## Marginal Revenue Exercise

1. Will an increase in the demand for a monopolist's product always result in a higher price? Explain. Will an increase in the supply facing a monopsonist buyer always result in a lower price? Explain.

2. Caterpillar Tractor is one of the largest producers of farm tractors in the world. They hire you to advise them on their pricing policy. One of the things the company would like to know is how much a 5 percent increase in price is likely to reduce sales. What would you need to know to help the company with their problem? Explain why these facts are important.

3. A firm faces the following average revenue (demand) curve:

p = 100 - 0.01 Q where Q is weekly production and P is price, measured in cents per unit. The firm's cost function is given by C = 50Q + 30,000. Assuming the firm maximizes profits, a. What is the level of production, price, and total profit per week?

b. The government decides to levy a tax of 10 cents per unit on this product. What will the new level of production, price, and profit be as a result?

4. The table below shows the demand curve facing a monopolist who produces at a constant marginal cost of \$10:

 Price Quantity 27 0 24 2 21 4 18 6 15 8 12 10 9 12 6 14 3 16 0 18

a. Calculate the firm's marginal revenue curve.

b. What are the firm's profit-maximizing output and price? What is the firm's profit?

c. What would the equilibrium price and quantity be in a competitive industry?

d. What would the social gain be if this monopolist were forced to produce and price at the competitive equilibrium? Who would gain and lose as a result?

5. A firm has two factories, for which costs are given by:

Factory #1: C,(Q0 = 10Q? Factory #2: C2(Q2) = 20Qi The firm faces the following demand curve:

P =700 - 5Q where Q is total output, i.e., Q = Qi + Qi.

a. On a diagram, draw the marginal cost curves for the two factories, the average and marginal revenue curves, and the total marginal cost curve (i.e., the marginal cost of producing Q = Qi + Qi). Indicate the profit-maximizing output for each factory, total output, and price.

b. Calculate the values of Qi, Qi, Q, and P that maximize profit.

c. Suppose labor costs increase in Factory #1 but not in Factory #2. How should the firm adjust (i.e., raise, lower, or leave unchanged): Output in Factory #1? Output in Factory #2? Total output? Price?

6. A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The costs of production for the two plants are MCi = 20 + 2Qi, and MCi = 10 + 5 <22. The firm's estimate of the demand for the prod uct is P = 20 - 3(Qi + Qi). How much should the firm plan to produce in each plant, and at what price should it plan to sell the product?

7. One of the more important antitrust cases of this century involved the Aluminum Company of America (Alcoa) in 1945. At that time, Alcoa controlled about 90 percent of primary aluminum production in the United States, and the company had been accused of monopolizing the aluminum market. In its defense, Alcoa argued that although it indeed controlled a large fraction of the primary market, secondary aluminum (i.e., aluminum produced from the recycling of scrap) accounted for roughly 30 percent of the total supply of aluminum, and many competitive firms were engaged in recycling. Therefore, Alcoa argued, it did not have much monopoly power.

a. Provide a clear argument in favor of Alcoa's position.

b. Provi de a clear argument against Alcoa's position.

c. The 1945 decision by Judge Learned Hand has been called "one of the most celebrated judicial opinions of our time." Do you know what Judge Hand's ruling was?

8. A monopolist faces the demand curve P = 11 -Q, where P is measured in dollars per unit and Q in thousands of units. The monopolist has a constant average cost of \$6 per unit.

a. Draw the average and marginal revenue curves, and the average arid marginal cost curves. What are the monopolist's profit-maximizing price and quantity, and what is the resulting profit? Calculate the firm's degree of monopoly power using the Lerner index.

b. A government regulatory agency sets a price ceiling of \$7 per unit. What quantity will be produced, and what will the firm's profit be? What happens to the degree of monopoly power?

c. What price ceiling yields the largest level of output? What is that level of output? What is the firm's degree of monopoly power at this price?

9. Michelle's Monopoly Mutant Turtles (MMMT) has the exclusive right to sell Mutant Turtle t-shirts in the United States. The demand for these t-shirts is Q = 10,000/Pi. The firm's short-run cost is SRTC = 2000 + 5Q, and its long-run cost is LRTC = 6Q.

a. What price should MMMT charge to maximize profit in the short run? What quantity does it sell, and how much profit does it make? Would it be better off shutting down in the short run?

b. What price should MMMT charge in the long run? What quantity does it sell and how much profit does it make? Would it be better off shutting down in the long run?

c. Can we expect MMMT to have lower marginal cost in the short run than in the long run? Explain why.

10. The employment of teaching assistants (TAs) by major universities can be characterized as a monopsony. Suppose the demand for TAs is W = 30,000 -125n, where W is the wage (as an annual salary), and n is the number of TAs hired. The supply of TAs is given by W = 1000 + 75n.

a. If the university takes advantage of its monop-sonist position, how many TAs will it hire? What wage will it pay?

b. If, instead, the university faced an infinite supply of TAs at the annual wage level of \$10,000, how many TAs would it hire?

*11. Dayna's Doorstops, Inc. (DD), is a monopolist in the doorstop industry. Its cost is C = 100 - 5Q + Qi, and demand is P = 55 - 2Q.

a. What price should DD set to maximize profit, and what output does the firm produce? How much profit and consumer surplus does DD generate?

b. What would output be if DD acted like a perfect competitor and set MC = PI What profit and consumer surplus would then be generated?

c. What is the deadweight loss from monopoly power in part (a)?

d. Suppose the government, concerned about the high price of doorstops, sets a maximum price for doorstops at \$27. How does this affect price, quantity, consumer surplus, and DD's profit? What is the resulting deadweight loss?

e. Now suppose the government sets the maximum price at \$23. How does this affect price, quantity, consumer surplus, DD's profit, and deadweight loss?

f. Finally, consider a maximum price of \$12. What will this do to quantity, consumer surplus, profit, and deadweight loss?

*12. There are 10 households in Lake Wobegon, Minnesota, each with a demand for electricity of Q - 50 - P. Lake Wobegon Electric's (LWE) cost of producing electricity is TC = 500 + Q.

a. If the regulators of LWE want to make sure that there is no deadweight loss in this market, what price will they force LWE to charge? What will output be in that case? Calculate consumer surplus and LWE's profit with that price.

b. If the regulators want to make sure that LWE doesn't lose money, what is the lowest price they can impose? Calculate output, consumer surplus, and profit in that case. Is there any deadweight loss?

c. Kristina knows that deadweight loss is something that this small town can do without. She suggests that each household be required to pay a fixed amount just to receive any electricity at all, and then a per-unit charge for electricity. Then LWE can break even while charging the price you calculated in part (a). What fixed amount would each household have to pay for Kristina's plan to work? Why are you sure that no household will choose instead to refuse the payment and go without electricity?

*13. A monopolist faces the following demand curve: Q = 144/P2

where Q is the quantity demanded and P is price. Its average variable cost is

a. What are its profit-maximizing price and quantity? What is the resulting profit?

b. Suppose the government regulates the price to be no greater than \$4 per unit. How much will the monopolist produce, and what will its profit be?

c. Suppose the government wants to. set a ceiling price that induces the monopolist to produce the largest possible output. What price will do this? 