Chapter 6 Solutions PDF

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CHAPTER 6 Modern Principles of Economics:

Taxes and Subsidies Facts and Tools 1. As we saw in Chapter 4, economists’ idea of equilibrium borrows a lot from physics. Let’s push the physics metaphors a bit further. Here, we focus just on the supply side. For each set of words in brackets, circle the correct choice: a. When the government subsidizes an activity, resources such as labor, machines, and bank lending will tend to gravitate [toward/away from] the activity that is subsidized and will tend to gravitate [toward/away from] the activity that is not subsidized. b. When the government taxes an activity, resources such as labor, machines, and bank lending will tend to gravitate [toward/away from] the activity that is taxed and will tend to gravitate [toward/away from] the activity that is not taxed. Solution 1. a. Toward the activity that is subsidized and away from the activity that is not subsidized b. Away from the activity that is taxed and toward the activity that is not taxed 2. Junk food has often been criticized for being unhealthy and too cheap, enticing the poor to adopt unhealthy lifestyles. Suppose that the state of Oklakansas imposes a tax on junk food. a. What needs to be true for the tax to actually deter people from eating junk food: Should junk food demand be elastic or should it be inelastic? b. If the Oklakansas government wants to strongly discourage people from eating junk food, when will it need to set a higher tax rate: When junk food demand is elastic or when it is inelastic? c. But hold on a moment: The supply side matters as well. If junk food supply is highly elastic—perhaps because it’s not that hard to start selling salads with low-fat dressing instead of mayonnaise- and cheese-laden burgers—does that mean that a junk food tax will have a bigger effect than if supply were inelastic? Or is it the other way around? d. Let’s combine these stories now. If a government is hoping that a small tax can actually discourage a lot of junk food purchases, it should hope for: I. Elastic supply and inelastic demand II. Elastic supply and elastic demand III. Inelastic supply and elastic demand IV. Inelastic supply and inelastic demand Solution 2. a. Demand should be elastic, which means sensitive to price.

b. The government will need to set a higher tax rate when consumers have inelastic junk food demand— only an extremely high price will discourage these stubborn consumers. c. Elastic supply is better from the government’s point of view, just as elastic demand is better. As long as the goal is getting the quantity to move a lot, you want elasticity. d. II: Both should be elastic. 3. As we saw in the chapter, a lot turns on elasticity. Decades ago, Washington, D.C., a fairly small city, wanted to raise more revenue by increasing the gas tax. Washington, D.C., shares borders with Maryland and Virginia, and it’s very easy to cross the borders between these states without even really noticing: The suburbs just blend together. a. How elastic is the demand for gasoline sold at stations within Washington, D.C.? In other words, if the price of gas in D.C. rises, but the price in Maryland and Virginia stays the same, will gasoline sales at D.C. stations fall a little, or will they fall a lot? b. Take your answer in part a into account when answering this question. So, when Washington, D.C., increased its gasoline tax, how much revenue did it raise: Did it raise a little bit of revenue, or did it raise a lot of revenue? c. How would your answer to part b change if D.C., Maryland, and Virginia all agreed to raise their gas tax simultaneously? These states have heavily populated borders with each other, but they don’t have any heavily populated borders with other states. Solution 3. a. Washington, D.C., gas sales are very elastic: It’s easy to drive across the border to buy gas where it’s cheapest. Hence, we can say that gasoline sales at D.C. stations will fall a lot. b. Gasoline sales in Washington, D.C., plummeted and the tax raised very little revenue. c. If they all raised the gas tax simultaneously, they could raise a lot of revenue. The demand within these three states is more inelastic, since drivers don’t have many good alternatives to filling up within the tri-state area. 4. In Figure 6.5, what is the total revenue raised by the tax, in dollars? What is the deadweight loss from the tax, in dollars? (Note: You’ve seen the formula for the latter before. We’ll let you look around a little for this one.) Solution 4. Tax revenue: 500 × $1 = $500. Deadweight loss = $1 tax × 200 apples × ½ (because it’s a triangle) = $100. 5. a. Once again: Why does the chapter say that elasticity = escape? (This is worth remembering: Elasticity is one of the toughest ideas for most economics students.) b. Which two groups of workers did we say have a relatively high elasticity of labor supply? Keep this in mind as politicians debate raising or lowering taxes on different types of workers: These two groups are the ones most likely to make big changes in their behavior.

Solution 5. a. Elasticity = escape because someone with high elasticity is someone who can easily escape to another market, either as a supplier or as a demander. b. Men nearing retirement and married women have the highest labor supply elasticity. They respond to labor-market incentives the most, while middle-aged men tend to work the same hours even when the wage changes. 6. Suppose that Maria is willing to pay $40 for a haircut, and her stylist Juan is willing to accept as little as $25 for a haircut. a. What possible prices for the haircut would be beneficial to both Maria and Juan? How much total surplus (i.e., the sum of consumer and producer surplus) would be generated by this haircut? b. If the state where Maria and Juan live instituted a tax on services that included a $5 per haircut tax on stylists and barbers, what happens to the range of haircut prices that benefit both Maria and Juan? Will the haircut still happen? Will this tax alter the total economic benefit of this haircut? c. What if instead the tax was $20? Solution 6. a. Any price greater than $25 will make Juan better off; any price lower than $40 will make Maria better off. No matter what the price is, the sum of consumer and producer surplus (the total gains from trade) will be $15. b. If Juan has to pay a $5 tax for every haircut he gives, then his willingness-to-accept price will rise to $30. At a price of $30, he will give $5 to the government and have $25 left over for himself, which was originally the minimum he was willing to accept. Now Juan and Maria must find a price greater than $30 but less than $40. There are a lot of prices in between these numbers, so it is still likely that the haircut would take place. The tax will not necessarily alter the total economic benefit of the haircut. While the benefit to Maria and Juan will sum only to $10, the government also receives $5 in tax revenue, so the total economic benefit generated by the haircut is still $15. c. If the tax was $20, Juan’s minimum willingness-to-accept price rises to $25 + $20 = $45. Now, there are no prices high enough to satisfy Juan (higher than $45) but low enough to satisfy Maria (lower than $40). Therefore, the haircut will not take place. It will, therefore, not generate any tax revenue. The total economic benefit will be reduced to $0.

Thinking and Problem Solving 7. Some people with diabetes absolutely need to take insulin on a regular basis to survive. Pharmaceutical companies that make insulin could find a lot of other ways to make some money. a. If the U.S. government imposes a tax on insulin producers of $10 per cubic centimeter of insulin, payable every month to the U.S. Treasury, who will bear most of the burden of the tax: insulin producers or people with diabetes? Or can’t you tell from the information given? b. Suppose instead that because of government corruption, the insulin manufacturers convince the U.S. government to pay the insulin makers $10 per cubic centimeter of insulin, payable every month from the U.S. Treasury. Who will get most of the benefit of this subsidy: Insulin producers, people with diabetes, or can’t you tell from the information given?

Solution 7. a and b: In both cases, it’s the diabetes patients who are affected: Inelastic buyers face a steep price hike under a tax and so bear the burden of the tax, and inelastic buyers reap the benefits of the insulin subsidy. 8. Let’s see if we can formulate any real laws about the economics of taxation. Which of the following must be true, as long as supply and demand curves have their normal shape (i.e., they aren’t perfectly vertical or horizontal, and demand curves have a negative slope while supply curves have a positive slope)? More than one may be true. If there is a tax: a. The equilibrium quantity must fall, and the price that buyers pay must rise. b. The equilibrium quantity must rise, and the price that sellers pay must rise. c. The equilibrium quantity must fall, and the price that sellers receive must fall. d. The equilibrium quantity must rise, and the price that buyers receive must fall. (Note: The correct answer[s] to this question was [were] actually controversial until Nobel Laureate Paul Samuelson created a simple mathematical proof in his legendary graduate textbook, Foundations of Economic Analysis.) Solution 8. Both a and c are correct: Quantity falls, the price received by suppliers falls, and the price paid by the buyer rises. 9. Using the following diagram, use the wedge shortcut to answer these questions: a. If a tax of $2 were imposed, what price would buyers pay and what price would suppliers receive? How much revenue would be raised by the tax? How much deadweight loss would be created by the tax? b. If a subsidy of $5 were imposed, what price would buyers pay and what price would suppliers receive? How much would the subsidy cost the government? How much deadweight loss would be created by the subsidy?

Solution 9. a. The answers can be found in this diagram.

b. The answers can be found in this diagram.

10. When government is trying to raise tax revenue, it sometimes attempts to target higher-income people, because they are in a better position to bear the burden of a tax. However, it can be very difficult to earn tax revenue from wealthy people. a. Consider the progressive nature of the U.S. federal income tax system: It’s designed so that higher incomes are taxed at higher tax rates. Thinking about the elasticity of labor supply, why might it be more difficult to collect tax revenue from a wealthy individual than from a poor person, all else equal? b. Another way governments have tried to collect taxes from the wealthy is through the use of luxury taxes, which are exactly what they sound like: taxes on goods that are considered luxuries, like jewelry or expensive cars and real estate. What is true about the demand for luxuries? Consider jewelry. Is a luxury tax more likely to hurt the buyers of jewelry or the sellers of jewelry? c. The chapter began by discussing another tax that targets wealthy individuals: the estate tax. Comment on the effectiveness of this tax (in terms of government revenue), considering the demand of wealthy individuals for leaving an inheritance.

Solution 10. a. We might expect the wealthy to have a more elastic labor supply. One reason might be related to mobility: A wealthy person may have the resources necessary to move in order to find a better job, while a poorer person may not. Likewise, a poorer person cannot take time out of the labor market to wait for a better opportunity, but a wealthy person can. If a wealthy person has a greater labor supply elasticity, then this means he or she is in a better position to escape the impact of an income tax. Likewise, the total compensation of higher-paying jobs generally involves more components than just a wage or salary, such as benefits, vacation days, comfortable and clean working environments, and so on. So, if a person at a higher-paying job faces an increase in income taxes, he or she can simply substitute lower income but with more fringe benefits and other job amenities; they avoid paying the income tax by switching their “compensation” from income to some other thing. Low-skilled workers in low-paid work do not have these options, and they cannot avoid income taxes simply by changing the nature of their total compensation. b. The demand for luxuries is necessarily elastic. If the supply of these goods is not likewise elastic, then the buyers of luxuries will escape the luxury tax and it will be borne primarily by the sellers of luxuries, for example, sellers of jewelry. c. Although the text points out that in some cases people are able to time deaths to accommodate estate tax changes, in reality no one can avoid dying forever. Further, when considering whether to leave an inheritance, a wealthy person is choosing between using all of their wealth while alive or passing some of it on. There is good reason to believe that the estate tax would have to be quite high for a person (especially a wealthy person) to feel that it is better to spend all of their wealth while alive. For a poor person, the “wealth” may be needed to purchase necessities, but this is not the case for a wealthy person. In this sense, the estate tax represents a method of taxing wealthy people that could be more effective than the other two mentioned above. 11. As we learned in Chapter 4, the competitive market equilibrium maximizes gains from trade. Taxes and subsidies, by altering the market outcome, reduce the gains from trade. Does this happen primarily because of the impact of taxes and subsidies on prices or the impact of taxes and subsidies on quantities? Solution 11. The gains from trade are reduced primarily through the impact of taxes and subsidies on the market quantity. In the case of taxes, too few transactions take place, which means that there are some unexploited opportunities to exchange goods with value higher than their costs. In the case of subsidies, too many transactions take place, so that some goods are exchanged that have costs higher than their value. So quantity is the key, and economic welfare can be reduced if too many or too few transactions take place. 12. Consider the following diagram of a tax. The triangular area representing deadweight loss is highlighted, and its dimensions are labeled “Base” and “Height” (recall that the formula for the area of a 1

triangle is 2 × Base × Height).

a. In order to calculate the deadweight loss of a tax, you don’t need the entire demand and supply diagram; you just need to know two numbers, the base and height of the deadweight loss triangle. What is the real-life meaning of the base? What about the height? b. Can you turn your answers to part a into general rules about the deadweight loss associated with taxes? Try phrasing it like this but replacing the part in brackets: “The larger the [base or height], the more deadweight loss is generated by a given tax.” c. Holding the base constant, the height and thus the deadweight loss would get larger if the demand curve or the supply curve were more ______. d. Without having a diagram as a reference, can you answer the preceding questions for a subsidy? Solution 12. a. The base represents the per-unit size of the tax, and the height represents the decrease in quantity caused by the tax. b. The larger the per-unit size of the tax, the more deadweight loss is generated by a given tax. The larger the decrease in quantity caused by a tax, the more deadweight loss is generated by a given tax. c. Holding the base (per-unit tax) constant, the height and thus the deadweight loss would get larger if the demand curve or the supply curve were more elastic. d. For a subsidy, the base would be the per-unit size of the subsidy, and the height would be the increase in quantity caused by the subsidy. The general rules would be: The larger the per-unit size of the subsidy (or the larger the increase in quantity caused by a subsidy), the more deadweight loss is generated by a given subsidy. 13. Suppose your state government has decided to tax donuts. Currently in your state, 300,000 donuts are sold every day. Three possible taxes are being considered by lawmakers: a 20-cent per donut tax, which would decrease donut sales by 50,000 per day; a 25-cent per donut tax, which would decrease donut sales by 100,000 per day; and a 50-cent per donut tax, which would decrease donut sales by 150,000 donuts per day. a. Calculate the amount of tax revenue generated by each tax and the deadweight loss caused by each tax. b. If the goal of your state government is simply to raise the most tax revenue, which tax is preferable?

c. If the goal of your state government is to raise tax revenue in the most efficient manner (with the least deadweight loss per dollar of revenue), which tax is preferable? d. What other goal might your state government have when creating this kind of tax besides raising tax revenue? Solution 13. a. The tax revenues generated by the three taxes are $50,000, $50,000, and $75,000 per day, respectively. The deadweight losses caused by the three taxes are $5,000, $12,500, and $37,500 respectively. b. The $0.50 tax raises the most tax revenue. c. This question can be answered by calculating the deadweight loss per dollar of revenue for each tax, using the numbers calculated in part a. The values are $0.20, $0.25, and $0.50 for the three taxes, respectively (in other words, the $0.50 tax increases government revenues by $75,000, but it decreases consumer and producer surplus by a total of $112,500). Therefore, the most efficient tax is the $0.20 tax, which raises $50,000 in revenue with only $5,000 in deadweight loss. d. Another goal might simply be to reduce donut consumption. In that case, the biggest tax would be the most preferred because it reduces quantity the most. 14. How is it that a tax creates a deadweight loss by decreasing quantity, but a subsidy creates a deadweight loss by increasing quantity? Solution 14. One way to answer this is that the free market equilibrium quantity maximizes total gains from trade, so that any other quantity (whether higher or lower) necessarily causes a reduction in the gains from trade (causes a deadweight loss). Going a step further, a tax reduces the quantity below the free market equilibrium quantity and therefore causes some transactions not to take place that would have generated gains for trade. Thus the deadweight loss associated with a tax is from unrealized potential gains from trade. A subsidy, on the other hand, leads to a greater quantity than the free market equilibrium quantity, causing some transactions to take place that should not take place because the cost of the unit(s) in question exceeds the value of the unit(s). The deadweight loss associated with a subsidy is thus from wasted resources— resources used to produce goods that are not valued enough by consumers to justify their production. 15. Go to the FRED Economic Database (https://fred.stlouisfed.org/) and find tobacco taxes in Texas. In what year (1991–2016) would you guess Texas raised the sales tax on tobacco? Solution 15.

The sales tax very likely increased in 2007 (2006 would also be an acceptable answer, but 2007 is the first year of the higher sales tax revenue).

Challenges 16. Let’s apply the economics of taxation to romantic relationships. a. What does it mean to have an inelastic demand for your boyfriend or girlfriend? How about an elastic demand? b. Sometimes relationships have taxes. Suppose that you and your boyfriend or girlfriend live one hour apart. Using the tools developed in the chapter, how can you predict which one of you will do most of the driving? That is, which one of you will bear the majority of the relationship tax? Solution 16. a. An inelastic demand means you can’t live without him or her. An elastic demand means that there are good substitutes for the current boyfriend or girlfriend. b. All other things being equal, the more inelastic party will do most of the driving—the other party has good substitutes. 17. a. In the opening scene of the classic Eddie Murphy comedy Beverly Hills Cop, Axel Foley, a Det...