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Goods and services analysis, Exercises of Mathematics

Danang College of Technology (DCT)Mathematics

Public finance and public policy solutions manual, Lecture notes for Social Statistics and Data Analysis. University of East Anglia

Typology: Exercises

2017/2018

Uploaded on 09/03/2018

henry9009
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CHAPTER 1
1/Some goods and services are provided directly by the government, while others are funded publicly but
provided privately. What is the difference between these two mechanisms of public financing? Why do
you think the same government would use one approach sometimes and the other approach at other
times?
2/Why does redistribution cause efficiency losses? Why might society choose to redis-tribute resources
from one group to another when doing so reduces the overall size of the economic pie?
3/ Consider the four basic questions of public finance listed in the chapter. Which of these questions are
positive—questions that can be proved or disproved—and which are normative—questions of opinion?
Explain your answer.
4/ One rationale for imposing taxes on alcohol consumption is that people who drink al-cohol impose
negative spillovers on the rest of society—for example through loud and unruly behavior or intoxicated
driving. If this rationale is correct, in the absence of governmental taxation, will people tend to consume
too much, too little, or the right amount of alcohol?
5/ In order to make college more affordable for students from families with fewer resources, a
government has proposed allowing the student of any family with less than $50,000 in savings to attend
public universities for free. Discuss the direct and possible indirect effects of such a policy.
CHAPTER 2
1/ You have $100 to spend on food and clothing. The price of food is $5 and the price of clothing is $10.
a. Graph your budget constraint.
b. Suppose that the government subsidizes clothing such that each unit of clothing is half-price, up
to the first 5 units of clothing. Graph your budget constraint in this circumstance.
2/ Explain why a consumer’s optimal choice is the point at which her budget constraint is tangent to an
indifference curve.
3/ Use utility theory to explain why people ever leave all-you-can-eat buffets.
4/ Since the free market (competitive) equilibrium maximizes social efficiency, why would the
government ever intervene in an economy?
5/ A good is called normal if a person consumes more of it when her income rises (for example, she might
see movies in theaters more often as her income rises). It is called inferior if a person consumes less of it
when her income rises (for example, she might be less inclined to buy a used car as her income rises).
Sally eats out at the local burger joint quite frequently. The burger joint suddenly lowers its prices.
a. Suppose that, in response to the lower burger prices, Sally goes to the local pizza restaurant less
often. Can you tell from this whether or not pizza is an inferior good for Sally?
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CHAPTER 1

1/Some goods and services are provided directly by the government, while others are funded publicly but provided privately. What is the difference between these two mechanisms of public financing? Why do you think the same government would use one approach sometimes and the other approach at other times? 2/Why does redistribution cause efficiency losses? Why might society choose to redis-tribute resources from one group to another when doing so reduces the overall size of the economic pie? 3/ Consider the four basic questions of public finance listed in the chapter. Which of these questions are positive—questions that can be proved or disproved—and which are normative—questions of opinion? Explain your answer. 4/ One rationale for imposing taxes on alcohol consumption is that people who drink al-cohol impose negative spillovers on the rest of society—for example through loud and unruly behavior or intoxicated driving. If this rationale is correct, in the absence of governmental taxation, will people tend to consume too much, too little, or the right amount of alcohol? 5/ In order to make college more affordable for students from families with fewer resources, a government has proposed allowing the student of any family with less than $50,000 in savings to attend public universities for free. Discuss the direct and possible indirect effects of such a policy. CHAPTER 2 1/ You have $100 to spend on food and clothing. The price of food is $5 and the price of clothing is $10. a. Graph your budget constraint. b. Suppose that the government subsidizes clothing such that each unit of clothing is half-price, up to the first 5 units of clothing. Graph your budget constraint in this circumstance. 2/ Explain why a consumer’s optimal choice is the point at which her budget constraint is tangent to an indifference curve. 3/ Use utility theory to explain why people ever leave all-you-can-eat buffets. 4/ Since the free market (competitive) equilibrium maximizes social efficiency, why would the government ever intervene in an economy? 5/ A good is called normal if a person consumes more of it when her income rises (for example, she might see movies in theaters more often as her income rises). It is called inferior if a person consumes less of it when her income rises (for example, she might be less inclined to buy a used car as her income rises). Sally eats out at the local burger joint quite frequently. The burger joint suddenly lowers its prices. a. Suppose that, in response to the lower burger prices, Sally goes to the local pizza restaurant less often. Can you tell from this whether or not pizza is an inferior good for Sally?

b. Suppose instead that, in response to the lower burger prices, Sally goes to the burger joint less often. Explain how this could happen in terms of the income and substitution effects by using the concepts of normal and/or inferior goods. 6/ Consider a free market with demand equal to Q = 1,200 – 10P and supply equal to Q = 20P. a. What is the value of consumer surplus? What is the value of producer surplus? b. Now the government imposes a $10 per unit subsidy on the production of the good. What is the consumer surplus now? The producer surplus? Why is there a deadweight loss associated with the subsidy, and what is the size of this loss? CHAPTER 3 1/ Peterson, Hoffer, and Millner (1995) showed that air bag use has led to increases in car crashes. Despite this finding, the government mandates that new cars have airbags, rather than taxing their use. Is this policy a contradiction? 2/ Can an activity generate both positive and negative externalities at the same time? Explain your answer. 3/ Can government assignment and enforcement of property rights internalize an exter-nality? Will this approach work as well as, better than, or worse than direct government intervention? Explain your answers and describe one of the difficulties associated with this solution 4/ Suppose that a firm’s marginal production costs are given by MC = 10 + 3Q. The firm’s production process generates a toxic waste, which imposes an increasingly large cost on the residents of the town where it operates: the marginal external cost associ-ated with the Qth unit of production is given by 6Q. What is the marginal private cost associated with the 10th unit produced? What is the total marginal cost to society as-sociated with producing the 10th unit (the marginal social cost of the 10th unit)? 5/ Warrenia has two regions. In Oliviland, the marginal benefit associated with pollution cleanup is MB = 300 – 10Q, while in Linneland, the marginal benefit associated with pollution cleanup is MB = 200 – 4Q. Suppose that the marginal cost of cleanup is con-stant at $12 per unit. What is the optimal level of pollution cleanup in each of the two regions? 6/ The private marginal benefit associated with a product’s consumption is PMB = 360 – 4Q and the private marginal cost associated with its production is PMC = 6Q. Further- more, the marginal external damage associated with this good’s production is MD = 2P. To correct the externality, the government decides to impose a tax of T per unit sold. What tax T should it set to achieve the social optimum?

radio broadcasting a public good? To what degree is a highway a public good?

3/ Think of an example of a free rider problem in your hometown. Can you think

of a way for your local government to overcome this problem?

4/ Think back to Chapter 5. Why can the public good provision problem be thought

of as an externality problem?

5/ Suppose 10 people each have the demand Q = 20 – 4P for streetlights and 5

people have the demand Q = 18 – 2P for streetlights. The cost of building each

streetlight is $3. If it is impossible to purchase a fractional number of streetlights,

how many street-lights are socially optimal?

6/ Andrew, Beth, and Cathy live in Lindhville. Andrew’s demand for bike paths, a

public good, is given by Q = 12 – 2P. Beth’s demand is Q = 18 – P, and Cathy’s is

Q = 8 – P/3. The marginal cost of building a bike path is MC = 21. The town

government decides to use the following procedure for deciding how many paths to

build. It asks each resident how many paths they want, and it builds the largest

number asked for by any resident. To pay for these paths, it then taxes Andrew,

Beth, and Cathy the prices a, b, and c per path, respectively, where a + b + c = MC.

(The residents know these tax rates before stating how many paths they want.)

a. If the taxes are set so that each resident shares the cost evenly (a = b = c), how

many paths will get built?

b.Show that the government can achieve the social optimum by setting the correct

tax prices a, b, and c. What prices should it set?

CHAPTER 5

1/A new public works project requires 200,000 hours of labor to complete. a. Suppose the labor market is perfectly competitive and the market wage is $15. What is the opportunity cost of the labor employed? b. Suppose that there is currently unemployment among workers, and that there are some workers who would willingly work for $10 per hour. What is the opportunity cost of the labor employed? Does this vary depending on the fraction of would-be unemployed workers hired for the project?

c. If your answers to a and b differ, explain why. 2/ How does the opportunity cost of a government purchase vary depending on whether the market for the purchased good is perfectly competitive or monopolistic?

3/ A city government is considering building a new system of lighted bike paths. A

councilor supporting their construction lists the following as potential benefits of the

paths: (1) more enjoyable bike rides for current and future bikers, (2) reduced rush-hour

automobile traffic from increases in bike commuting, and (3) the creation of 15

construction-related jobs. Can all of these actually be considered to be benefits? Explain.

4 / The city of Metropolita added a new subway station in a neighborhood between

two existing stations. After the station was built, the average house price increased

by $10,000 and the average commute time fell by 15 minutes per day. Suppose that

there is one commuter per household, that the average commuter works 5 days a

week, 50 weeks a year, and that the benefits of reduced commuting time apply to

current and future residents forever. Assume an interest rate of 5%. Produce an

estimate of the average value of time for commuters based on this information.

5/ The city of Gruberville is considering whether to build a new public swimming pool. This pool would have a capacity of 800 swimmers per day, and the proposed admis-sion fee is $6 per swimmer per day. The estimated cost of the swimming pool, aver-aged over the life of the pool, is $4 per swimmer per day. Gruberville has hired you to assess this project. Fortunately, the neighboring iden-tical town of Figlionia already has a pool, and the town has randomly varied the price of that pool to find how price affects usage. The results from their study follow:

Swimming pool price per day Number of swimmers per day

a. If the swimming pool is built as planned, what would be the net benefit per day from the swimming pool? What is the consumer surplus for swimmers? b. Given this information, is an 800-swimmer pool the optimally sized pool for Gru-

2/ The demand for rutabagas is still Q = 2,000 – 100P and the supply is still Q = –

100 + 200P, as in Question 2. Governor Sloop decides that instead of imposing the

$2 sales tax described in Question 2, the government will instead force stores to

pay the tax directly. What will happen to the “sticker price” on rutabagas? How

will the size of the consumer tax burden change?

3/ The demand for football tickets is Q = 360 – 10P and the supply of football

tickets is Q = 20P. Calculate the gross price paid by consumers after a per-ticket tax

of $4. Calculate the after-tax price received by ticket sellers

4/ The government is considering imposing taxes on the sellers of certain classes of products. The first tax they are considering is a tax on 2% milk. The second is a tax on all dairy products. The third is a tax on all food products. Which of these three taxes would you expect to have the largest impact on the sticker prices of the taxed products? 5/ To finance a new health insurance program, the government of Millonia imposes a new $2 per hour payroll tax to be paid by employers. a. What do you expect to happen to wages and the size of the workforce? b. How will this answer change in markets where labor is inelastically demanded? 6/ The market demand for super-sticky glue is Q = 240 – 6P and the market supply is Q = –60 + 4P. a. Calculate the deadweight loss of a tax of $4 per unit levied on producers of super-sticky glue. b. b. How does deadweight loss change if the tax is levied on consumers of super- sticky glue? 7/ The market demand for stuffed rabbits is Q = 2,600 – 20P, and the government in-tends to place a $ per bunny tax on stuffed rabbit purchases. Calculate the dead-weight loss of this tax when: a. Supply of stuffed rabbits is Q = 400. b. Supply of stuffed rabbits is Q = 12P. c. Explain why the deadweight loss calculations differ between a and b.