Application: The Costs of Taxation
- 8-1 The Deadweight Loss of Taxation
- 8-2 The Determinants of the Deadweight Loss
- 8-3 Deadweight Loss and Tax Revenue as Taxes Vary
- 8-4 Conclusion
- Key Concept
Taxes are often a source of heated political debate. In 1776, the anger of the American colonists over British taxes sparked the American Revolution. More than two centuries later, the American political parties still debate the proper size and shape of the tax system. Yet no one would deny that some level of taxation is necessary. As Oliver Wendell Holmes, Jr., once said, “Taxes are what we pay for civilized society.”
Because taxation has such a major impact on the modern economy, we return to the topic several times throughout this book as we expand the set of tools we have at our disposal. We began our study of taxes in Chapter 6. There we saw how a tax on a good affects its price and quantity sold and how the forces of supply and demand divide the burden of a tax between buyers and sellers. In this chapter, we extend this analysis and look at how taxes affect welfare, the economic well-being of participants in a market. In other words, we see how high the price of civilized society can be.
The effects of taxes on welfare might at first seem obvious. The government enacts taxes to raise revenue, and this revenue must come out of someone’s pocket. As we saw in Chapter 6, both buyers and sellers are worse off when a good is taxed: A tax raises the price buyers pay and lowers the price sellers receive. Yet to fully understand how taxes affect economic well-being, we must compare the reduced welfare of buyers and sellers to the amount of revenue the government raises. The tools of consumer and producer surplus allow us to make this comparison. Our analysis will show that the cost of taxes to buyers and sellers typically exceeds the revenue raised by the government.
8-1 The Deadweight Loss of Taxation
We begin by recalling one of the surprising lessons from Chapter 6: The impact of a tax on a market outcome is the same whether the tax is levied on buyers or sellers of a good. When a tax is levied on buyers, the demand curve shifts downward by the size of the tax; when it is levied on sellers, the supply curve shifts upward by that amount. In either case, when the tax is enacted, the price paid by buyers rises, and the price received by sellers falls. In the end, the elasticities of supply and demand determine how the tax burden is distributed between producers and consumers. This distribution is the same regardless of how the tax is levied.
Figure 1 shows these effects. To simplify our discussion, this figure does not show a shift in either the supply or demand curve, although one curve must shift. Which curve shifts depends on whether the tax is levied on sellers (the supply curve shifts) or buyers (the demand curve shifts). In this chapter, we keep the analysis general and simplify the graphs by not showing the shift. For our purposes here, the key result is that the tax places a wedge between the price buyers pay and the price sellers receive. Because of this tax wedge, the quantity sold falls below the level that would be sold without a tax. In other words, a tax on a good causes the size of the market for the good to shrink. These results should be familiar from Chapter 6.
8-1a How a Tax Affects Market Participants
Let’s use the tools of welfare economics to measure the gains and losses from a tax on a good. To do this, we must take into account how the tax affects buyers, sellers, and the government. The benefit received by buyers in a market is measured by consumer surplus—the amount buyers are willing to pay for the good minus the amount they actually pay for it. The benefit received by sellers in a market is measured by producer surplus—the amount sellers receive for the good minus their costs. These are precisely the measures of economic welfare we used in Chapter 7.
8-1b Deadweight Losses and the Gains from Trade
To better understand why taxes cause deadweight losses, consider an example. Imagine that Mike cleans Mei’s house each week for $100. The opportunity cost of Mike’s time is $80, and the value of a clean house to Mei is $120. Thus, Mike and Mei each receive a $20 benefit from their deal. The total surplus of $40 measures the gains from trade in this particular transaction.
Now suppose that the government levies a $50 tax on the providers of cleaning services. There is now no price that Mei can pay Mike that will leave both of them better off. The most Mei would be willing to pay is $120, but then Mike would be left with only $70 after paying the tax, which is less than his $80 opportunity cost. Conversely, for Mike to receive his opportunity cost of $80, Mei would need to pay $130, which is above the $120 value she places on a clean house. As a result, Mei and Mike cancel their arrangement. Mike loses the income, and Mei lives in a dirtier house.
The tax has made Mike and Mei worse off by a total of $40 because they have each lost $20 of surplus. But note that the government collects no revenue from Mike and Mei because they decide to cancel their arrangement. The $40 is pure deadweight loss: It is a loss to buyers and sellers in a market that is not offset by an increase in government revenue. From this example, we can see the ultimate source of deadweight losses: Taxes cause deadweight losses because they prevent buyers and sellers from realizing some of the gains from trade.
8-2 The Determinants of the Deadweight Loss
What determines whether the deadweight loss from a tax is large or small? The answer is the price elasticities of supply and demand, which measure how much the quantity supplied and quantity demanded respond to changes in the price.
Let’s consider first how the elasticity of supply affects the size of the deadweight loss. In the top two panels of Figure 5, the demand curve and the size of the tax are the same. The only difference in these figures is the elasticity of the supply curve. In panel (a), the supply curve is relatively inelastic: Quantity supplied responds only slightly to changes in the price. In panel (b), the supply curve is relatively elastic: Quantity supplied responds substantially to changes in the price. Notice that the deadweight loss, the area of the triangle between the supply and demand curves, is larger when the supply curve is more elastic.
Similarly, the bottom two panels of Figure 5 show how the elasticity of demand affects the size of the deadweight loss. Here the supply curve and the size of the tax are held constant. In panel (c), the demand curve is relatively inelastic, and the deadweight loss is small. In panel (d), the demand curve is more elastic, and the deadweight loss from the tax is larger.
The lesson from this figure is apparent. A tax has a deadweight loss because it induces buyers and sellers to change their behavior. The tax raises the price paid by buyers, so they consume less. At the same time, the tax lowers the price received by sellers, so they produce less. Because of these changes in behavior, the equilibrium quantity in the market shrinks below the optimal quantity. The more responsive buyers and sellers are to changes in the price, the more the equilibrium quantity shrinks. Hence, the greater the elasticities of supply and demand, the greater the deadweight loss of a tax.
CASE STUDY: The Deadweight Loss Debate
8-3 Deadweight Loss and Tax Revenue as Taxes Vary
Taxes rarely stay the same for long periods of time. Policymakers in local, state, and federal governments are always considering raising one tax or lowering another. Here we consider what happens to the deadweight loss and tax revenue when the size of a tax changes.
Figure 6 shows the effects of a small, medium, and large tax, holding constant the market’s supply and demand curves. The deadweight loss—the reduction in total surplus that results when the tax reduces the size of a market below the optimum— equals the area of the triangle between the supply and demand curves. For the small tax in panel (a), the area of the deadweight loss triangle is quite small. But as the size of the tax rises in panels (b) and (c), the deadweight loss grows larger and larger.
Indeed, the deadweight loss of a tax rises even more rapidly than the size of the tax. This occurs because the deadweight loss is the area of a triangle, and the area of a triangle depends on the square of its size. If we double the size of a tax, for instance, the base and height of the triangle double, so the deadweight loss rises by a factor of 4. If we triple the size of a tax, the base and height triple, so the deadweight loss rises by a factor of 9.
The government’s tax revenue is the size of the tax times the amount of the good sold. As the first three panels of Figure 6 show, tax revenue equals the area of the rectangle between the supply and demand curves. For the small tax in panel (a), tax revenue is small. As the size of the tax increases from panel (a) to panel (b), tax revenue grows. But as the size of the tax increases further from panel (b) to panel (c), tax revenue falls because the higher tax drastically reduces the size of the market. For a very large tax, no revenue would be raised because people would stop buying and selling the good altogether.
The last two panels of Figure 6 summarize these results. In panel (d), we see that as the size of a tax increases, its deadweight loss quickly gets larger. By contrast, panel (e) shows that tax revenue first rises with the size of the tax, but as the tax increases further, the market shrinks so much that tax revenue starts to fall.
CASE STUDY: The Laffer Curve and Supply-Side Economics
One day in 1974, economist Arthur Laffer sat in a Washington restaurant with some prominent journalists and politicians. He took out a napkin and drew a figure on it to show how tax rates affect tax revenue. It looked much like panel (e) of our Figure 6. Laffer then suggested that the United States was on the downward-sloping side of this curve. Tax rates were so high, he argued, that reducing them might actually increase tax revenue.
Most economists were skeptical of Laffer’s suggestion. They accepted the idea that a cut in tax rates could increase tax revenue as a matter of economic theory, but they doubted whether it would do so in practice. There was scant evidence for Laffer’s view that U.S. tax rates had in fact reached such extreme levels.
Nonetheless, the Laffer curve (as it became known) captured the imagination of Ronald Reagan. David Stockman, budget director in the first Reagan administration, offers the following story:
[Reagan] had once been on the Laffer curve himself. “I came into the Big Money making pictures during World War II,” he would always say. At that time the wartime income surtax hit 90 percent. “You could only make four pictures and then you were in the top bracket,” he would continue. “So we all quit working after four pictures and went off to the country.” High tax rates caused less work. Low tax rates caused more. His experience proved it.
When Reagan ran for president in 1980, he made cutting taxes part of his platform. Reagan argued that taxes were so high that they were discouraging hard work and thereby depressing incomes. He argued that lower taxes would give people more incentive to work, which in turn would raise economic well-being. He suggested that incomes could rise by so much that tax revenue might increase, despite the lower tax rates. Because the cut in tax rates was intended to encourage people to increase the quantity of labor they supplied, the views of Laffer and Reagan became known as supply-side economics.
Economists continue to debate Laffer’s argument. Many believe that subsequent history refuted Laffer’s conjecture that lower tax rates would raise tax revenue. Yet because history is open to alternative interpretations, other economists view the events of the 1980s as more favorable to the supply siders. To evaluate Laffer’s hypothesis definitively, we would need to rerun history without the Reagan tax cuts and see if tax revenues would have been higher or lower. Unfortunately, that experiment is impossible.
Some economists take an intermediate position on this issue. They believe that while an overall cut in tax rates normally reduces revenue, some taxpayers may occasionally find themselves on the wrong side of the Laffer curve. Other things being equal, a tax cut is more likely to raise tax revenue if the cut applies to those taxpayers facing the highest tax rates. In addition, Laffer’s argument may be more compelling for countries with much higher tax rates than the United States. In Sweden in the early 1980s, for instance, the typical worker faced a marginal tax rate of about 80 percent. Such a high tax rate provides a substantial disincentive to work. Studies have suggested that Sweden would have indeed raised more tax revenue if it had lowered its tax rates.
Economists disagree about these issues in part because there is no consensus about the size of the relevant elasticities. The more elastic supply and demand are in any market, the more taxes distort behavior, and the more likely it is that a tax cut will increase tax revenue. There is no debate, however, about the general lesson: How much revenue the government gains or loses from a tax change cannot be computed just by looking at tax rates. It also depends on how the tax change affects people’s behavior.
ASK THE EXPERTS: The Laffer Curve
In this chapter, we have used the tools developed in the previous chapter to further our understanding of taxes. One of the Ten Principles of Economics discussed in Chapter 1 is that markets are usually a good way to organize economic activity. In Chapter 7, we used the concepts of producer and consumer surplus to make this principle more precise. Here we have seen that when the government imposes taxes on buyers or sellers of a good, society loses some of the benefits of market efficiency. Taxes are costly to market participants not only because taxes transfer resources from those participants to the government but also because they alter incentives and distort market outcomes.
The analysis presented here and in Chapter 6 should give you a good basis for understanding the economic impact of taxes, but this is not the end of the story. Microeconomists study how best to design a tax system, including how to strike the right balance between equality and efficiency. Macroeconomists study how taxes influence the overall economy and how policymakers can use the tax system to stabilize economic activity and to achieve more rapid economic growth. So as you continue your study of economics, don’t be surprised when the subject of taxation comes up yet again.
A tax on a good reduces the welfare of buyers and sellers of the good, and the reduction in consumer and producer surplus usually exceeds the revenue raised by the government. The fall in total surplus—the sum of consumer surplus, producer surplus, and tax revenue—is called the deadweight loss of the tax.
Taxes have deadweight losses because they cause buyers to consume less and sellers to produce less, and these changes in behavior shrink the size of the market below the level that maximizes total surplus. Because the elasticities of supply and demand measure how much market participants respond to market conditions, larger elasticities imply larger deadweight losses.
As a tax grows larger, it distorts incentives more, and its deadweight loss grows larger. Because a tax reduces the size of the market, however, tax revenue does not continually increase. It first rises with the size of a tax, but if the tax gets large enough, tax revenue starts to fall.
the fall in total surplus that results from a market distortion, such as a tax