DEAD WEIGHT 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 a 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. The reason IS that the deadweight loss is an 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 dead weight loss rises by a factor of 4. If we triple the size of a tax, the base and height triple, so the deadweight loss rise by a factor of 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 a 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 increases, its deadweight loss quickly gets larger. By contrast, panel (e) shows that tax revenue first rises with the size of the tax; but then as the tax gets larger,. the market shrinks so much that tax revenue starts to fall.
Figure 6 How Dead weight Loss and Tax Revenue Vary with the Size of a Tax The deadweight loss is the reduction in total surplus due to the tax. Tax revenue is the amount of the tax times the amount of the good sold. In panel (a), a small tax has a small deadweight loss and raises a small amount of revenue. In panel (b), a somewhat larger tax has a larger deadweight loss and raises a larger amount of revenue. In panel (c), a very large tax has a very large deadweight loss, but because it has reduced the size of the market so much, the tax raises only a same amount of revenue. Panels (d) and (e) summarize these conclusions. Panel (d) shows that .as the size of a tax grows larger, the deadweight loss grows larger. Panel (e) shows that tax revenue first rises and then falls. This relationship is sometimes caued
the Laffer curve.
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