Econ 1 - Problem Set 6 With Solutions

Problem Set 6 Hard copies of your answers are due at the beginning of your section, either on Thursday, November 3, or Friday, November 4. For example, if your section starts at 10:00am on Friday, you should submit your answers to your TA in your section classroom at 10:00am on Friday, November 4. Late problems earn zero points. Note: you can work on these problems or your own, or in a small group with other current Econ 1 students. If you choose to work in a group, each student needs to hand in a separate, individual copy to his/her TA. 1. According to economists Becker and Grossman, each pack of cigarettes smoked creates about 68 cents of externalities borne by other members of society. The externalities include the costs of cigarette smokers’ excess use of health services, costs of fetal death, secondhand smoke, etc. a. Explain how a tax could be used to correct the externality. Show it graphically. b. Mention another way that the government may try to use to correct the overproduction of cigarettes due to the negative externality. 2. Suppose that it costs $25,000 per day to build and maintain a bridge potentially serving 20,000 people. 10,000 of these people are willing to pay $2 per day to cross the bridge, while the other 10,000 value the bridge at $1 per day. a. Assuming that there is no congestion, is it efficient to build the bridge? b. Can you find a toll that will raise revenues sufficient to cover the costs of building and operating the bridge? c. Is the bridge a public good? What does your answer to parts (a) and (b) indicate about a possible role for government intervention? 3. A dentist and a writer live next door to each other, and each has her office at home. Screams of pain from the patients in the dentist’s office interfere with the writer’s creativity, causing her to write inferior novels and lose $800 per year in income. The dentist would have to spend $600 to install soundabsorbing material on her office walls, and this material would have to be replaced each year. The writer sues the dentist. The court can rule in favor of the author and require the dentist to soundproof her walls, or it can rule in favor of the dentist and dismiss the case. Explain what would happen under each ruling if: a. The dentist and the writer are on speaking terms (small transaction costs, ignoring court fees).

b. They are not speaking to each other under any circumstances (large transaction costs). Make sure that your answer for parts (a) and (b) contains some comparison between the socially optimal outcome and the outcome actually achieved in each circumstance. 4. The Farm Bill passed in May 2002 promises billions of dollars in additional subsidies for agricultural producers, with support programs for wheat, corn, dairy, and peanut production among others. Use economic analysis to describe and explain the effects of these subsidies. Why do you think the Farm Bill was passed? 5. Cardassia and the Dominion produce only two goods: phasers and transporters. Cardassia can produce either 200 phasers or 100 transporters in one day, while the Dominion can produce 500 phasers or 1000 transporters (all of them with constant opportunity costs). (a) What are the opportunity costs of producing phasers for Cardassia and the Dominion? (b) If trade were to occur between Cardassia and the Dominion, who would specialize in the production of phasers and who would produce starships. (c) What would be the range of prices that would allow trade to occur? (d) If Cardassia discovered a new technology that allowed it to produce 500 transporters per day with its existing resources, how would your answers to (a), (b) and (c) change? 6. The nation of Acirema is “small,” unable to affect world prices. The demand curve is QD=400-10P. The supply curve is QS=100+5P. (a) Fill the following table. What is the equilibrium price and quantity of peanuts without trade with other nations? Explain verbally and graphically. Price Demand Supply 0 5 10 15 20 30 40 (b) Suppose the world price of peanuts is $10 per bag. If trade with other nations is unrestricted, will Acirema import or export peanuts? How many bags of peanuts will be imported or exported? Explain verbally and graphically. (c) If there is an import quota of 75 bags, what will be the resulting domestic price and production? Explain verbally and graphically.

Extra practice problems (completely optional; no points awarded) A. Many agricultural crops are harmed by beetles and other insects. These harmful insects are prey for the praying mantis, a large insect. The praying mantis is not an endangered species, but several agricultural states still impose a fine on anyone caught killing a praying mantis. Is there a good economic reason for such a fine? Explain. B. Imagine that wine makers in the state of Washington petitioned the state government to tax wines imported from California. They argue that this tax would both raise tax revenue for the state government and raise employment in the Washington state wine industry. Do you agree or disagree with this claim? Is it a good policy? Explain. C. Assume that American rice sells for $100 per bushel, Japanese rice sells for 16,000 yen per bushel, and the nominal exchange rate is 80 yen per dollar. (a) Explain how you could make a profit from this situation. What would be your profit per bushel of rice? If other people exploit the same opportunity, what would happen to the price of rice in Japan and the price of rice in the United States. (b) Suppose rice is the only commodity in the world. What would happen to the real exchange rate between the United States and Japan? Explain. D. Capitol has 1200 workers, and it can produce two goods, apples and bananas. Three workers can produce a ton of apples, while just two are necessary to produce one ton of bananas. Worthing has a labor force of 800 workers. The production of apples and bananas require 5 and 1 workers, respectively. (a) Graph the production possibility frontiers for the two countries. (b) What are the opportunity costs of apples in terms of bananas in Capitol and Worthing? (c) In the absence of trade between Capitol and Worthing, what would the prices of apples in terms of bananas be in each country? (d) Describe the pattern of trade. (e) Show graphically that both Capitol and Worthing gain from trade.

Problem Set 6 Solutions Question 1. (a) In the case of a negative externality, the marginal social costs exceed the marginal private costs and the quantity produced (q) exceed socially optimal quantity q*. A tax on cigarettes could be imposed. A tax equal to the difference between the marginal private cost and the marginal social cost (in this case a tax of 68 cents/pack) would shift the supply curve up such that the marginal private cost with tax would be equal to the marginal social cost. This would reduce the equilibrium quantity produced to the efficient level. Thus, the quantity of cigarettes produced would decrease from q to q*.

Marginal Social Cost P tax

Marginal Private Cost

D Q q* q

b. Other possible means that the government could use to correct the overproduction of cigarettes include: • Government Quota: Assuming the government could know the efficient level, it could impose a quota, limiting production of cigarettes to q*. The challenge for the government is estimating the q* perfectly. Additionally, if supply and demand change, the government would need to adjust the quota. • Government regulation of cigarette quality: The government could impose “quality standards” and allow production only of cigarettes that meet minimum health standards. This would decrease the negative externality and also increase the marginal private cost, both of which would bring the MPC closer to the MSC. Question 2. (a) Assuming there is no congestion, it is efficient to build the bridge. The total willingness to pay of all 20,000 people is $2*10,000 + $1*10,000 = $30,000 per day, while the bridge only costs $25,000 per day. So, building the bridge would provide a net social surplus of $5,000 per day. (b) It is not possible to find a single toll that will raise revenues sufficient to cover the costs of building the bridge. To see this, think about whether the government could raise the necessary $25,000 per day to finance the bridge. It could charge a $2 toll, in which case, 10,000 people would use the bridge, bringing in $2*10,000 = $20,000 per day in revenue. Alternatively, the government could charge a $1 toll, in which case, all 20,000 people would use the bridge, bringing in $1*20,000 = $20,000 per day in revenue. Any other toll would bring in less revenue.

Thus, assuming a single toll, only $20,000 per day could be raised, falling $5,000 short of the $25,000 per day necessary to finance the bridge. If the government was able to price discriminate, such that it could discern the 10,000 who were willing to pay $2 per day to cross the bridge from those who were only willing to pay $1 per day, then it could charge those willing to pay $2 more. This would allow it to bring in enough revenue to cover the costs of building and operating the bridge. An example of this may be if those willing to pay $2 per day all commuted across the bridge in the morning and returned in the evening. In that case, a toll that varied by the time of day could be implemented. (c) Assuming that there is no congestion, this bridge is non-rival (one person’s use of the bridge does not infringe on anyone else’s use of the bridge) and non-excludable (no one can be excluded from the bridge), and hence it is a public good. The answers to parts (a) and (b) indicate that it would be socially optimal for the bridge to be in place, but the bridge could not be financed by the private market or a single toll. Government intervention would have to find a way to charge a higher toll to those with a higher willingness to pay. The government could also finance the construction of the bridge by imposing some other sort of tax, such as a property tax, on the 20,000 people who use the bridge (e.g., if everyone in the town uses the bridge). If the costs were distributed equally, the cost per person per day would be $1.25. The socially optimal outcome could be achieved in this manner, but note that there would be distributional consequences. More specifically, the 10,000 people who were only willing to pay $1 would actually face a net loss of $0.25, while the 10,000 people who were willing to pay $2 would have a net gain of $0.75. Question 3. a. The dentist and the writer are on speaking terms (small transaction costs, ignoring court fees) Court rules in favor of dentist Court rules in favor of writer If the court rules in favor of the dentist, the dentist would If the court rules in favor of the writer, have no incentive to soundproof her walls. However, we the dentist would have to pay $600 to know by the Coase theorem that if property rights are soundproof the walls. In this case, the clearly defined and transaction costs are low, then the dentist would be forced to internalize efficient resolution of externalities will be reached. In this the costs of the negative externality. case, the writer would have the incentive to pay the dentist Since the costs of the negative $600 to soundproof the walls. This is because the writer externality will be internalized, the would be better off by paying the $600 and not losing any efficient outcome will be reached. money from the screams of pain than by not paying the $600 and losing $800. Thus, given the small transaction costs, the efficient outcome would be reached because the negative externality would be internalized by the writer.

b. The dentist and the writer are NOT on speaking terms (large transaction costs) Court rules in favor of dentist Court rules in favor of writer If the court rules in favor of the dentist, the dentist would If the court rules in favor of the writer, have no incentive to soundproof the walls. Since the the dentist would have to pay $600 to dentist and the writer are not speaking to each other under soundproof the walls. In this case, the any circumstances, the costs of negotiation (perhaps dentist would be forced to internalize through a third party) would be high. Thus, in addition to the costs of the negative externality.

paying the dentist the $600 to soundproof the walls, the writer would also incur the costs of negotiating the agreement. If these costs exceeded $200 (and assuming the negotiations would have to occur each year), then the writer would not have the incentive to pursue negotiations because the costs of getting the dentist to soundproof the walls would exceed the benefits. Thus, with high transaction costs, the efficient outcome would be less likely. This situation illustrates the importance of low transaction costs in the application of the Coase theorem.

Since the costs of the negative externality will be internalized, the efficient outcome will be reached.

Question 4. There are two possible answers for this: 1. The subsidy is given per unit of quantity. P

S

With the subsidy, price decreases (P1 Æ P2) and quantity increases (Q1 Æ Q2). Consumers of Ssubsidy agricultural goods benefit; CS increases (a Æ a+b+e+f). Agricultural producers also benefit; PS a P1 h increases (b+c Æ c+d+g). However, society as a b e f i whole is worse off, because now there is a deviation P2 g from the efficient quantity due to overproduction. c This is shown in the creation of DWL (h+i). Note that the government pays out the size of the subsidy d times the quantity produced with the subsidy, which D can be seen on the graph as the area between the Q1 Q2 Q supply curve with the subsidy and the supply curve without the subsidy (d+e+f+g+h+i). So, the DWL can also been seen as the social surplus after the subsidy (PS_after+CS_after-govt cost) minus the social surplus before the subsidy (PS_before+CS_before) 2. The subsidy is given in terms of a price floor when the government buys the extra unsold quantity of agricultural products at a set price. With the subsidy, the price increases to the minimum price floor level (P2), and the overall quantity sold increases. However, quantity demanded by consumers decreases (Q1 Æ Qd), but quantity supplied increases (Q1 Æ Qs) because the government buys Qsubsidy - Qd. Consumers of agricultural goods are worse off, as CS decreases (a+b+d Æ a). However, agricultural producers benefit, as PS increases (c+e Æ c+e+b+d+f). Overall, society as a whole is worse off because once again, the producers are producing more than the efficient market quantity (Q1). The subsidy results in the creation of DWL (g).

P

P2

S

a f

P1

b

d

c

e

g

D Qd

Q1

Qsubsidy

Q

See the dairy example in Problem Set 3, Extra Practice D, for a more in-depth analysis of the welfare effects of a price floor. It is likely that the Farm Bill passed for food security and other political reasons (e.g., the political clout of farmers, lobbying, etc). Consumers also tend to like low food prices.

Question 5. (a) Cardassia’s tradeoff is 200 phasers for 100 transporters. Hence, the opportunity cost of one phaser is 0.5 transporters in Cardassia. Dominion trades off 500 phasers for 1000 transporters, so one phaser costs 2 transporters in Dominion. (b) Because the opportunity cost of one phaser is lower is Cardassia (0.5 < 2), Cardassia would specialize in phasers. Dominion would specialize in transporters. (c) The range of prices lies between the respective countries’ opportunity costs of production. The price would have to be between 0.5 and 2 transporters per phaser. (d) Cardassia’s tradeoff changes to 200 phasers for 500 transporters. The opportunity cost of one phaser rises to 5/2 = 2.5 transporters. Dominion’s opportunity cost remains unchanged at 2 transporters per phaser. Dominion now has a lower opportunity cost of producing phasers, so Dominion would specialize in phasers, and Cardassia in transporters (the specialization is reversed). The trading price would be between 2 and 2.5 transporters per phaser.

Question 6. (a) Price 0 5 10 15 20 30 40

Demand 400 350 300 250 200 100 0

Supply 100 125 150 175 200 250 300

Without trade to other nations, the equilibrium price and quantity are when supply is equal to demand in Acirema. This occurs at a price of $20, and a quantity of 200. Graphically, the market for peanuts in Acirema can be seen as follows:

Peanut Price

Supply

40

30

20

10 Demand

100

200

300

400

Quantity of Peanuts

(b) If the world price of peanuts was $10 per bag and trade with other nations was unrestricted, then Acirema would import peanuts, because the cost of the imported peanuts would be below the market price in Acirema prior to trade. In this case, Acirema can be thought of as a price taker, because the nation is “small” and unable to affect world prices. So, the equilibrium price when trade is unrestricted would be $10 per bag. At this price, the demand for peanuts is 300 bags, and the supply of peanuts is 150 bags. The difference, or shortage, will be made up for by importing 300-150 = 150 bags of peanuts. This can be seen graphically:

Peanut Price

Supply

40

30

20

world price

10

Demand 100

150

200

300

400

Quantity of Peanuts

imports

(c) If there is an import quota for 75 bags, then the “shortage” or difference between supply and demand is limited to 75 bags. The resulting domestic price and quantity can be read off the graph where demand exceeds

supply by 75. This price is a price of $15, since supply is 250 and demand is 175, giving a difference of 250-175 = 75. Alternatively, this difference can be solved for by using the equations for supply and demand in the peanut market. Setting QD – QS = 75, allows us to solve for the price: QD – QS = 75 [400-10P] – [100+5P] = 75 300-15P = 75 P = $15 As mentioned above, from reading off the table, at a price of $15, the resulting domestic production is 175, and the domestic consumption is 250. This can be seen graphically: Peanut Price

Supply

40

30

20 15 Demand 10

100

175 200 250 Imports = 75

300

400

Quantity of Peanuts

EXTRA PRACTICE PROBLEMS SOLUTIONS A. There is a reasonable economic reason for the fine imposed on anyone killing a praying mantis in agricultural states. Because the preying mantis provides a valuable service to farmers by keeping down the population of beetles and other insects that harm crops, killing a preying mantis can be thought of as imposing a negative externality. That is, the killing a preying mantis has negative spillover effects on farmers by allowing beetles and other insects to damage the crop more than they would have had the preying mantis been around. Thus, the agricultural states with fines on killing a preying mantis are attempting to “internalize the externality” by forcing those who would kill a preying mantis to pay for the negative externality they cause. This raises the effective price that people pay for killing a preying mantis—thus reducing the number of people will kill a preying mantis (reducing the quantity). If the fine is fully enforced, and is at the level of the externality, then only the socially optimal number of preying mantises will be killed. B. We could approach this problem with two different sets of assumptions. 1. First, let’s begin by assuming that WA wine and CA wine are perfect substitutes. Assume also that WA is a small state (WA is a price taker). In addition, assume WA is small enough that the decreased demand for CA wine will not influence the price of CA wine. As can be seen in the graph above, the tax (tariff) imposed on CA wine results in a decrease in CS, an increase in PS, and DWL for the WA society. Increased production of WA wine would lead to increased employment in the WA wine industry. And the WA government would receive a tax (tariff) revenue of E. However, not only would consumers in WA be worse off but WA society as a whole would suffer DWL.

Washington Wine Market

Pre-Tariff Post-Tariff

P S

Producer Surplus

G

G+C

Consumer Surplus

A+B+C +D+E+ F

A+B

Revenue from Tax

-

E

Deadweight Loss

-

D+F

(Domestic

Supply of Wine)

A B

P0+tariff C P0

D

E

F D

G

(Domestic Demand for Wine)

S1 S2

D2

Imports after tariff Imports before tariff

D1

Q

2. Secondly, assume that CA wine and WA wine are not perfect substitutes. In this case, the price of CA wine may be different than the price of WA wine. We now need to analyze the two markets separately, First, let’s consider the WA market for CA wine. As can be seen below, the tax (tariff) does produce tax revenue but also results in DWL (in this case, borne by CA producers and WA consumers). Washington Market for CA wine New Export Supply Curve

P Export Supply Curve (Supply of exported wine from CA) Shaded area = government revenue

Price paid by Wash Consumers with tariff

DWL Price without tariff Price received by CA producers (with tariff)

Import Demand Curve (WA’s demand for CA wine)

q1 q0

Q

Secondly, let’s consider the WA market for WA wine. The demand for WA wine will shift up (depending on the degree to which the two wines are substitutes). This will increase the quantity produced and the price of WA wine. The increase in quantity produced will lead to increased employment. The evaluation of the policy thus depends on the assumptions made. However, in both cases, WA risks provoking retaliatory measures by CA and perhaps provoking a tariff war.

C. (a) When American rice sells for $100 per bushel and Japanese rice sells for 16,000 yen per bushel and the nominal exchange rate is 80 yen per dollar, you could make a profit on this situation by buying rice in America, and selling it in Japan. Rice can be sold for 16,000 yen per bushel / 80 yen per dollar = $200 per bushel in Japan. Assuming negligible transportation costs, buying rice in American and selling rice in Japan yields a profit of $200 - $100 = $100 per bushel. With transportation costs of T, the profit would be $200 - $100 – T = $100 – T per bushel. This difference in price across countries is what is called an arbitrage opportunity. If other people exploit the same opportunity, the demand for rice in the United States would rise (due to people demanding rice to export to Japan), while the supply of rice in Japan would rise (due to importers selling their imported rice). This would lead to the price in the United States rising and the price in Japan falling. The arbitrage profit opportunity would continue until the price rises enough in

the United States and falls enough in Japan that no more additional profit can be made. Assuming negligible transportation costs, this would imply that the price in Japan would be exactly equal to the price in the United States. If there are transportation costs of T, the price in the United States would be the price in Japan minus the transportation costs: PUS = PJap – T (b) If rice is the only commodity in the world, then the real exchange rate between the United States and Japan would fall. That is, the yen will appreciate in value relative to the dollar. This is because the exchange rate is greatly affected by the price of goods and services in one country compared to another. In this case, the price of rice is falling in Japan relative to the United States. So, since rice is the only commodity, the average price of goods and services is decreasing in Japan relative to the United States. This means that relative to before the trade, the demand for Japanese goods (in this case rice) in the United States is greater than is was before. So, the yen will appreciate in value. (See Taylor p. 421) D. a. To graph the production possibility frontiers, the following chart may be helpful: If all resources devoted to If all resources devoted to apples, none to bananas bananas, none to apples 400 tons apples 600 tons bananas Capitol 160 tons apples 800 tons bananas Worthing (b) Opportunity cost of apples in terms of bananas: Capitol: cost of an apple = 1.5 bananas Worthing: cost of an apple = 5 bananas (c) In the absence of trade between Capitol and Worthing: Price of apples in Capitol in terms of bananas: apple = 1.5 bananas Price of apples in Worthing in terms of bananas: apple = 5 bananas (d) Pattern of trade: As can be seen from the calculations above, Capitol has the comparative advantage (is relatively more efficient) in producing apples while Worthing has the comparative advantage in producing bananas. We know that by exporting the goods it has a comparative advantage in, a country can increase consumption of both goods. Thus, Capitol should export apples and Worthing should export bananas. The relative price with trade would be somewhere between the range of prices in the two countries before trade. That is, the price of apples in terms of bananas would be somewhere between 1.5 and 5. (e) Capitol and Worthing both gain from trade: Assume that with trade, the price of an apple = 2 bananas (the price determines the slope of the Consumption Possibility Curve for each country).

apples

400

Capitol Before Trade

apples

Worthing Before Trade

400

Production Possibilities Curve

Production Possibilities Curve

bananas

bananas

800

800 apples

400

apples

Capitol After Trade

Consumption Possibilities Curve

400

Worthing After Trade

Consumption Possibilities Curve

bananas

bananas

800

800