10.11 CONCEPTUAL PROBLEMS IN MEASURING SURPLUS. Consumer surplus is an ad-hoc measure, not derived from a welfare measure

Transcription

1 Module 10 Lecture 36 Topics Conceptual Problems in Measuring Surplus Expenditure Function Compensating Vs. Equivalent Variations Compensating Variations Equivalent Variations Excess Burden Using CV and EV Tax Burden: Extensions Preexisting Distortions Proportional Vs. Progressive Tax Tax Smoothing CONCEPTUAL PROBLEMS IN MEASURING SURPLUS Consumer surplus is an ad-hoc measure, not derived from a welfare measure Question of interest: how much utility is lost because of tax beyond revenue transferred to government? Need units to measure utility loss. Introduce expenditure function to translate the utility loss into money metric 1

2 10.12 EXPENDITURE FUNCTION Fix utility at U and prices at q Find bundle that minimizes cost or expenditure to reach utility level U, for a given vector of price, q These generate Hicksian (or compensated) demand functions for consumption, Define individual s loss from tax increase as Difference in cost to achieve the same level of utility at different price vectors. Single-valued function - coherent measure of welfare cost COMPENSATING VS. EQUIVALENT VARIATION But where should utility, U be measured? Consider a price change from q 0 to q 1 Initial utility: u 0 Utility at new price q 1 : u 1 Two concepts: compensating variation (CV) and equivalent variation (EV) depending on which utility level, u 0 or u 1 is used as the reference utility level COMPENSATING VARIATION (CV) Measures the reference utility at initial utility level (u 0 ) Amount agent must be compensated in order to be indifferent about tax increase How much compensation is needed to reach original utility level at new prices? 2

3 CV is lump sum amount of ex-post cost that must be covered to yield same exante utility: Where, CV = Compensating Variation Figure 36.1 Consider the utility maximization problem: max Subject to:.. W= wealth level. Tax on From figure 36.1 compensating variation is the distance between DE and CB. i.e. Since individual s wealth is constant 3

4 10.15 EQUIVALENT VARIATION Measures utility at new utility level (u 1 ) Lump sum amount agent willing to pay to avoid tax (at pre-tax prices) EV is lump sum amount that can be taken from agent to leave him with same expost utility: It measures the amount of money a consumer would pay to avoid a price change Where, EV = Equivalent Variation Figure EXCESS BURDEN USING CV AND EV In general, measures of Excess Burden based on CV and EV, derived from Hicksian demand functions, will differ. Marshallian measure overstates excess burden because it includes income effects Income effects are not a distortion in transactions 4

5 Buying less of a good due to having less income is not an efficiency loss; no surplus foregone because of transactions that do not occur When there are no income effects for the good, then TAX BURDEN: EXTENSIONS Preexisting distortions Progressivity Tax smoothing PREEXISTING DISTORTIONS Preexisting distortions are market failures that are in place before any government intervention. Externalities or imperfect competition are examples PROPORTIONAL VS. PROGRESSIVE TAX Figure 36.3 a 5

6 Figure 36.3 b In a market with pre existing distortions, taxes can create larger/ smaller DWL. Figure 36.3 (a and b) contrasts the use of a tax in a market without any distortions and in one with positive externalities. Imposing the tax in the first market, without externalities, results in a modest deadweight loss triangle equal to BAC. When an existing distortion already exists where the firm is producing below the socially efficient level, the deadweight loss is much higher. The marginal deadweight loss from the same tax is now GEFH. Of course, if there were negative externalities, such a tax would actually improve efficiency. This insight about deadweight loss also demonstrates that a progressive tax system can be less efficient. Consider two tax systems one a proportional 30% income tax, and the other a progressive tax that imposes a 60% rate on the rich, and a 0% rate on the poor. 6

7 Figure 36.4 a Figure 36.4 b Under proportional system, the efficiency loss is ABC + DEF. Under progressive system, the efficiency loss is GDI Under the proportional system the efficiency loss for society is the sum of two deadweight loss triangles, BAC and EDF. Under the progressive system, the efficiency loss is the triangle GDI that is, it adds the area GEFI but does not include BAC. In this case, a proportional tax is more efficient. In general, this would depend on the relative size of the traingles ABC and GDI i.e. on the relative elasticities of the poor and the rich labor supply curves. 7

8 The large increase in deadweight loss arises because the progressive tax is levied on a smaller tax base. In order to raise the same amount of revenues on a smaller base, the tax rate must be higher meaning a higher marginal DWL. The more one loads taxes onto one source, the faster DWL rises. The most efficient tax systems spread the burden most broadly TAX SMOOTHING The fact that DWL rises with the square of the tax rate also implies that government should not raise and lower taxes in the short run, but rather set a longrun tax rate that will meet its budget needs on average. For example, to finance a war, it is more efficient to raise the rate by a small amount for many years, rather than a large amount for one year (and run deficits in the short-run). This notion can be thought of as tax smoothing, similar to the notion of individual consumption smoothing. 8