Unit 9: Market Failure – Problems
9.1: Efficiency and inefficiency in markets
CORE PROBLEMS
Problem 1
Anna and Bob both have cows on their property. Anna values a cow at $2000 but Bob is a better butcher, and so he values a cow at $3000.
For each transaction below, indicate (i) whether Anna is better off, worse off or the same, (ii) whether Bob is better off, worse off or the same, (iii) whether the transaction is an efficiency improvement in the Pareto sense, and (iv) whether the transaction is an efficiency improvement in the Hicks-Kaldor sense.
a. Anna sells a cow to Bob for $2500. b. Anna sells a cow to Bob for $3000.
c. While drunk, Anna sells a cow to Bob for $1500.
9.2: Information problems
CORE PROBLEMS
Problem 1
You own an ice cream shop and need to hire employees to make sundaes. Fast workers can make your shop $100 of profit every day. They know they are fast and will only work for a daily wage of $80 or more. But some workers are slow, and can only make your shop $50 of profit every day. These workers know they are slow, so they will work for a daily wage of $40 or more. You know that half of the workers in town are fast and half are slow, but you can’t tell them apart before you give them the job and agree on a wage.
a. If both types of workers are equally likely to look for a job at your shop, what is the highest daily wage you are willing to pay?
b. Which type of workers will be willing to work for you at the wage you found in (a)? c. Considering (b), how much are you willing to pay workers now?
d. What market failure does this exercise illustrate?
Problem 2
Prior to 2008, farmers in Ghana grew and sold their own crops. After 2008, the government collected and sold all of the crops together, dividing up the revenue evenly among farmers. What do you think happened to the output and quality of crops as a result? What kind of market failure does this exercise illustrate?
Problem 3
SUPPLEMENTARY PROBLEMS
Problem 4
The magical lands of Oz and Narnia are neighboring countries. In Oz, each worker is paid a wage equal to her productivity. In Narnia, on the other hand, the government finds the average productivity of workers in the economy and pays all workers this wage (i.e. all workers earn the same wage). The year is currently 2210.
The table below shows the five workers who presently live in Narnia.
Worker Productivity
Ariel $100
Beatrix $90
Cassandra $50
Diomede $35
Echo $5
a. How much are workers in Narnia paid in 2210?
b. At the beginning of 2211, workers in Narnia have an opportunity to leave and move to Oz. Which workers will leave?
c. How much are the remaining workers in Narnia paid in 2211?
d. At the beginning of 2212, the remaining workers in Narnia have another opportunity to leave and move to Oz. Which workers will leave?
e. Who is left in Narnia in 2212? What is the wage there?
f. One problem that economists talk about in communist economies is moral hazard – when
pay is not tied to productivity, people have less incentive to work hard. This exercise points out a different problem. What is it?
Problem 5
Problem 6
The US government gives loans to students who cannot afford to go to college, which students repay once they start working. At one point, the government experimented with “income-contingent loans”. That is, people who ended up earning a lot of money in their jobs had to repay more than people who end up earning low incomes, even if both borrowed the same amount. These programs turned out to be a disaster, but economists had predicted this in advance.
a. Describe the adverse selection problem associated with income-contingent loans. b. Describe the moral hazard problem associated with income-contingent loans.
Problem 7
Consider an entrepreneur who has an idea for a business and a financier (e.g. a bank) that provides the startup funds. There are different ways to arrange the financing. In the Western banking system, the entrepreneur pays a fixed return to the lender – basically, the interest on the loan. By contrast, in the Islamic banking system, the profits paid to the financier are proportional to the profits of the project – a profit-sharing arrangement.
a. Why might an economist consider the Islamic arrangement to be more efficient than the Western financing system?
b. Given your answer to (a) why do you think Western banks continue to use fixed interest instead of a profit-sharing system?
Problem 8
9.3: Public Goods
CORE PROBLEMS
Problem 1
For each good, indicate whether the good is excludable or nonexcludable, then indicate whether it is rival or nonrival. Are there any pure public goods on the list?
a. Wilderness areas
b. Medical school education c. Public television programs
d. An Internet site providing information on airline schedules
e. Immunizations
Problem 2
A community has 100 residents who are worried about security. The table below gives the cost of hiring security guards, as well as the benefit enjoyed by each resident, depending upon the number of guards who are hired.
Guards Total Benefit
(each resident)
Marginal Benefit (each resident)
Marginal
Social Benefit Total Cost
Marginal Cost
0 0 -- -- 0 --
1 10 150
2 16 300
3 18 450
4 19 600
a. Complete the table.
b. Explain why the guards are a public good for residents of the neighborhood.
c. If each individual resident decides about hiring and paying for guards on his own, how many guards will be hired?
d. If the residents act together, what is the optimal number of guards for them to hire? e. Does the private market yield an efficient outcome here? If not, what is the source of the
SUPPLEMENTARY PROBLEMS
Problem 3
The table below shows Tanisha’s and Ari’s marginal benefit for cleaning the street in front of their house, depending on the number of cleanings per month. The street cleaning is a public good that benefits both Tanisha and Ari. The marginal cost for each cleaning is equal to $9.
Cleanings MB (Tanisha) MB (Ari)
0 - -
1 10 8
2 6 4
3 2 1
a. If Tanisha has to pay for the cleanings on her own, how many cleanings will there be? b. If Ari has to pay for the cleanings on his own, how many cleanings will there be? c. What is the socially efficient number of street cleanings?
Problem 4
A neighborhood consisting of 200 men and 100 women is planning to build a nature reserve. The table below shows the total benefit to each man and to each woman of the reserve, based on its total size. Acreage can be added to the reserve at $22,500 per acre. The reserve is a public good: once built, all residents benefit from it. What is the efficient size of the reserve?
Acres TB (each man) TB (each woman)
0 0 0
1 100 150
2 160 280
3 200 400
4 220 500
Problem 5
The government is considering whether to build a paved access road from a highway that would benefit three firms. The first firm would experience a $12 million increase in its profits if the road is built. The second firm would experience a $5 million increase in profits and the third firm would experience a $2 million increase in profits. The cost to build the road is $16 million. The government is willing to build the road, but only if it can raise the $16 million from the three firms.
a. Is it efficient to build the road?
b. Suppose that, in order to build the road, the government has to evenly divide the cost among the three businesses. This is called a uniform tax. If the businesses vote on whether to build the road, financed by a uniform tax, will the road be built?
c. If the business owners negotiated with each other before the vote took place, might they be able to reach a different outcome than the one you identified in (b)?
Problem 6
9.4: Externalities
CORE PROBLEMS
Problem 1
Smoking causes significant external costs for society. The table below shows the private benefits and costs, depending on the number of packs of cigarettes that Tanja smokes per week. Note that each pack of cigarettes costs $4.40. In addition to the private costs, each pack of cigarettes smoked also creates an external cost of $6.00.
Packs Total Benefit MB Total Cost
(Private) MPC MSC
0 $0 -- $0 -- --
1 $15.00 $4.40
2 $25.00 $8.80
3 $32.00 $13.20
4 $36.00 $17.60
5 $37.00 $22.00
a. Complete the table.
b. How many packs of cigarettes will Tanja choose to smoke?
c. What is the efficient number of packs of cigarettes for Tanja to smoke? d. What is the appropriate Pigouvian tax per pack of cigarettes for this example?
Problem 2
Education creates a positive externality. The table below shows Sam’s private costs and benefits associated with various levels of education that he can choose to acquire. But each year of education that he acquires also creates an external benefit of $8000 for the rest of society.
Years Total Benefit
(Private) MPB MSB Total Cost MC
10 $120,000 -- -- $25,000 --
11 $139,000 $41,000
12 $157,000 $58,000
13 $174,000 $76,000
14 $190,000 $95,000
15 $205,000 $115,000
16 $219,000 $136,000
17 $232,000 $158,000
a. Complete the table.
b. How many years of education will Sam choose on his own?
c. What is the socially efficient number of years of education for Sam to acquire?
d. If you were in charge of education funding, would you add a tax for schooling, or would you pay a subsidy? What is the amount of the tax or subsidy?
e. How many years of education will Sam choose with the tax or subsidy from (d)?
Problem 3
Erin, a smoker, was assigned to live in a room with two nonsmoking roommates, Melissa and Molly. It is worth $125 for Erin to be able to smoke in the room. The smoke irritates Melissa and Molly in the amount of $50 each.
a. Is banning all smoking in dorm rooms an efficient solution here? b. Is it efficient for Erin to smoke in the dorm room?
c. If school policy is that smoking is allowed in all rooms, will Erin smoke in the room? Will any side payments be made?
Problem 4
Erin, a smoker, was assigned to live in a room with two nonsmoking roommates, Melissa and Molly. It is worth $125 for Erin to be able to smoke in the room. The smoke irritates Melissa in the amount of $50. But Molly gets horrible headaches, so she would pay $200 to not have to live with the smoke.
a. Is it efficient for Erin to smoke in the dorm room?
b. If school policy is that smoking is allowed in all rooms, will Erin smoke in the room? Will any side payments be made?
c. If school policy is that smoking is not allowed in dorm rooms unless all roommates agree, will Erin smoke in the room? Will any side payments be made?
d. How could Melissa benefit from a free-rider problem in this example?
SUPPLEMENTARY PROBLEMS
Problem 5
Two dry cleaning companies are a major source of air pollution – Aphrodite’s Cleaners and Juno’s Cleaners. Aphrodite emits 230 tons of pollution every year, and Juno emits 120 tons of pollution every year. Aphrodite can reduce pollution at a cost of $500 per ton. Juno can reduce pollution at a cost of $200 per ton.
a. If the government passes a law requiring each company to reduce its pollution to 100 tons, what is the total cost of pollution reduction?
b. Now suppose that the government issues 100 pollution vouchers to each company, entitling the company to emit 100 tons of pollution. The vouchers can be traded and resold. How much is a voucher worth to Aphrodite? How much is a voucher worth to Juno?
c. Who will sell vouchers and who will buy them? How many vouchers will be traded?
d. What is the total cost of pollution reduction under this system?
Problem 6
Getting a flu shot not only reduces your chance of getting the flu, but also reduces the chance that you will pass it on to someone else. This is a positive externality.
a. Draw the marginal private benefit and marginal social benefit associated with various quantities of flu shots. Assume that the marginal cost is constant, and draw this as well. b. Show the market equilibrium level of flu shots and the socially optimal level of flu shots. c. Many University health centers offer free flu shots to students. Does this solution
Problem 7
The production of drums creates an externality. The diagram below shows the marginal private cost (MPC) and marginal social cost (MSC) associated with drums. Also shown are the demand (MB) curve and the corresponding marginal revenue (MR) curve for a monopolist.
a. Is the externality positive or negative? b. What is the socially optimal level of output?
c. Suppose that drums are produced by a single-price monopoly. i. What is the monopolist’s output level?
ii. What price will the monopolist charge?
iii. To induce the monopolist to produce the socially optimal output, should the government levy a tax or grant a subsidy?
iv. What is the dollar value of the necessary tax or subsidy? d. Suppose that drums are produced in a perfectly competitive market.
i. How much output will be produced?
ii. What price will firms charge?
iii. To induce competitors to produce the socially optimal output, should the government levy a tax or grant a subsidy?
Problem 8
Developing a piece of land along a beach would generate $40,000 of profit for a developer. However, three nearby neighbors would sustain damages. Anna would sustain $20,000 in damages. Beth would sustain $15,000 in damages. Chloe would sustain $11,000 in damages.
a. Is it efficient for the land to be developed?
b. Suppose a judge rules that the developer is allowed to develop the land if he wants to. If negotiation is allowed freely after the ruling, what will happen?
c. Suppose instead that the judge rules that the developer is not allowed to develop the land. If negotiation is allowed freely after the ruling, what will happen?
d. Suppose that it would cost $10,000 for the neighbors to hire a lawyer and bargain with the developer. Does this change the answer to (b)?
e. When negotiation is free, does it matter in terms of reaching the efficient outcome how the judge initially rules in the case?
f. When negotiation is costly, does it matter in terms of reaching the efficient outcome how the judge initially rules in the case?
Problem 9
Bill and Doug have properties that adjoin Matt’s farm. Current law permits Matt to use his farm for any purpose that he wants. There are two potential uses for his farm. He could grow tomatoes, for a profit of $200,000 or he could raise pigs, for a profit of $500,000. The problem is that the pig farm smells horrible. Bill would be willing to pay $200,000 to eliminate the pig farming and Doug would be willing to pay $150,000 to eliminate the pig farming.
a. What is the lowest payment that Matt will accept to grow tomatoes instead of raising pigs? b. Suppose that Bill pays $200,000 and Doug pays $150,000 to Matt for him to raise tomatoes
instead of pigs. Who gains and who loses? Is this a Pareto improvement?
Problem 10
The diagram below shows the marginal benefit to Firm A and Firm B associated with being able to emit pollution as they produce paper. The diagram shows the benefit to the firms per unit of pollution emitted. The marginal private cost is zero.
a. Suppose that the government does not regulate pollution emissions. How much pollution will be emitted?
b. Now suppose that the government wants to limit total emissions to 1600 tons of pollution. What emissions tax (per ton of pollution) could the government levy to achieve this outcome?
