How a Tax Apeects Market Participants

Let's use the tools Ot" 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 selk-rs in a market is measured by producer surplus— the amount sellers receive for the good minus their costs. These arc precisely the measures of economic welfare we used in Chapter 7.

What about the third interested party, the government? If T is the size of the tax and Q is the quantity of the good sold, then the government gets total tax revenue of T x Q. It can use this lax revenue to provide services, such as roads, police, and public education, or to help the needy. Therefore, to analyze how taxes affect economic well-being, we use the government's tax revenue to measure the public benefit from the tax, Keep in mind, however, that this benefit actually accrues not to government but to those on whom the revenue is spent.

Figure 2 shows that the government'* tax revenue is represented by the rectangle between the supply and demand curves. The height of this rectangle is the size of the tax, T. and the width of the rectangle is the quantity of the good sold, Q. Because a rectangle's area is its height times its width, this rectangle's are-a is T x Q, which equals the tax revenue.

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Welfare without a Tax To see how a tax affects welfare, we begin by considering welfare before the government imposes a lax. Figure 3 shows the supply-and-d em and diagram and marks the key areas with the letters A through F.

Without a tax, the equilibrium prke and quantity are found at the intersection of the supply and demand curves. The prke is P:. and the quantity sold is Q,.

Because the demand curve reflects buyers' willingness to pay. consumer surplus is the area between the demand curve and the price, A + B + ¿.Similarly, because Ihe supply curve reflects sellers' costs, producer surplus is the area between the supply curve and the price. D +■ E + F. In this case, because there is no tax. tax revenue equals zero.

Total surplus, the sum of consumer and producer surplus, equals the area A ♦ B + C-tD + E + F.In other words, as we saw in Chapter 7, total surplus is ihe area between the supply and demand curves up to the equilibrium quantity. The first column of the table in Figure 3 summarizes these conclusions.

Welfare with a Tax Now consider welfare after the tax is enacted. The price paid by buyers rises from P, to Pf, so consumer surplus now equals only area A (the area below the demand curve and above the buyer's price). The price received by sellers falls from P, to P„so producer surplus now equals only area F(lhe area above the supply curve and below the seller's price). The quantity sold falls from Q, to Q., and the government collects tax revenue equal to the area B - D-

To compute total surplus with the tax, we add consumer surplus, producer surplus, and lax revenue. Thus, we find that total surplus is area A +■ B + I) + F. The second column of the table summarizes these results.

Changes in Wo Ha re We can now see the effects of the tax by comparing welfare before and after the tax is enacted. The third column of the table in Figure 3 show> the changes. The tax causes consumer surplus to fall by the area B + C and producer surplus to fall by the area D + E. Tax revenue rises by the area B + D. Not surprisingly, the tax makes buyers and sellers worse off and the government better off.

The change in total welfare includes the change in consumer surplus (which is negative), the change in producer surplus (which is also negative), and the change in tax revenue (which is positive). When we add these three pieces together, we find that total surplus in the market falls by the area C + E. Thus, the loaei to (wyers and t*Uer* from it tax acred the revenue raited by the government. The fall in total surplus that results when a tax (or some other policy) distorts a market outcome is called the deadweight loss. The area C + E measures the size of the deadweight loss.

To understand why taxes impose deadweight losses, recall one of the Ten Principles of Economics in Chapter I: People respond to incentives. In Chapter 7, we saw that free markets normally allocate scarce resources efficiently. That is, the equilibrium of supply and demand maximizes the total surplus of buyers and sellers in a market. When a tax raises the price to buyers and lowers the price to sellers, however, it gives buyers an incentive to consume less and sellers an incentive to produce less tlian they would in the absence of the tax. As buyers and sellers respond to these incentives, the size of the market shrinks bek'w its optimum (as shown in the figure by the movement from Q, to Q:). Thus, because taxes distort incentives, ihey cause markets lo allocate resources inefficiently.

deadweight loss the fall «1 total surpt-ji that results from a market distortion, such ai a tax

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