2IntroductionAre people unaffected by a tax increase if they pay zero in taxes afterwards?No, consumption may have changed in response to the tax increaseBundle consumed is less desirableExcess burden is a loss of welfare above and beyond the tax revenues collected.
3Excess Burden Defined Two commodities Fixed income Barley and cornFixed incomePb and Pc are prices of goodsNo distortions such as externalities, imperfect competition, public goods, etc.
4Excess Burden DefinedFigure 13.1 shows the budget constraint (AD), with utility maximized at bundle E1.Ad-valorem tax levied on barley at rate tb raises the price to (1+tb)Pb and rotates the budget constraint along the x-axis. The new budget constraint is AF.
6Excess Burden DefinedAt each consumption level of barley, the vertical distance between AD and AF shows tax payments in terms of forgone corn.Normalize Pc=$1, so that vertical distance can be measured in either quantity of corn or dollars.
7Excess Burden DefinedFigure 13.2 shows new optimizing choice with the higher prices along budget constraint AF.Utility maximized at bundle E2.Vertical distance between old and new budget constraints is GE2, the “tax bill.”
8Excess Burden DefinedAny tax will lower utility, but is there an alternative tax that raises the same revenue, GE2, but entails a smaller utility loss? Or greater revenue with the same utility loss?If so, the tax on barley leads to excess burden.
10Excess Burden DefinedEquivalent variation is the amount of income we would have to take away (before any tax was imposed) to induce a move to the lower indifference curve (Increasing price is equivalent to a income reduction).Taking away income is equivalent to a parallel movement inward on the budget constraint.Budget constraint HI in Figure 13.3 shows this.
12Excess Burden DefinedNote that ME3=GN>GE2, but both give the consumer the same utility.Thus, the difference E2N is the excess burden of the barley tax. The barley tax makes the person worse off by an amount that exceeds the revenue it generates.
13Excess Burden DefinedLump sum tax is a tax that must be paid regardless of the taxpayer’s behavior.Budget constraint HI satisfies this. Revenue yield exactly equals the equivalent variation.Conclusion: Lump sum tax has no excess burden.
14Questions and Answers Why aren’t lump sum taxes widely used? Construed as unfair because people’s abilities to pay varyHow do lump sum taxes relate to welfare economics?The equilibrium conditions become:
15Questions and AnswersIntuitively, when MRS>MRT the marginal utility of substituting barley consumption for corn consumption exceeds the change in production costs from doing so.In the presence of the tax, there is no financial incentive to do so.
16Questions and Answers Does an income tax entail excess burden? It usually does entail excess burden, if a third commodity, leisure, exists.If demand for a commodity is perfectly inelastic, is there excess burden?Yes, see Figure 13.4.
18Questions and AnswersIn Figure 13.4, the ordinary (uncompensated) demand curve is inelastic – B1=B2 when the price increases.But this is because the income effect offsets the substitution effect.The substitution effect is the part necessary to compute excess burden. The compensated demand curve (which holds utility constant as prices change) is the relevant one, and the elasticity for it is non-zero.
19Excess Burden Measurement with Demand Curves Consider a compensated demand curve, such as the one in Figure 13.5.Impose an ad-valorem tax on barley, so that its price increases to (1+tb)Pb.Equivalent to the supply curve shifting upward.
21The measurement of excess burden The concept of excess burden can be reinterpreted using (compensated) demand curves. Assume that the compensated demand curve for barley can be represented by the straight line Db For convenience, we continue to assume that the social marginal cost of barley is constant at Pb. Suppose that a tax at percentage rate tb is levied on barley, so the new price, (1 + tb)Pb, is associated with supply curve Sb.The excess burden of the tax, fid, is one-half the product of its base (the tax-induced change in the quantity of barley) and height (the tax per pound), that is-(1/2)( P) (q)…………………..(*)Since q=(q1/pb) (P)e, with P=tbPb , some simple algebra leads to the conclusion that the excess burden (*) can be written-(1/2)ePbql(tb) (10.3)where e is the value of the compensated price elasticity of demand (in general e <0) for barley.
22A high absolute value of e indicates that the compensated quantity demanded is quite sensitive to changes in price. Thus, the presence of e in Equation (10.3) makes intuitive sense--the more the tax distorts the (compensated) consumption decision, the higher the excess burden.Finally, the presence of (tb)2 suggests that as the tax rate increases, excess burden goes up with its square. Doubling a tax quadruples its excess burden, other things being the same. Because excess burden in- creases with the square of the tax rate, the marginal excess burden from raising one more dollar of revenue exceeds the average excess burden. That is, the incremental excess burden of raising one more dollar of revenue exceeds the ratio of total excess burden to total revenues. This fact has important implications for cost- benefit analysis.
23-(1/2)( ps) (q)…………………..(**) Similarly, the concept of excess burden can be reinterpreted using (compensated) supply curves. Assume that the social marginal cost of barley is upward sloping. The excess burden of the tax can be approximated by-(1/2)( ps) (q)…………………..(**)Since q=(q1/ps) (ps)h, with ps=-tsp , some simple algebra leads to the conclusion that the excess burden (**) can be written(1/2)hpq(ts) (10.**)where h is the value of the compensated price elasticity of supply (in general h >0) for barley.
24Excess Burden Measurement with Demand Curves Excess burden equal to triangle fid.Through some mathematical manipulation, this can be expressed as:
25Excess Burden Measurement with Demand Curves Implications of formula:Higher (compensated) elasticities lead to larger excess burden.Excess burden increases with the square of the tax rate.The greater the initial expenditure on the taxed commodity, the larger the excess burden.
26Differential Taxation of Inputs Some inputs are taxed differently depending on where they are used:Capital used in the corporate sector is subject to a higher tax rate than capital used in the noncorporate sector.Labor used in the household is untaxedFigure 13.8 measures the efficiency cost
28Differential Taxation of Inputs In this figure, total amount of labor is fixed at OO’. Moving along the x-axis simply shifts labor from the labor market to the household sector.VMP is the value of marginal product, or the dollar value of the additional input produced from an hour of work.VMP declines with hours worked in a sector. Optimal allocation of hours equates margins, such that OH* is spent in household production, and O’H* is spent in the market.
29Differential Taxation of Inputs If a tax is levied on market work, but not household production, then the “effective” VMP curve for market work rotates downward.Figure 13.9 shows the effects.
31Differential Taxation of Inputs People shift hours into nonmarket work.Household production increases from OH* to OHt, while market work decreases from O’H* to O’Ht.Excess burden equal to abe.
32Overall excess burdenTo summarize: Given that the tax on rum was already in place, the tax on gin creates an excess burden of efd in the gin market and simultaneously decreases excess burden by cbhg in the rum market. If cbhg is sufficiently large, the tax can actually reduce overall excess burden. This is an example of the theory of the second best: In the presence of existing distortions, policies that in isolation would increase efficiency can decrease it and vice versa.This discussion is a special case of the result that the excess burden of a set of taxes generally depends on the whole set of tax rates, as well as on the degree of substitutability and complementarity among the various commodities. Specifically, suppose that n commodities are subject to taxation.Let Pi be the before-tax price of the ith commodity; ti the ad valorem taxon the ith commodity; and Sij, the compensated response in the demand of the ith good with respect to a change in the price of the jth good. Then the overall excess burden is
33Recap of Taxation and Efficiency Excess Burden DefinedQuestions and AnswersExcess Burden Measurement with Demand CurvesDifferential Taxation of Inputs