ECO 110M (1645)
Fall 1999
ANSWERS to HOMEWORK #4

1. A competitive firm faces a more elastic demand curve than a monopolist; in fact, a competitive firm faces a perfectly elastic demand curve since it is a price taker. The larger elasticity arises when a good has many perfect substitutes.

FIGURE 1

3. a. The following table shows total revenue and marginal revenue for each price and quantity sold:

b. Profits are maximized at a price of $16 and quantity of 50,000. At that point, profit is $550,000.

c. As Johnny's agent, you should recommend that he demand $550,000 from them, so he gets all the profit instead of the record company.

4. a. The following table shows revenue and marginal revenue for the bridge:

The profit-maximizing price would be where revenue is maximized, which will occur where marginal revenue equals zero, since marginal cost equals zero. This occurs at a price of $4 and quantity of 400. The efficient level of output is 800, since that's where price equals marginal cost equals zero. The profit-maximizing quantity is lower than the efficient quantity because the firm is a monopolist.

b. The company shouldn't build the bridge because its profits are negative. The most revenue it can earn is $1,600,000 and the cost is $2,000,000, so it would lose $400,000.

c. If the government were to build the bridge, it should set price equal to marginal cost to be efficient. But marginal cost is zero, so the government shouldn't charge people to use the bridge.

d. Yes, the government should build the bridge, because it would increase society's total surplus. As shown in Figure 2, total surplus has area 1/2 x 8 x 800,000 = $3,200,000, which exceeds the cost of building the bridge.

FIGURE 2

FIGURE 3

6. Though Rod Stewart has a monopoly on his own singing, there are many other singers in the market. If Stewart were to raise his price too much, people would substitute to other singers. So there's no need for the government to regulate the price of his concerts.

FIGURE 4

b. The monopolist's profit consists of the two areas labeled X, consumer surplus is the two areas labeled Y, and the deadweight loss is the area labeled Z.

d. The monopolist's profit increases from X to X+Y+Z, an increase in the amount Y+Z. The change in total surplus is area Z. The rise in monopolist's profit is greater than the change in total surplus, since monopolist's profit increases both by the amount of deadweight loss (Z) and by the transfer from consumers to the monopolist (Y).

e. A monopolist would pay the fixed cost that allows it to discriminate as long as Y+Z (the increase in profits) exceeds C (the fixed cost).

f. A benevolent social planner who cared about maximizing total surplus would want the monopolist to price discriminate only if Z (the deadweight loss from monopoly) exceeded C (the fixed cost) since total surplus rises by Z - C.

g. The monopolist has a greater incentive to price discriminate (it will do so if Y+Z>C) than the social planner would allow (she would allow it only if Z>C). Thus if Z<C but Y+Z>C, the monopolist will price discriminate even though it's not in society's interest.

8. a. If there were many suppliers of diamonds, price would equal marginal cost ($1 thousand), so quantity would be 12 thousand.

b. With only one supplier of diamonds, quantity would be set where marginal cost equals marginal revenue. The following table derives marginal revenue:

With marginal cost of $1 thousand per diamond, or $1 million per thousand diamonds, the monopoly will maximize profits at a price of $7 thousand and quantity of 6 thousand. Additional production would lead to marginal revenue (0) less than marginal cost.

c. If Russia and South Africa formed a cartel, they would set price and quantity like a monopolist, so price would be $7 thousand and quantity would be 6 thousand. If they split the market evenly, they'd share total revenue of $42 million and costs of $6 million, for a total profit of $36 million. So each would produce 3 thousand diamonds and get a profit of $18 million. If Russia produced 3 thousand diamonds and South Africa produced 4 thousand, the price would decline to $6 thousand. South Africa's revenue would rise to $24 million, costs would be $4 million, so profits would be $20 million, which is an increase of $2 million.

d. Cartel agreements are often not successful because one party has a strong incentive to cheat to make more profit. In this case, each could increase profit by $2 million by producing an extra thousand diamonds. Of course, if both countries did this, both would lose profits.

9. a. Dropping the letter grade by two letters (e.g., A to C) if you have no fun gives the payoffs shown in this table:

b. The likely outcome is that both of you will shirk. If your classmate works, you're better off shirking, because you'd rather have an overall B (a B grade and fun) then an overall C (an A grade and no fun). If your classmate shirks, you're indifferent between working for an overall D (a B grade with no fun) and shirking for an overall D (a D grade and fun). So your dominant strategy is to shirk. Your classmate faces the same payoffs, so will also shirk. But, if you're likely to work with the same person again, you have a greater incentive to work, so that your classmate will work, so you'll both be better off. In repeated games, cooperation is more likely.