Public Finance Prof. Farshid Mojaver

Problem Set 3

ECN 131

Public Finance Prof. Farshid Mojaver

Part A. Problem Solving

1. Suppose that the demand for apples is perfectly elastic and the government levies a tax on the producers of apples. Assume that the supply of apples is neither perfectly elastic nor perfectly inelastic.

a)  How will the price paid by consumers change? Is this change bigger or smaller than the price change that would result if the demand for apples were not perfectly elastic?

b)  How will the quantity of apples consumed change due to the tax? Is this change in quantity larger or smaller than the change that would result if the demand for apples were not perfectly elastic?

c)  Explain the significance of your answers in both part a and part b in terms of how the tax affects the welfare of consumers in the apple market

2. Suppose that a monopolist has a cost function given by:

C(q) = 10 + 2q + 0.5q2.

The (inverse) demand for the product is given by P(q) = 47 - q. The government levies a tax of $9 per unit, to be paid to the government by the monopolist.

a)  What is the market quantity and price?

b)  The government levies a tax of $9 per unit, to be paid to the government by the monopolist. What is the new market price and quantity?

c)  How much of the tax do the consumers bear? How much does the monopolist bear?

3.

a) In the market for Thneeds[1], the demand curve is: Q=50-3P and the supply curve is: Q=2P. Assume for now that there are no externalities or pre-existing market distortions, so these represent the true social marginal benefit and marginal cost curves. The government decides to raise revenue by taxing consumers 5/3 for every Thneed purchased.

i)  Graph the supply and demand curves, and indicate how the curves shift after implementation of the tax. Label deadweight loss, tax revenue, consumer and producer surplus. Show the price paid by consumers and the price received by producers, and use these to indicate the burden borne by each party due to the tax.

ii)  Calculate the change in consumer and producer surplus from the tax. Also, using the pre-tax market price, and the prices paid by consumers and received by producers, calculate the “burden” of the tax borne by each party (i.e. how much of the 5/3 tax is paid by consumers, how much is paid by producers).

iii)  Check your answer by using the formulas for change in producer and consumer price as provided in the appendix to chapter 19. (Note: to use the formulas, you will first have to calculate the elasticity of supply and demand)

iv)  Using your diagram from (a), calculate the deadweight loss from the tax. Then, use the formula for deadweight loss as provided in the appendix to chapter 20 to confirm your answer.

v)  Intuitively, why is there deadweight loss from a tax? That is, what exactly does deadweight loss represent?

b) Since the Thneed is such a wonderful product (“It’s a shirt. It’s a sock. It’s a glove. It’s a hat. But it has other uses, yes, far beyond that.”), the government wanted Thneedsto be affordable to everyone. Hence, prior to implementing the tax, the government had capped the price of Thneeds at $8. Now, once the tax is implemented, how does the burden of the tax change from (a) – i.e. what is the burden borne by consumers and producers, and how does it differ from (a ii)? Explain why this is so.

c) Realizing that the price cap was a bad idea, the government instead decides that it wants to encourage Thneed production by offering subsidies. Specifically, it will tax consumers the same amount as before for Thneed consumption, but it will provide a subsidy of 5/6 to Thneed producers for every unit sold.

i)  Intuitively, how should deadweight loss under this scheme differ from (a)?

ii)  This business-friendly government hopes that by offering businesses a subsidy, it will reduce producer’s share of the burden from taxation. Is this true – will producers now bear a smaller proportion of the total burden from taxation? Why or why not?

iii)  If, due to administrative reasons, it was expensive to implement the subsidy for producers, what specific tax scheme could the government use instead to raise the same amount of revenue (and end up with the same market outcome) as if the subsidy existed?

B. Discussion

1.  According to estimates by Goolsbee (1998), purchases on the Internet are highly sensitive to tax rates, and applying existing sales taxes to such purchases would substantially reduce the number of online buyers and the amount of online spending. What are the implications for the incidence of a tax levied on Internet sales?

2. One of the biggest economic and social issues nowadays in South Korea is the surging of house prices. For example, the price of an apartment in Seoul about 1000 sq. ft. large was 600 thousand dollars one month ago, but it is now over 800 thousand dollars. These kinds of surging of house prices have been happened intermittently, but too often. These surging of house price are blamed for the main reason of aggravating economic inequality.

For these reasons, Korean government has introduced many kinds of tax policies.

(1)  Property Tax; The owner of the real estate has to pay 1-3% of the total value of the real estate every year.

(2)  Capital Gain Tax; The owner of the real estate has to pay 36-50% of the total capital gain of the real estate when he or she sell the real estate.

(3)  Income tax; The owner of the real estate has to pay 9-36% of the total rent income.

(4)  Acquisition Tax; The owner of the real estate has to pay 1% of the total value of the real estate when he or she acquire the real estate.

(5)  Registration Tax; The owner of the real estate has to pay 1-2% of the total value of the real estate when he or she buy and register the real estate as their property.

Although these kinds of taxes are aimed to burden the rich people who have the real estate, however there are also many criticisms on them related to the tax incidence.

Explain how the tax incidence problem can be related to these taxes. What kind of tax would be most desirable to avoid tax incidence problem do you think? What kind of tax would be most desirable to solve the inequality problem do you think?

3. The city of Malaise is considering a 10% tax on the revenues of all hotels/motels inside the city limits. Although not completely different from hotels and motels in the nearby suburbs, the ones in Malaise have a distinct advantage in their proximity to the interesting sights and convention centers. So individuals will pay some premium to stay in Malaise rather than to stay nearby. Furthermore, all land is used equally well by hotels/motels and other forms of business; any Malaise land not taken by a hotel/motel is readily absorbed by other forms of business. Mayor Maladroit calls you in to advise him on the incidence of such a tax. He is particularly concerned with who will bear this tax in the short run (e.g., one month) and the long run (e.g., five years).

(a)  What is the incidence of the tax in the short run? Answer intuitively, and use a diagram if possible.

(b)  What is the long-run incidence? Once again, use a diagram if possible.

(Suppose hotels/motels in the suburbs are not good substitute.)

(c)  How would your analysis in b change if hotels/motels in the suburbs were perfect substitutes for those in Malaise? What would happen to tax revenues

(For example suppose that there is new light rail connecting the city center to the suburbs)

[1] What’s a “thneed”? “A Thneed’s a Fine-Something-That-All-People-Need.” Theeds are made from

Truffala Trees, of course.