Taxes are generally considered to be inefficient and generat

Taxes are generally considered to be inefficient and generate excess burdens. Using a simple framework, and with reference to a social welfare function and util- ity possibilities curve, explain why the inefficiency of taxes might be desirable for a society. Also, describe a situation in which a tax would increase efficiency.

Solution

The theory of excess burden

Basic definitions

Excess burden (or deadweight loss) is well defined only in the context of a specific comparison, or conceptual experiment. If one simply seeks “the” excess burden of a particular tax policy, there are many equally plausible answers, so in order to obtain a unique meaning, it is necessary to be more specific. For example, the excess burden of a 10 percent tax on retail sales varies not only with the initial conditions of the tax system, but also with the direction of change, i.e., whether the tax is being added or removed. To illustrate this ambiguity and its resolution, consider the simple case in which there are two goods, an untaxed numeraire good and a second good with a constant relative producer price of p0. In the absence of taxation, a population of identical consumers1 demands quantity x0 of the second good, as depicted by point 0 . The imposition of a tax per unit of p1 – p0 raises the consumer price of the taxed good to p1, with the producer price remaining at p0. Thus, the quantity purchased falls to x1, and the government collects revenue equal to (p1–p0)x1, as represented in the figure by the shaded area labeled A. What is the excess burden of this tax? If one were to use the Marshallian measure of the consumers’ surplus generated by consumption in this market – the area under the demand curve, D, between x=0 and x=x0 – it would appear that consumers lose an area equal to that of regions A+B, or B in excess of the revenue actually collected. By this approach, the roughly triangular area B – commonly known as a “Harberger” triangle in recognition of Arnold Harberger’s influential empirical contributions – measures the excess burden of the tax. Unfortunately (see Auerbach 1985), this particular measure of excess burden is not uniquely defined in a setting with more than one tax, due to the well-known problem of path dependence of consumers’ surplus: the measure of excess burden is affected by the order in which one envisions the taxes being imposed. Path dependence is disconcerting, but more importantly reflects the imprecision of consumers’ surplus-based measures of excess burden. There is no well-defined economic question to which the difference between the change in consumers’ surplus and tax revenue is the answer. Thus, economists have sought alternative measures of excess burden that are not path-dependent and that answer meaningful questions. Path dependence does not arise if excess burden is measured by Hicksian consumers’ surplus, based on schedules that hold utility, rather than income, constant as prices vary. Because actual tax policy changes typically do not hold utility constant, it is therefore necessary to construct a measure based on a conceptual experiment in which utility is held constant. One intuitive experiment is to imagine that, as a tax is imposed, utility is held constant at its pre-tax level. this measure is based on the compensated demand curve D(u0), which by definition passes through the original, no-tax equilibrium point 0. If the tax is imposed, and consumers are compensated to remain at original utility levels, then demand follows this schedule and the tax reduces consumption to point 1\'. At this point, revenue raised is the sum of areas A and C, rather than the actual level of revenue represented by area A, because compensation induces consumers to purchase more of the taxed good (if, as is assumed here, the good is normal) and hence pay more taxes. Excess burden is defined as the amount, in excess of this revenue, that the government must compensate consumers to maintain initial utility in the face of a tax-induced price change. The amount of compensation, which corresponds to the Hicksian measure of the compensating variation of the price change, may be calculated using the expenditure function , which is well-defined even for a vector of changing prices p – the Hicksian variations are singlevalued, regardless of the order of integration of the different price changes in . For each market, this measure equals the area between prices p0 and p1 to the left of the compensated demand curve D c (U0). Thus, the deadweight loss equals area D in the figure – still approximately a “Harberger triangle”, but different than that defined by the ordinary demand curve.An alternative conceptual experiment is to begin with the tax already in place and then remove it, extracting from consumers in lump-sum fashion an amount that prevents them from changing their utility levels while the tax is removed. Because the initial tax is distortionary, it is necessary to extract more from consumers than the tax revenue, the difference representing the excess burden of the initial tax. Starting from point 1 in Figure 2.2, this experiment follows the compensated demand curve D c (U1) down to point 0\', where the price reaches its no-tax level but utility remains unchanged. Again using the expenditure function to calculate the amount the government extracts in this case – the Hicksian equivalent variation This exceeds the forgone revenue – in this case the actual revenue defined by area A – and again does so by a “triangle.” Although these two measures are the most intuitive, they are actually just examples drawn from a class of measures based on arbitrary levels of utility.