Goolsbee 2e Solutions Manual Ch08 PDF

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Supply in a Competitive Market

8

1. Consider three industries: organic onion farming, aluminum production, and car production. a. Drawing on the characteristics of a competitive market outlined in the chapter, explain which of the industries named is most likely to be perfectly competitive. Be sure to explain why those industries you believe are less competitive fail to meet the criteria outlined in the chapter. b. The vast majority of industries are probably not perfectly competitive. Why, then, do you suppose economics courses emphasize the study of perfect competition as much as they do? 1. a. Organic onion farming is most likely to be perfectly competitive, because there are a large number of firms selling an identical product in an industry without barriers to entry. Aluminum production is an industry with a small number of dominant producers, and the need for access to key raw materials can be a barrier to entry. Because cars are differentiated between producers, the automobile industry does not qualify as one in which products are identical. b. Perfect competition is the most straightforward industry structure, and it serves as a benchmark for comparison when measuring the efficiency of other markets. Also, many industries are close enough to perfect competition that the model of perfect competition makes accurate predictions of how these firms will behave.

2. Assume that soybean production is perfectly competitive. When we study the behavior of the firm, we assume that the demand faced by that firm is perfectly elastic. Yet in the marketplace, demand may be highly inelastic. Drawing on the determinants of the elasticity of demand outlined in chapter 2, resolve this apparent paradox. 2. The number of available substitutes is a key determinant for the elasticity of demand. Although there may not be a lot of substitutes for soybeans, there are many substitutes for soybeans from any one individual producer. The more narrowly the product is defined, the greater the elasticity due to more substitutes being available.

*3. Nancy sells beeswax in a perfectly competitive market for $50 per pound. Nancy’s fi xed costs are $15, and Nancy is capable of producing up to 6 pounds of beeswax each year. a. Use that information to fill in the table below. (Hint: Total variable cost is simply the sum of the marginal costs up to any particular quantity of output!)

Quantity

Total Revenue

Fixed Cost

0

0

15

Variable Cost

Total Cost

Profit

Marginal Revenue

Marginal Cost

—

—

1

30

2

35

3

42

4

50

5

60

6

72

b. If Nancy is interested in maximizing her total revenue, how many pounds of beeswax should she produce? c. What quantity of beeswax should Nancy produce in order to maximize her profi t? d. At the profit-maximizing level of output, how do marginal revenue and marginal cost compare?

99

100

Part 3

Markets and Prices

e. Suppose that Nancy’s fi xed cost suddenly rises to $30. How should Nancy alter her production to account for this sudden increase in cost? f. Suppose that the bee’s union bargains for higher wages, making the marginal cost of producing beeswax rise by $8 at every level of output. How should Nancy alter her production to account for this sudden increase in cost? 3. a.

b. c. d. e. f.

Quantity

Total Revenue

Fixed Cost

Variable Cost

Total Cost

Profit

Marginal Revenue

Marginal Cost

0

0

15

0

15

–15

—

—

1

50

15

38

53

–3

50

38

2

100

15

81

96

4

50

43

3

150

15

131

146

4

50

50

4

200

15

189

204

–4

50

58

5

250

15

257

272

–22

50

68

6

300

15

337

352

–52

50

80

Nancy should produce 6 pounds of beeswax to maximize total revenue. Nancy’s maximum profi t is $28; she should produce 4 pounds of beeswax to generate that profit. Marginal revenue and marginal cost are equal. The marginal cost does not change, so the profit-maximizing quantity stays the same. Nancy maximizes profit by producing 3 pounds of beeswax.

4. The egg industry comprises many firms producing an identical product. Supply and demand conditions are indicated in the left-hand panel of the figure below; the long-run cost curves of a representative egg producer are shown in the right-hand panel. Currently, the market price of eggs is $2 per dozen, and at that price consumers are purchasing 800,000 dozen eggs per day. (b) Firm

(a) Market Price ($)

Price & cost ($/unit)

S

$2

$2

1.50

1.50

1

1

0.50

LMC LATC

0.50 D

0

0

800 1,200 1,600 2,000 2,400 Quantity (thousands of dozens)

1,000

2,000 2,300 2,400 Quantity (dozens)

a. Determine how many eggs each firm in the industry will produce if it wants to maximize profi t. b. How many firms are currently serving the industry? c. In the long run, what will the equilibrium price of eggs be? Explain your reasoning, and illustrate your reasoning by altering the graphs above. d. In the long run, how many eggs will the typical firm produce? e. In the long run, how many firms will comprise the industry? 4. a. Since fi rms will produce where MR = MC, the representative firm in the industry will produce 2,400 dozen eggs. b. The market demand is 800,000 dozen eggs at a price of $2. At the same time, each fi rm produces 2,400 dozens of eggs. Therefore, the number of firms serving the industry is 800,000 _ ≈ 333 2,400

Supply in a Competitive Market

Chapter 8

c. The long-run equilibrium price of eggs will be $1, which equals the minimum of the LATC curve, thepoint at which firms earn zero profi t (P = LATC = MC ). (b) Firm

(a) Market Price ($)

Price & cost ($/unit)

S

$2

$2

1.50

1.50

1

1

0.50

LMC LATC

0.50 D

0

800 1,200 1,600 2,000 2,400 Quantity (thousands of dozens)

0

1,000

2,000 2,300 2,400 Quantity (dozens)

d. In the long run, the typical firm will produce 2,000 dozen eggs. e. In the long run, at a market price of $1, the market demand is 1,600,000 dozens of eggs. Each fi rm 1,600,000 produces 2,000 dozen. Hence, there will be_ = 800 firms in the industry. 2,000 5. The diagram on the right depicts the revenues and costs of a Firm TC revenue firm producing vodka. & cost ($) TR a. Why is total revenue represented as a straight line instead of a curve? What assumption of perfect competition does that linearity refl ect? b. What will the fi rm’s profi t be if it decides to produce 20units of output? 120 units? c. Suppose the fi rm is producing 70 units of output and decides to cut output to 60. What will happen to the fi rm’s 0 20 Quantity profit as a result? 70 120 d. Suppose the firm is producing 70 units of output and decides to increase output to 80. What will happen to the firm’s profit as a result? e. At an output level of 70, draw a line tangent to the total cost curve. Does your line look similar to the total revenue curve? What does the slope of the total revenue curve indicate? What does the slope of the total cost curve indicate? 5. a. Total Revenue = Price × Quantity. Because price is constant, the total revenue function has a constant slope. Each fi rm in perfect competition is a small part of the market, and so it can increase the quantity it brings to the market without creating any downward pressure on price. b. At both production levels, 20 and 120 units of vodka, the profit is equal to 0 (TR = TC ). c. At the production level of 70 units of vodka, the firm earns the highest profi t, since this is the output at which the difference between total revenue and total cost is maximized. As the production level decreases, the difference between the total revenue and total cost declines, decreasing the firm’s profi t. d. Similarly to (c), the profi t will decrease. e. Firm TC revenue & cost ($)

0

TR

20

70

120

Quantity

The line tangent to the TC curve at a quantity equal to 70 is parallel to the TR curve. This indicates that the highest profit that the firm can obtain occurs at the production level of 70. The slope of the TR curve indicates that the marginal revenue is constant. The slope of the TC curve indicates that marginal cost is increasing over all output levels shown here.

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Part 3

Markets and Prices

*6. Jiang’s Pussycats sells ceramic kittens. The marginal cost of producing a particular kitten depends on how many kittens Jiang produces, and is given by the formula MC = 0.8Q. Thus, the first kitten Jiang produces has a marginal cost of $0.80, the second has a marginal cost of $1.60, and so on. Assume that the ceramic kitten industry is perfectly competitive, and Jiang can sell as many kittens as she likes at the market price of $16. a. What is Jiang’s marginal revenue from selling another kitten? (Express your answer as an equation.) b. Determine how many kittens Jiang should produce if she wants to maximize profit. How much profit will she make atthis output level? (Assume fixed costs are zero. It may help to draw a graph of Jiang’s marginal revenue and marginalcost.) c. Suppose Jiang is producing the quantity you found in (b). If she decides to produce one extra kitten, what will her profi t be? d. How does your answer to part (c) help explain why “bigger is not always better”? 6. a. Firms in perfectly competitive markets are price takers. Therefore, the marginal revenue is constant at MR = $16 b. To maximize profit, the marginal revenue must equal marginal cost; that is, 16 = 0.8Q, which implies that Q = 20 Thus, Jiang should produce 20 kittens to maximize her profit. The total revenue is $16 × 20 = $320 and the total cost is the sum of marginal costs, that is, the first kitten Jiang produces has a marginal cost of $0.80, the second has a marginal cost of $1.60, and so on: $0.80 + $1.60 + … + $15.20 + $16 = $168. The profit is $320 – $168 = $152. c. In this case, the marginal revenue of the additional unit is less than its marginal cost. Profit will decrease. Jiang’s total revenue is then 21 × $16 = $336 while the total cost is $0.80 + $1.60 + … + $16 + $16.80 = $184.80. The profit is $336 – $184.80 = $151.20. d. In part (b), the profit is $152. In part (c), the profi t is $151.20. An extra kitten subtracts more dollars than it adds, because the kitten costs more to produce than the revenue it generates.

7. Heloise and Abelard produce letters in a perfectly competitive industry. Heloise is much better at it than Abelard: On average, she can produce letters for half the cost of Abelard’s. True or False: If Heloise and Abelard are both maximizing profi t, the last letter that Heloise produces will cost half as much as the last letter written by Abelard. Explain your answer. t by producing until M R = P = MC. Since the price is the same for both, 7. The statement is false. Each maximizes profi the MC of the last unit produced will also be the same for both. Each of the two producers faces different marginal cost curves, but both produce until the marginal cost is equal to the market price, and then stop.

*8. Hack’s Berries faces a short-run total cost of production given by TC = Q3 – 12Q2 + 100Q + 1000, where Q is the number of crates of berries produced per day. Hack’s marginal cost of producing berries is 3Q 2 – 24Q + 100. a. What is the level of Hack’s fi xed cost? b. What is Hack’s short-run average variable cost of producing berries? c. If berries sell for $60 per crate, how many berries should Hack produce? How do you know? (Hint: You may want to remember the relationship between MC and AVC when AVC is at its minimum.) d. If the price of berries is $73 per crate, how many berries should Hack produce? Explain.

Supply in a Competitive Market

Chapter 8

8. a. Hack’s fixed cost is 1000. (Q 3 – 12Q2 + 100Q) b. AVC = __ = Q 2 – 12Q + 100 Q c. AVC is minimized when it equals MC. Find this point by setting the two expressions equal and solving for Q: 3Q2 – 24Q + 100 = Q2 – 12Q + 100 2Q2 = 12Q 2Q = 12 Q=6 The minimum value of AVC occurs when quantity is 6. To fi nd the value of AVC at this point, substitute 6 for Q in either MC or AVC: 3(6) 2 – 24(6) + 100 = (6)2 – 12(6) + 100 = 64 The minimum value of AVC is 64. Therefore, Hack should not provide any berries at a price of 60, which is below AVC. The loss-minimizing quantity is 0. d. Begin by setting P = MC and then solve for Q: 73 = 3Q 2 – 24Q + 100 3Q 2 – 24Q + 27 = 0 This does not factor easily, so you will have to use the quadratic formula where a = 3, b = –24, and c = 27: 4(3)(27)] 0.5} Q = {24 ±[(–24)2 – _ 2(3) Q = 1.354 or 6.646 Hack would choose the larger number, because it is on the upward sloping portion of the marginal cost curve. So, he would produce 6.646 crates of berries.

*9. Janis is one producer in the perfectly competitive pearl industry. Price Janis’s cost curves are shown on the right. Pearls sell for $100, and & cost MC ATC in maximizing profits, Janis produces 1,000 pearls per month. ($/unit) A B C D a. Find the area on the graph that illustrates the total revenue $100 AVC from selling 1,000 units at $100 each. K J E b. Find the area on the graph that indicates the variable cost of M L producing those 1,000 units. I F c. Find the area on the graph that indicates the fixed cost of producing those 1,000 units. H G d. Add together the two areas you found in (b) and (c) to show 0 Quantity 1,000 the total cost of producing those 1,000 units. e. Subtract the total cost of producing those 1,000 units from the total revenue from selling those units to determine the fi rm’s profit. Show the profit as an area on the graph. 9. a. The rectangle ADGH represents the total revenue when selling 1,000 units at $100 each. b. The variable cost at 1,000 units is represented by the area MLGH. c. The fixed cost of producing 1,000 units is equal to the area KJLM. d. The total cost of producing 1,000 units is shown by the area KJGH. e. The profit from producing 1,000 units is represented by the area ADJK.

Price & cost ($/unit) A B $100 K M I

F H

0

MC ATC D AVC J E

C

L G 1,000

Quantity

103

104

Part 3

Markets and Prices

10. The diagram below depicts the cost curves for a perfectly competitive jump drive producer that is currently operating at a loss. Price & cost ($/unit) $20 18 16 14 12 10 8 6 4 2

ATC MC AVC

Quantity

a. Suppose the market price of jump drives is $7. In the graph, outline an area that represents this firm’s losses if it produces where MR = MC. b. If the firm in (a) instead shuts down and produces zero units, it will lose only its fixed costs. Outline an area that represents this fi rm’s fixed costs. c. Which area is larger—its losses from producing where MR = MC, or its losses from producing zero units of output? What should the fi rm do? d. Do your answers to (a), (b), and (c) change if the price of jump drives is $11 rather than $7? 10. a. The firm’s loss from operating is (ATC – P) × Q. Price $20

MC ATC

16 14 12 7

AVC

8

MR = 7

4 Quantity

b. The fi rm’s fixed costs are (ATC – AVC) × Q. Price $20 16 14 12 7

MC

ATC AVC

8 4 Quantity

c. The loss from operating at MR = MC is greater. The firm should shut down immediately. d. At a price of $11, the firm’s loss from operating would be less than its fixed costs. The firm should continue to operate. Price $20 16 14 12 11 8 7 4

Loss from operating = (ATC – P) × Q MC

ATC AVC

Quantity

Supply in a Competitive Market

Chapter 8

11. Marty sells flux capacitors in a perfectly competitive market. His marginal cost is given by MC = Q. Thus, the fi rst capacitor Marty produces has a marginal cost of $1, the second has a marginal cost of $2, and so on. a. Draw a diagram showing the marginal cost of each unit that Marty produces. b. If flux capacitors sell for $2, determine the profit-maximizing quantity for Marty to produce. c. Repeat part (b) for $3, $4, and $5. d. The supply curve for a firm traces out the quantity that firm will produce and offer for sale at various prices. Assuming that the fi rm chooses the quantity that maximizes its profits [you solved for these in (b) and (c)], draw another diagram showing the supply curve for Marty’s fl ux capacitors. e. Compare the two diagrams you have drawn. What can you say about the supply curve for a competitive firm? 11. a.

Price & cost ($/capacitor)

MC = Q

$5

0

5

Quantity of flux capacitors

b. The condition P = MC implies that if flux capacitors are sold for $2, the marginal revenue is 2; hence, the quantity produced is 2. c. Equivalently to part (b), for prices $3, $4, and $5, the profit-maximizing quantities are 3, 4 and 5, respectively. d. Price & cost Supply ($/capacitor)

$5

0

5

Quantity of flux capacitors

e. The two diagrams are the same. The supply curve for a competitive firm overlaps with the marginal cost curve for the part of the marginal cost curve that lies above minimum average variable cost. In this particular case, that is true for all positive levels of output.

* 12. Consider the graph on the right, which depicts the cost curves of a perfectly competitive seller of potatoes. Potatoes currently sell for $3 per pound. Price ATC MC & cost a. To maximize profit, how many pounds of potatoes ($/pound) should this seller produce? AVC $3 Suppose that the potato grower’s bank ratchets up the interest rate applicable to the grower’s adjustable-rate mortgage loan. This increases the size of the potato grower’s monthly mortgage payment. b. Illustrate the change in the mortgage payment by shifting the appropriate cost curves. 0 c. Which curves shift? Which do not? Why? 1,000 3,000 5,000 7,000 d. How does the change in interest rates affect the growQuantity er’s decision on how many potatoes to produce? of potatoes e. What happens to the potato grower’s profi t as a result of the increased interest rate? f. How does the change in interest rates affect the shape and/or position of the grower’s short-run supply curve?

105

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Part 3

Markets and Prices

12. a. The seller should produce at the level of output where Price ATC2* ATC*1 & cost MR equals MC, which occurs at 5,000 pounds of MC ($/pound) potatoes. AVC $3 b. An increase in the mortgage payment increases the fixed cost of produ...