# Lecture 3 - 2 2.1 Excise taxation Efﬁciency Introduction...

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Unformatted text preview: 2 2.1 Excise taxation: Efﬁciency Introduction Of course, taxes are costly to those who must pay them. What is the cost of a tax to the taxpayer? First insight: it is not the revenue collected. Reasons: 1. Revenues are used to produce government goods and services, which have a value that should not be ignored in the calculation. 2. We want to be able to compare two tax systems that both generate the same revenue, and rank them in terms of their economic effects. In this lecture, we discuss the idea of excess burden of a tax: a monetary measure of the loss in consumer welfare from the tax above the amount that is actually paid to government. We then compare the excess burdens created by alternative tax systems. Y Ev R U X 1 ^ X X 0 X Figure 2.1: Excess burden of taxation Copyright c 2008 by Michael Smart 1 Printed on: September 11, 2009 LECTURE 2. EXCISE TAXATION: EFFICIENCY 2.2 Effects of an excise tax A single consumer buys two goods ( X , Y ) with ﬁxed lump-sum income I and at ﬁxed producer prices ( p x , py ). Consider an excise tax on X : the budget constraint is (1 + t ) p x X + p y Y = I . We seek a monetary measure of welfare loss of the tax, net of revenue paid to government. Consider removing the tax entirely; the consumer is better off, but how much better of in monetary terms, compared to the revenue lost to government? Deﬁne the excess burden as (minus) the compensating variation for eliminating the tax, net of revenue received by government. (See Figure 2.1.) (Recall that CV for a price change is the amount of income we must give or take away for the consumer to bring back to the same utility as before the price change.) Compare a uniform tax on both goods, with budget constraint (1 + t ) p x X + (1 + t ) p y Y = I . The EB of this tax is zero. We say a uniform tax on all goods is a lump-sum tax: a tax for which the consumer’s tax liability is independent of his or her behaviour. Note that the tax does not change behaviour, except for the inevitable income effects of raising revenue. The uniform tax is equivalent to a tax on lump-sum income oft /(1 + t ) I . This tells us that EB is “caused” by substitution effects, Questions: Why are lump-sum taxes so rarely used? Is uniform taxation of all commodities feasible in practice? Is the GST therefore a lump-sum tax? 2.2.1 Measuring excess burden from demand curves. It is convenient to also measure excess burden as area under demand curve (Harberger triangle). (See Figure 2.2.) Recall that demand curves measure marginal willingness to pay : the amount the sonumer would pay for one more unit, given current consumption; so the area under a demand curve and above the price line is consumer surplus for the current quantity, Raising the price of X from 1 to 1 + t reduces consumer surplus by the shaded area, from which we must subtract the rectangular area equal to government revenue from the tax. Using ordinary demand curves to calculate excess burden can give incorrect results. Consider a perfectly inelastic demand curve: does a tax on this good have zero excess burden? (See Figure 2.3.) This tax has offsetting income and substitution effects, so that observed demand is unchanged, but excess burden remains positive. This highlights the importance of measuring distortionary substitution effects of differential excise taxes. All taxes, including lump-sum ones, leave consumer worse off and have income effects on demands. But differential excise taxes also have substitution effects. Compensated demand curves measure the substitution effect of a price change, while the consumer’s nominal income is changed to compensate him for the income effects of the price change. (This demand curve can be constructed from the indifference curve analysis; see Figure 2.4.) Excess burden can be measured by the Harberger triangle under the compensated demand curve. 2 Multiple tax bases. This formula assumed that only one good was taxed. What if there are preexisting taxes on other goods? In this case, introducing a new tax effects not only the demand for the good that is taxed, but also the demand for other goods. Example: Consider two goods where c is the compensated price elasticity of demand. x Implications: ¨¡§¡§¡§¡¡§¡¡§¡§¡§¡§¡§¡¦¨¡¡¦¨¡¦¨¡¦¨¡¦¨¡¡¦¨¡¦¨¡¡¦¨¡¦¨ ¨ ¨ ¨ §¨ ¨ §¨ ¨ ¨ ¨ ¨ ¨ ¥¡¡¥¡¥¡¥¡¥¡¡¥¡¥¡¡¥¡ ¨ ¦¨¥¦§¨ ¨ ¨ ¨ ¨ ¦¨¥¦§¨ ¨ ¨ ¦¨¥¦§¨ ¨ ¦¡¡¦¡¦¡¦¡¦¡¡¦¡¦¡¡¦¡ §¡¡§¡§¡§¡§¡¡§¡§¡¡§¡ §§¡¨§¡¨§¡¨§¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¥§ ¨¨¡¡§¡§¡¡§¡¡§¡§¡§¡§¡§¡¨¡¡¨¡¨¡¨¡¨¡¡¨¡¨¡¡¨¡¦¨ ¨¨§ ¨§ ¨¨§ ¨§ ¨§ ¨§ ¨§ ¨§ ¦¡¡¦¡¦¡¦¡¦¡¡¦¡¦¡¡¦¡ ¨¡¡¨¡¨¡¨¡¨¡¡¨¡¨¡¡¨¡ §¡¨¡¨¡¨¡¡¨¡¡¨¡¨¡¨¡¨¡¨¡§¡¡§¡§¡§¡§¡¡§¡§¡¡§¡¥§ §¥§ ¥¦§¨¦¨¥§¥§ §¥§ §¥§ §¥§ §¥§ ¥¦§¨¦¨¥§¥§ §¥§ §¥§ ¥¦§¨¦¨¥§¥§ §¥§ ¥¡¡¥¡¥¡¥¡¥¡¡¥¡¥¡¡¥¡ ¨¡§¡¨¡¨¡¡¨¡¡¨¡¨¡¨¡¨¡¨¡¦¡¡¦¡¦¡¦¡¦¡¡¦¡¦¡¡¦¡¦¨ §¡¨¡§¡§¡¡§¡¡§¡§¡§¡§¡§¡¥¡¡¥¡¥¡¥¡¥¡¡¥¡¥¡¡¥¡¦¨¥§ §¨§ §¨§ ¦¨ ¦¨ §¨¡§¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦¨¥§¡¦¨¥§¡¡¦¨¡¦¨¡¡¦¨¡¥§ ¨¡¨§¨¡£¤ ¡¡¡¤ ¡¡¡¡¡¡¡¨¡¡¨¡¨¡¦¡¦¡¡¦¡¦¡¡¦¡¦¨ ¨§¨ ¤ ¨ ¤ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¦¨¥§ ¥¦§¨¦¨¥§ ¦¨¥§ ¦¨¥§ §¡§¡¡§¡§¡¡§¡ ¨¡¨¡¡¨¡¨¡¡¨¡ §¡§¡¡£ §¡£ ¡£ § § § § § § § §¡¡§¡§¡¥¡¥¡¡¥¡¥¡¡¥¡¥§ §¡¨§ ¨§ ¥¦§¨¥§ ¥§ ¥§ ¥¦§¨¥¦§¨¥§ ¥§ ¨¡¨¡¤¡¡¤¤¡¤ ¡¡¨¡§¨¡¨¡¨¡¨¡¦§¡¡¦§¡¦§¡¥¡¥¡¡¥¡¥¡¡¥¡¦¨ ¨¤¡¡¡ ¡¡¡¡¡¡¡¥¡¡¥¡¥¡§¡§¡¡§¡§¡¡§¡ ¨¤ ¡¡¨ ¨ ¨ ¨ ¨ ¨ ¦¡¡¦¡¦¡¨¡¨¡¡¨¡¨¡¡¨¡ §¡§¡£¡¡£¡¤£ ¨§¡¡§¡¨¡§¡§¡¡¡¡¡¡¥¦§¨¡¥¦§¨¡¡¥¦§¨¡¥¦§¨¡¡¥¦§¨¡¦¨¥§ §£ ¡§¡¡ ¡£¤£ ¡£ ¡§ §¨§ § § § § ¨¡¡¨¡¨¡¦¡¦¡¡¦¡¦¡¡¦¡ §¨§ ¦¨¥¦§¨ ¦¨¥¦§¨ ¦¨ §¨¡§¨¡£¤¡¡£¤¡ §¨¡¡§¨¡§§¡§¨¡§¨¡§ ¥¡¡¥¡¥¡¨¡¨¡¡¨¡¨¡¡¨¡ ¡¨¡¤¡¡¤¡£ ¨¡¡¡¨¨¡¡¡¨¡¦¨¡¡¦¨¡¦¨¡§¡§¡¡§¡§¡¡§¡¥§ ¨¡¡¡¡¡£¤£¤ ¡¡¨¡¡¨¡§¨¡¢ §¨¡ ¢¢ ¥¦§¨¡¢ ¡¢ ¥¦§¨¡¢ ¥¦§¨¡¥¡¥¡¡¥¡¥¡¡¥¡¥¦§¨ ¨§¨ ¤ ¨§¨ §¨§¨ ¨ §¡§¡£¡¡£¡ §¡¡§¡§¡§¡¡§ ¥§ ¥¦§¨¥§ ¥§ ¥§ ¦¡¦¡¡¦¡¦¡¡¦¡ §¡§¡¡ ¡£¤£ ¡¡ §¨§ ¥¦§¨¥§ ¥¦§¨¥§ ¢¡¡ ¢¡ ¢¡ ¢¡¢ ¡¡¡¡¡¡¡¥¦§¨ ¢¡¡¢¡¢¡¢¡¢ ¢ ¢ ¡¡ ¡ ¡ ¡ ¡¡ ¢¡ ¢¡ ¢¡ ¢¡¡ ¢¡ ¢¡ ¢¡ ¢ ¢ ¢ ¢¡¡¢¡¢¡¢¡¢ ¢ ¢ ¡¡ ¡ ¡ ¡¢ ¢¡¡ ¢¡ ¢¡ ¢¡ ¡¡¡¡¡ ¢ ¢ Revenue or Approximating excess burden. Using formula for area of a triangle, LECTURE 2. EXCISE TAXATION: EFFICIENCY 2. EB increases with 1. EB increases with the square of the tax rate. So big tax differences should be avoided—rates should be averaged out. 3. EB ≈ 0 when t ≈ 0. So a small tax does negligible harm. c+t c. x c P So high tax rates on highly elastic bases should be avoided. Figure 2.2: The Harberger triangle EB 1 t px ∂Xc 1t ≈− = tX 2 px X ∂ px 2 px EB ≈ X 1 ∂Xc 1 t ∆ X c = − t2 2 2 ∂ px 1 3 X Excess burden 0 D(p) c x X LECTURE 2. EXCISE TAXATION: EFFICIENCY Y E v R U 0 U1 ^ X X X 0 Figure 2.3: Offsetting income and substitution effects that are net substitutes, and suppose only one good is taxed initially. Introducing a small tax on the second good causes government revenue from taxation of the ﬁrst good to rise, permitting a reduction in all taxes. Thus the excess burden of the new tax is negative. 2.3 Applications of excess burden Taxes on labour. One of the most important taxes to think about is the personal income tax (about 60 per cent of government revenue) on labour income (about 75 per cent of total income in the economy). Labour income taxes can be analyzed using the two-good excise model above, as purchased commodities become more expensive relative to untaxed leisure time. In developed countries, empirical evidence suggests that labour supply is highly wage-inelastic. However, as we have seen, the fact that observed labour supply responds little to changes in tax rates does not imply that the tax has no excess burden. Rather, there are offsetting income and substitution effects of the tax, and excess burden is positive as long as the substitution effect is positive. Labour income taxation has effects on many aspects of behaviour other than the decision about how many hours to work, such as 1. the decision to participate in the labour force, 2. occupational choices, 4 LECTURE 2. EXCISE TAXATION: EFFICIENCY Y 1 0 Slope = P > P Slope = P 1 0 U P P =P +t 1 0 X P 0 Figure 2.4: Approximating excess burden with the compensated demand curve 3. decision to work in the formal or informal sectors of the economy – including the decision of married women to supply household services instead of market labour. 4. In the longer run, decisions about education and when to retire. Other applications. Excess burden can be applied to measure the economic cost of any policy that changes the market price or equilibrium quantity of a commodity. Examples: 1. Subsidies for certain activities (charitable giving), 2. Supply mamangement programs (milk, taxi licences, etc.) 3. Price controls (e.g. for housing). ¢¡¢¡¢¡¢¡¢¡¢¡¡ ¡¢¡¢¡¢¡¢¡¢¡¡ ¢¢ ¢¡ ¡ ¡ ¡ ¡ ¡¡ ¢ ¢¡¡¡¡¡¡¡ ¢ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ ¡¡ ¢¡¢¡¢¡¢¡¢¡¢¡¡¢ ¡¢¡¢¡¢¡¢¡¢¡¡ ¢¡¡¡¡¡¡¡ ¢ ¢¢ ¢¡¢ ¡¢ ¡¢ ¡¢ ¡¢ ¡¡ ¢ ¡ ¢¢ ¡¢¡¢¡¢¡¢¡¢¡¡¢ ¢¡ ¡ ¡ ¡ ¡ ¡¡ ¢¡ ¡ ¡ ¡ ¡ ¡¡¢ ¢ ¢¡¢¡¢¡¢¡¢¡¡ ¢ ¢ ¢ ¡ ¢¡ ¢¡ ¢¡ ¢¡ ¢¡¡ ¢¡¢¡¢¡¢¡¢¡¢¡¡¢ ¡ ¡ ¡ ¡ ¡ ¡¡ ¡¡¡¡¡¡¡ ¢ ¢ C ≅ t δX δP X (P, U ) ^ X X C 1 X1 5 ...
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