function.
4.
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The facts are as follows: all markets are competitive; the product price is $p = $1 per unit; the wage rate is $W = 12 per hour; the firm's production function is , where L is the level of employment; and the firm's fixed costs are zero.

(a) Write down the firm's profits in terms of L.

(b) What is the marginal-revenue product and marginal cost of labor. (Hint: )

(c) Use your answer to (b) to calculate the profit maximizing level of employment, denoted L*. What are the firm's maximum profits?

(d) Suppose that the firm employs L* + 1 hours. What happens to its profits?
5.
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Good news! Dave landed a plum job as the manager of a division at a large corporation. Even better news! He has read scores of textbooks that demonstrate that setting the is necessary for profit maximization. Tragic news! After a mere year of employment, he was fired. His division made its largest recorded loss ever. What was Dave's mistake?
6.
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What is meant by monopoly power? Is it plausible that a firm may possess some monopoly power, but face a perfectly competitive labor market? Give an example.
7.
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Explain why, in the context of the monopsony model, a wage floor can raise the optimal level of employment.
8.
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Suppose that the firm possesses some monopsony power and that it faces the labor supply curve L = 2w. Assume the product market is competitive and that its product price is $p = $10. Finally, suppose that its marginal product of labor schedule is .

(a) Evaluate its and schedules.

(b) Characterize and calculate the optimal level of employment, L* and the optimal wage, $W*.

(c) What would happen to the optimal level of employment if a union imposes a wage floor of $40?

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