Principles of Microeconomics

Transcription

1 Principles of Microeconomics David C. Broadstock December 25, 2013 The following questions are to be completed by hand and submitted during the final class on December 23rd. Final homework questions Question 1 Suppose the book printing industry is competitive and begins in a long run equilibrium. Draw a diagram describing the typical firm in the industry. Hi-Tech printing company invents a new process that sharply reduces the cost of printing books. What happens to Hi-Tech s profits and the price of books in the short-run when Hi-Tech s patent prevents other firms from using the new technology? What happens in the long run when the patent expires and other firms are free to use the technology? Question 1: Solution Figure 7 shows the the typical firm in the industry, with average total cost ATC 1, marginal cost MC 1 and price P 1. 1

2 Figure 7 The new process reduces Hi-Tech s marginal cost to MC 2 nad its average total cost to ATC 2, but the price remains at P 1 since other firms cannot use the new process. Thus Hi-Tech earns positive profits. When the patent expires and other firms are free to use the technology, all firms average total cost curves decline to ATC 2, so the market price falls to P 3 and firms earn no profits. Question 2 Suppose the U.S. textiles industry is competitive, and there is no international trade in textiles. In long-run equilibrium, the price per unit of cloth is $30. part a Describe the equilibrium using graphs for the entire market and for the individual producer. part b Now suppose that textile producers in other countries are willing to sell large quantities of cloth in the united states for only $25 per unit. Assuming that U.S. textile producers have large fixed costs, what is the short run effect of these imports on the quantity produced by an individual 2

3 Figure 9 producer? What is the short run effect on profits? Illustrate your answer with a graph. What is the long run effect on the number of U.S. firms in the industry? Question 2: Solution part a Figure 9 illustrates the situation in the U.S. textile industry. With no international trade, the market is in long run equilibrium. Supply intersects demand at quantity Q 1 and price $30, with a typical firm producing output q 1. part b The effect of imports at $25 is that the market supply curve follows the old supply curve up to a price of $25, then becomes horizontal at that price. As a result, demand exceeds domestic supply, so the country imports textiles from other countries. The typical domestic firm now reduces its output from q 1 to q 2, incurring losses, since the large fixed costs imply that average total cost will be much higher than the price. In the long run, domestic firms will be unable to compete with foreign firms because their costs are too high. All the domestic firms will exit the industry 3

4 and other countries will supply enough to satisfy the entire domestic demand. Question 3 A publisher faces the following demand schedule for the next novel of one of its popular authors; P Q $ ,000 The author is paid $2 million to write the book, and the marginal cost of producing the book as a constant $10 per book. Compute total revenue, total cost, and profit at each quantity. What quantity would a profit maximising publisher choose? What price would it charge? Compute marginal revenue. (Recall that MR = TR.) How does marginal Q revenue compare to the price? Explain. Graph the marginal revenue, marginal cost, and demand curves. At what quantity do the marginal revenue and marginal cost curves cross? What does this signify? Part d In your graph, shade in the deadweight loss. Explain in words what this means. 4

5 Part e If the author were paid $3 million instead of $2 million to write the book, how would this affect the publisher s decision regarding the price to charge? Explain. Part f Suppose the publisher was not profit maximising but was concerned with maximising economic efficiency. What price would it charge for the book? How much profit would it make at this price? Question 3: Solution The following table shows revenue, costs and profits, where quantities are in thousands, and total revenue, total cost, and profit are in millions of dollars. P Q TR MR TC π $100 0 $0 $2 $ $ , A profit-maximising publisher would choose a quantity of 400,000 at a price of $60 or a quantity of 500,000 at a price of $50; both combinations would lead to profits of $18 million. Marginal revenue is always less than price. Price falls when quantity rises because the demand curve slopes downward, but marginal revenue falls even more than price because the firm loses revenue on all the units of the good sold when it lowers the price. 5

6 Figure 2 Figure 2 shows the marginal revenue, marginal cost, and demand curves. The marginal revenue and marginal cost curves cross between quantities of 400,000 and 500,000. This signifies that the firm maximises profits in that region. Part d The area of deadweight loss is marked DWL in the figure. Deadweight loss means that the total surplus in the economy is less than it would be if the market were competitive, since the monopolist produces less than the socially efficient level of output. Part e If the author were paid $3 million instead of $2 million, the publisher wouldn t change the price, since there would beno change in marginalcost or marginal revenue. The only thing that would be affected would be the firm s profit, which would fall. Part f To maximise economic efficiency, the publisher would set the price at $10 per book, since that s the marginal cost of the book. At that price, the publisher would have negative profits equal to the amount paid to the author. 6

7 Question 4 Johnny Rockabilly has just finished recording his latest CD. His record company s marketing department determines that the demand for the CD is as follows: P Q 24 10, , , , , ,000 The company can produce the CD with no fixed cost and a variable cost of $5 per CD. Find total revenue for quantity equal to 10,000, 20,000, and so on. What is the marginal revenue for each 10,000 increase in the quantity sold? What quantity of CD s would maximise profit? What would the price be? What would the profit be? If you were Johnny s agent, what recording fee would you advise Johnny to demand from the record company? Why? Question 4: Solution The following table shows total revenue and marginal revenue for each price and quantity sold: 7

8 P Q TR MR TC π 24 10,000 $240,000 $50,000 $190, , ,000 $20 100, , , , , , , , , , , , , , , , , ,000 Profits are maximised at a price of $16 and quantity of 50,000. At that point profit is $550,000. As Johnny s agent, you should recommend that he demand $550,000 from them, so he instead of the record company receives all of the profit. Question 5 A company is considering building a bridge across a river. The bridge would cost $2 million to build and nothing to maintain. The following table shows the company s anticipated demand over the lifetime of the bridge: P Q $ If the company were to build the bridge, what would be its profit maximising price? Would that be the efficient level of output? Why or why not? 8

9 If the company is interested in maximising profit, should it build the bridge? What would be its profit or loss? If the government were to build the bridge, what price should it charge? Part d Should the government build the bridge? Explain. Question 5: Solution The table below shows total revenue and marginal revenue for the bridge. The profit maximising price would be where revenue is maximised, 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 maximising quantity is lower than the efficient quantity because the firm is a monopolist. P Q TR MR $8 0 $ $ , , , , , The company should not 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. 9

10 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 should not charge people to use the bridge. Part d Yes, the government should build the bridge, because it would increase society s total surplus. As shown in Figure 7, total surplus has area 1/ ,000 = $3,200,000, which exceeds the cost of building the bridge. Figure 7 Question 6 Larry, Curly, and Moe run the only saloon in town. Larry wants to sell as many drinks as possible without losing money. Curly wants the saloon to bring in as much revenue as possible. Moe wants to make the largest possible profits. Using a single diagram of the saloon s demand curve and it s cost curves, show the price and quantity combinations favoured by each of the three partners. Explain. Question 6: Solution Larry wants to sell as many drinks as possible without losing money, so he wants to set quantity where price(demand) equals average cost, which occurs 10

11 at quantity Q L and price P L in Figure 10. Curly wants to bring in as much revenue as possible, which occurs where marginal revenue equals zero, at quantity Q C and price P C. Moe wants to maximise profits, which occurs where marginal cost equals marginal revenue, at quantity Q M and price P M. Figure 10 Question 7 Explain why a monopolist will always produce a quantity at which the demand curve is elastic. (Hint: If demand is inelastic and the firm raises its price, what happens to total revenue and total costs?) Question 7: Solution A monopolist always produces a quantity at which the demand curve is elastic. If the firm produced at a quantity for which the demand curve were inelastic, then if the firm raised its price, quantity would fall by a smaller percentage than the rise in price, so revenue would increase. Since costs would decrease at a lower quantity, the firm would have higher revenue and lower costs, so profit would be higher. Thus the firm should keep raising its price until profits are maximised, which must happen on an elastic portion of the demand curve. Another way to see this is to note that on an elastic portion of the demand curve, marginal revenue is negative. Increasing quantity requires 11

12 a greater percentage reduction in price, so revenue declines. Since a firm maximises profit where marginal cost equals marginal revenue, and marginal cost is never negative, the profit maximising quantity can never occur where marginal revenue is negative, so can never be on an inelastic portion of the demand curve. Question 8 TheNew York Times (Nov. 30,1993)reportedthat theinabilityofopecto agree last week to cut production has sent the oil market into turmoil...[leading to] the lowest price for domestic crude oil since June Why were the members of OPEC trying to agree to cut production? Why do you suppose that OPEC was unable to agree on cutting production? Why did the oil market go into turmoil as a result? The newspaper also noted OPEC s view that producing nations outside the organisation, like Norway and Britain, should do their share and cut production. What does the phrase do their share suggest about OPEC s desired relationship with Norway and Britain? Question 8: Solution OPEC members were trying to reach an agreement to cut production so they could raise the price. They were unable to agree on cutting production because each country has an incentive to cheat on any agreement. The turmoil is a decline in the price of oil because of increased production. 12

13 OPEC would like Norway and Britain to join their cartel so they could act like a monopoly. Question 9 A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is constant at $1,000 per diamond, and the demand for diamonds is described by the following schedule: Price Quantity $8,000 5,000 7,000 6,000 6,000 7,000 5,000 8,000 4,000 9,000 3,000 10,000 2,000 11,000 1,000 12,000 part a If there were many suppliers of diamonds, what would be the price and quantity? part b If there were only one supplier of diamonds, what would be the price and quantity? If Russia and South Africa formed a cartel, what would be the price and quantity? If the countries split the market evenly, what would be South Africa s production and profit? What would happen to South Africa s profit if it increased its production by 1,000 while Russia stuck to the cartel agreement? Part d Use your answer to part (c) to explain why cartel agreements are often not successful. 13

14 Question 9: Solution part a If there were many suppliers of diamonds, price would equal marginal cost ($1,000), so the quantity would be 12,000. part b With only one supplier of diamonds, quantity would be set where marginal cost equals marginal revenue. The following table derives marginal revenue: Price Quantity Total revenue Marginal Revenue $8,000 5, ,000 6, ,000 7, ,000 8, ,000 9, ,000 10, ,000 11, ,000 12, With marginal cost of $1,000 per diamond, or $1,000,000 per thousand diamonds, themonopolywillmaximizeprofitsatapriceof$7,000andaquantity of 6,000. Additional production beyond this point would lead to a situation where marginal revenue is lower than marginal cost. If Russia and South Africa formed a cartel, they would set the price and quantity like a monopolist, so the price would be $7,000 and the quantity would be 6,000. If they split the market evenly, they would share total revenue of $42 million and costs of $6 million, for a total profit of $36 million. So each would produce 3,000 diamonds and get a profit of $18 million. If Russia produced 3,000 diamonds and South Africa produced 4,000, the price would decline to 6,000. 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. Part d Cartel agreements are often not successful because one party has a strong incentive to cheat to make moreprofit. Inthiscase, eachcould increase profit 14

15 by $2 million by producing an extra thousand diamonds. However, of both countries did this profit would decline for both of them. Question 10 What feature of the product being sold distinguishes the monopolistically competitive firm from the monopolistic firm? Question 10: Solution A monopolistic firm produces a product for which there are no close substitutes, but a monopolistically competitive firm produces a product that is only somewhat different from substitute goods. So the goods differ in terms of the degree to which substitutes exist. Question 11 Sparkle is one firm of many in the market for toothpaste, which is in long-run equilibrium. Draw a diagram showing Sparkle s demand curve, marginal revenue curve, average total cost curve, and marginal cost curve. Label Sparkle s profit maximising output and price. What is sparkle s profit? Explain. On your diagram, show the consumer surplus derived from the purchase of Sparkle toothpaste. Also show the deadweight loss relative to the efficient level of output. Part d If the government forced Sparkle to produce the efficient level of output, what would happen to the firm? What would happen to sparkles consumers? 15

16 Question 11: Solution Figure 4 illustrates the market for Sparkle toothpaste in long-run equilibrium. The profit-maximising level of output is Q M and the price is P M. Figure 4 Sparkle s profit is zero, since at quantity Q M, Price equals average total cost. The Consumer surplus from the purchase of Sparkle toothpaste is area A+B. The efficient level of output occurs where the demand curve intersects the marginal-cost curve, at Q C. So the deadweight loss is area C, the area above marginal cost and below demand, from Q M to Q C. Part d If the government forced Sparkle to produce the efficient level of output, the firm would lose money because average total cost would exceed price, so the firm would shut down. If that happened, Sparkle s customers would earn no consumer surplus. 16

17 Question 12 Describe three commercials that you have seen on TV. In what ways, if any, were each of these commercials socially useful? In what ways were they socially wasteful? Did the commercials affect the likelihood of your buying the product? Why or why not? Question 12: Solution Generally speaking, the commercials are socially useful to the extent that they provide consumers with information about the product or demonstrate from the existence of the commercial that the product is worth advertising, and thus is not of low quality. Commercials are socially wasteful to the extent that they manipulate people s tastes and try to make products seem more different than they really are. Question 13 For each of the following pairs of firms, explain explain which firm would be more likely to engage in advertising: a A family owned farm or a family owned restaurant. b A manufacturer of forklifts or a manufacturer of cars. c A company that invented a very reliable watch or a company that invented a less reliable watch that costs the same amount to make. Question 13: Solution A family owned restaurant would be more likely to advertise than a family owned farm because the output of the farm is sold in a perfectly competitive market, in which there is no reason to advertise, while the output of the restaurant is sold in a monopolistically competitive market. A manufacturer of cars is more likely to advertise than a manufacturer of forklifts because there is little difference between different brands of industrial products like forklifts, while there are greater perceived differences between consumer products like cars. The possible return to advertising is greater in the case of cars than in the case of forklifts. 17

18 A company that invented a reliable watch is likely to advertise more than a company that invented a less reliable watch that costs the same amount to make because the company with the reliable watch will get many repeat sales over time to cover the cost of the advertising, while the company with the less reliable watch will not. 18