Goolsbee 2e Solutions Manual Ch17 PDF

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Externalities and Public Goods

17

*1. Kansas City is famous for its barbeque. But, good barbeque comes at a cost: Pit masters have to bear the costs of producing slow-roasted pulled pork and beef briskets. There is also an external cost: Every time a pit master roasts another rack of ribs, it offends the sensibilities of nearby animal lovers. Consider the graphical representation of a typical pit master in the competitive BBQ industry below: SMC = MC + EMC

Price ($/rack)

MC

$5

D

1

EMC

0

20

80

100 Quantity of (racks)

a. What is the market price of barbeque? b. How much psychic damage (external cost) do animal lovers suffer for each rack roasted? c. If our pit master accounts only for her private costs, how many racks will she roast? How much total damage will animal lovers suffer? d. If our pit master feels sympathy for animal lovers and wholly considers their feelings in her decision about how many racks to produce, how many racks will she roast? e. Does the decision to consider animal lovers’ feelings eliminate the damage they suffer from transactions in the rib market? f. Cutting output below the level you determined in (d) clearly benefi ts animal lovers. Who is hurt by such a decision? Explain why such an output cut would not be Pareto effi cient, that is, there is another allocation that would make someone better off without making anyone worse off. 1. a. The market price is $5, where marginal benefi t equals marginal cost. b. The external cost is $1 regardless of the number of racks roasted. c. The intersection of the marginal benefit curve (demand) and the marginal cost curve determines the number of racks. Thus, 100 racks will be roasted. Animal lovers will suffer damage of $1 for each rack, for a total damage of $100. d. Incorporating the external costs would lead the pit master to produce 80 racks. e. The total damage suffered by animal lovers will be $80. Some of the damage is eliminated, but not all. f. Cutting the level of output further would hurt the pit master, who would be foregoing profits. Such a cut is not Pareto optimal, because although the output cut would reduce damage to the animal lovers by $1 per rack roasted, below 80 units any output cut will cost the pit master more than $1 in lost profit.

2. Jill sells bouquets of fl owers that she grows in her backyard. Jill’s marginal cost of producing bouquets is given by MC = 0.25Q, where Q is the number of bouquets she makes. Jill can sell all the bouquets she wishes at the local farmers’ market for $6 per bouquet. Unfortunately, Jill’s fl oriculture aggravates the allergies of her next-door neighbor, Cooper: Every bouquet that Jill grows produces 50 cents’ worth of sneezes. a. Jill wants to maximize her profi t. Determine the profit-maximizing quantity of bouquets. b. Assume that Jill produces the quantity of bouquets you determined in (a). Add up the cost of the last bouquet to Jill and the cost that bouquet imposes on Cooper, and compare your answer to the $6 worth of benefi t the last bouquet creates for the buyer. Is producing the last bouquet a good thing for society?

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c. From society’s standpoint, is Jill overproducing or underproducing bouquets? d. Suppose that Jill marries Cooper. Determine the social marginal cost of producing bouquets by adding the 50cents’ worth of damage each bouquet causes Cooper to Jill’s private marginal cost. Express your answer as an equation. e. Determine how many bouquets Jill should produce if she fully considers the costs she imposes on her new husband. Explain why it makes a difference if Cooper is just a neighbor or is Jill’s husband. 2. a. The demand curve is a horizontal line at price $6. If Jill wants to maximize her profit, the profit-maximizing quantity of bouquets solves the following: D = MR = 6 – 0.25Q = MC Q = 24 b. The cost of the last bouquet to the society is the marginal cost to Jill, which is $6, and the cost of that bouquet to Cooper, which is 50 cents. Therefore, adding up the two costs, we get $6.50. Producing the last bouquet increases the social cost by $6.50 and the social benefit by $6. Thus, the net effect is negative and the production of the last bouquet is not a good development for society. c. Jill is overproducing; that is, the socially optimal level of output is below her profit-maximizing output. d. The social marginal cost of producing bouquets is 0.25Q + 0.5 = SMC e. The profit-maximizing quantity of bouquets becomes D = MR = 6 = 0.25Q + 0.5 = SMC Q = 22 When Cooper is married to Jill, Jill cares about Cooper’s well-being and any harm to him enters her marginal cost calculations, altering her optimal level of production.

3. Suppose that the inverse demand for marching band music is given by P = $1,000 – Q. Because marching bands across the world produce music of sufficient quality at increasing marginal cost, the industry marginal cost is given by MC = 0.75Q. Unfortunately, marching band music is not produced in a vacuum: People near marching bands become increasingly aggravated the more music they hear. At the industry level, the external marginal cost is given by E MC = 0.25Q. a. Graph the demand, marginal cost, and external marginal cost functions. b. If marching bands do not consider the external marginal costs they impose on others, how many songs will be played? i. Calculate the total consumer surplus. ii. Calculate the total producer surplus. iii. Calculate the total surplus to market participants. iv. Calculate the total damage to those harmed. (Hint: This damage can be represented as the area under the E MC curve. It’s up to you to fi gure out why!) v. Subtract the damage to those harmed from total surplus to market participants to determine the net value created for society by marching band music. c. Determine social marginal cost. d. Determine the quantity of marching band music that would be produced if marching bands were forced to consider the costs they imposed on others. e. What happens to the price of marching band music if the bands were forced to consider the external marginal costs? f. As you did in (b), calculate consumer surplus, producer surplus, and total damage. (Be sure to remember that producer surplus is the area between private marginal cost and the price!) Compared to your answers in (b), i. What happens to the total surplus received by market participants when external marginal costs are considered? ii. What happens to the damage created by marching band music? iii. What happens to the net value created for society by marching band music?

Externalities and Public Goods

3. a.

Price $1,000 MC CS 429 EMC

PS 142.75

D

0

571

1,000 Quantity of marching bands

b. The optimal amount of marching band music satisfies P = 1,000 – Q = 0.75Q = MC Q ≈ 571 Hence, approximately 571 bands will be hired. i. The total consumer surplus is _1 × (1,000 – 429) × 571 = $163,020.50 2 ii. The total producer surplus is _1 × 429 × 571 = $122,479.50 2 iii. The total surplus to market participants is CS + P S = $285,500 iv. The total damage to harmed people is the area under the EMC curve: _1 × 142.75 × 571 = $40,755.13 2 v. The net value created for society by marching band music is $285,500 – $40,755.13 = $244,744.87 c. The social marginal cost is SMC = MC + EMC = 0.75Q + 0.25Q = Q d. The quantity of marching band music is now 1,000 – Q = Q Q = 500 Price $1,000

SMC = Q MC = 0.75Q

500 375 D 0

500

1,000 Quantity of marching bands

e. The price of the band increases by $71 from $429 to $500. f. The consumer surplus is _1 × 500 × 500 = $125,000 2

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The producer surplus is the area between private marginal cost and the price, that is, 1 × 375 × 500 = $156,250 125 × 500 + _ 2 The total damage is _1 × 125 × 500 = $31,250 2 The consumer surplus decreases, producer surplus increases, and the damage decreases. i. The total surplus becomes $125,000 + $156,250 = $281,250. The total surplus decreases. ii. The damage created by marching band music decreases. iii. The net value created for society by marching band music is now $281,250 – $31,250 = $250,000 Thus, the net value created for society rises from $244,744.87 to $250,000.

*4. Gasoline brings great benefit to those who buy it, but burning it also creates external costs. Consider the graph below, which shows the demand for gasoline, the private marginal cost of producing gasoline, and the social marginal cost of producing gasoline. Price ($/gallon)

SMC1 MC1

D A H

P2

B

P1 C

E

F G

D Q2 Q1

Quantity of gasoline

a. Suppose that buyers and producers of gasoline do not consider the external marginal costs they impose on others. Determine the equilibrium quantity and price; then use the letters in the diagram to fi ll in the appropriate spaces in the table below: External Marginal Costs NotConsidered

External Marginal Costs Considered

Consumer Surplus Producer Surplus External Damage (−) Total net value to society

b. Suppose that conscientious sellers, out of the sheer goodness of their hearts, decide to incorporate external marginal costs into their production decisions. Determine the new quantity (Hint: Use the social marginal cost curve) and price, then use the letters in the diagram to fill in the appropriate spaces in the table above. (Be sure to remember that producer surplus is the area above private marginal cost and below the price, out to the relevant quantity.) c. Producers rarely do something out of the goodness of their hearts, and are likely to consider only their private marginal costs. Compare total surplus in both cases to determine the deadweight loss of the externality when external marginal costs are not considered.

Externalities and Public Goods

Chapter 17

4. a. The equilibrium price is P 1 and quantity is Q1. External Marginal Costs Not Considered

Consumer Surplus

A+B+D+F

Producer Surplus

C+E+G

External Damage (−) Total net value to society

External Marginal Costs Considered

D+E+F+G+H A+B+C–H

b. The new quantity is Q2 and price is P2. External Marginal Costs Not Considered

External Marginal Costs Considered

Consumer Surplus

A+B+D+F

A

Producer Surplus

C+E+G

B+C+D+E

D+E+F+G+H

D+E

External Damage (−) Total net value to society

A+B+C–H

A+B+C

c. As indicated in the table above, when external costs are ignored by producers, total net value is lower by area H. Thus, H is the deadweight loss.

5. The private demand for drive-in movies is given by P = 20 – 0.1Q. The industry marginal cost of showing drive-in movies is given by MC = 0.1Q. a. Graph the private demand and marginal cost curves, and determine the price and quantity of movies that will be shown. b. Drive-in movies can be viewed imperfectly from outside the fence. The external marginal benefits received by such viewers are given by E M B = 2 – 0.01Q. Graph the external marginal benefit curve, and then use that information to graph the social demand curve. c. Suppose that all drive-in movies are nationalized and shown for the public good. The Movie Czar chooses the price and quantity of movies that bring the greatest benefit net of costs to all viewers, regardless of the vantage point from which they view the movie. Determine the optimal price and quantity of drive-in movies. d. Indicate the deadweight loss created by the positive externality as an area on your graph, and calculate its value. (Hint: You’ll need to determine how much external marginal benefit the very last unit of output created when drive-ins were privately run.) e. Can government-run movies potentially improve on the private market outcome when a positive externality exists? 5. a.

Price

MC

$20

10

D 0

100

200 Quantity of drive-in movies

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The equilibrium quantity is 20 – 0.1Q = 0.1Q Q = 100 Hence, the price is 20 – 0.1 × 100 = $10. b.

Price $22 20

MC

SD D

DWL

10

2 0

EMB 105

200 Quantity of drive-in movies

The social demand curve (SD) is D + EMB = 20 – 0.1Q + 2 – 0.01Q = 22 – 0.11Q. c. The optimal quantity is now 22 – 0.11Q = 0.1Q Q ≈ 105 Thus, the optimal price becomes 22 – 0.11Q = 22 – 0.11 × 105 = $10.45 d. The deadweight loss is

_1 × (105 – 100) × (10.45 – 9.50) = $2.375

2 e. Yes. When privately operated, theaters underproduce. Government can increase output to a socially optimal level. It is also possible that the government can achieve this result through a price-based intervention such as a subsidy to private producers.

6. Suppose that growing flowers produces both a positive externality (people in the neighborhood get to view the flowers) and a negative externality (the flowers aggravate peoples’ allergies). a. True or false, and explain your answer (using a diagram): We can say for sure that too many fl owers are being produced. b. True or false, and explain your answer (using a diagram): We can say for sure that the market price of flowers is too high. 6. a. False. We cannot say which externality dominates. Price SMC MC P* PMKT D

SD Quantity of flowers

b. False. Referring to the graph above, the market price is always too low because both externalities move “up” the curves.

Externalities and Public Goods

Chapter 17

*7. The inverse demand for leather is given by P = 50 – 0.5Q. The industry supply of leather is determined by its marginal cost: MC = 0.45Q. Unfortunately, the production of leather causes noxious chemical residue to leach into groundwater supplies. The external marginal cost caused by these residues grows with the amount of output, and is measured as E MC = 0.05Q. a. Suppose that the government wishes to reduce the externality to effi cient levels by imposing a restriction on quantity (a quota). What maximum level of output should it set for leather production? What price would prevail in the marketplace once this quota is in place? b. Suppose that the government wishes to reduce the externality to efficient levels by levying a tax on leather production. How high would that tax need to be? What is the resulting net price paid by buyers once the tax is in place? How much leather is bought and sold with the tax in place? 7. a. The SMC is MC + EMC = 0.45Q + 0.05Q = 0.5Q. The efficient output level can be found where MB = SMC: 50 – 0.5Q = 0.5Q Q* = 50 Thus, government should set the quota at 50 units. The price that prevails in the marketplace once this quota is in place is P = 50 – 0.5Q* = 50 – 0.5 × 50 = $25 b. At the efficient level of production, Q*= 50, the external damage can be calculated as 0.05Q, or $2.50. If government imposes a $2.50 tax on producers, their private marginal costs will be given as MC = 0.45Q + 2.50 Producers will fi nd the profit-maximizing level of output where MB = MC, or where 50 – 0.5Q = 0.45Q + 2.50 Solving, we get 50 units for Q, the profi t-maximizing level of output. The prevailing market price can be found by substituting Q = 50 into the MB curve: P = 50 – 0.5(50) = $25 Buyers will pay $25. Sellers will receive that amount less the tax, or $22.50.

8. Consider the market for smelted kryptonite depicted below. A by-product of kryptonite smelting is the release of clouds of toxic blackish-yellow smoke. Each ton of toxic smoke emitted causes nearby residents’ health-care expenditures to rise; the external marginal costs associated with the toxic exhaust are depicted as E MC on the graph: Price ($/unit)

MC 1

$400 300 EMC 200 D 100

0

50

100

150

200 Quantity of kryptonite

a. On the diagram, carefully graph the social marginal cost curve associated with the kryptonite industry. Precision matters! b. Without any environmental regulation, how much kryptonite is produced? c. From society’s standpoint, how much kryptonite should be produced? d. Regulators can achieve the efficient level of kryptonite production by imposing a tax on kryptonite production. To achieve the efficient level of production, how big should that tax be?

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e. Draw an industry supply curve that reflects the tax you determined in part (d). Show that private producers, forced to internalize their externality by the tax, produce the socially optimal amount. f. Could the same result have been achieved by assessing a tax on the buyers of kryptonite? If so, how much would that tax need to be? 8. a.

Price ($/unit)

SMC

MC 1

$400 EMC

300 200

D

100 0

50

100 150 200

Quantity of kryptonite

b. Without any environmental regulation, the quantity of kryptonite produced is P = 400 – Q = 2Q = MC1 3Q = 400 Q ≈ 133 c. From society’s point of view, 100 units of kryptonite should be produced. d. The tax should be equal to the external marginal cost at the socially optimal output level: E MC(100) = $100 Therefore, impose a $100 tax on each unit of kryptonite produced. e. An industry supply curve is the S MC curve. Therefore, at S = D, the company produces the socially optimum amount of kryptonite. Price ($/unit)

MC 2

MC 1

$400 Lump-sum tax of $100

EMC

300 200

D

100 0

50

100 150 200 Quantity of kryptonite

f. The same result could have been achieved by assessing a tax on the buyers of kryptonite. The tax would need to be $100 so that the demand curve shifts downward in a parallel manner by $100.

*9. In Paris, hundreds of small bakeries produce bread for sale to their customers at a marginal cost of MC = 2 + 0.1Q. The inverse demand for bread is given by P = 10 – 0.1Q, where P is in euros per loaf and Q is loaves per hour. The baking of bread also creates a positive externality: There is nothing quite like the smell of fresh-baked bread. Tourists and residents receive external marginal benefi ts given by E M B = 2 – 0.02Q. a. Find the quantity of bread produced in Paris in the absence of any government intervention. b. To achieve the socially optimal output, government can use a price-based intervention. Determine the ideal measure for government to use to achieve this goal. Specify both the type of policy and its magnitude. 9. a. Without any government intervention, the quantity of bread produced is P = 10 – 0.1Q = 2 + 0.1Q = MC 0.2Q = 8 Q = 40

Externalities and Public Goods

Chapter 17

b. Ideally, society would like producers to consider all of the benefi ts their activity creates, both internal and external. Thus, the total social benefit is given as SD = P + EMB = 10 – 0.1Q + 2 – 0.02Q = 12 – 0.12Q So, the magnitude of a price-based intervention is 12 – 0.12Q = 2 + 0.1Q = MC 0.22Q = 10 Q ≈ 45.45 Producers are under-producing relative to the welfare-maximizing quantity of 45.45. The government can use a pricebased intervention to encourage them to produce more. In this case, the appropriate intervention is to subsidize production. At the ideal quantity, bread baking c...