,3, of course, is the estimate of _qTY in the logarithmic form of (2). This technique characteristically yields high estimates of qTy. For example, Soltow [7] and Groves and Kahn [3] both estimated that for Wisconsin during the 1933-1951 period of constant (quite progressive) state tax rates, rjTY was at least 1.75. Harris [4] estimated elasticities of about 1.22.4 for different states by applying constant state tax rates to distributions of federal adjusted gross income by states, and derived an overall income-elasticity of 1.8 for aggregate state income tax revenues. In an earlier study [6], I used dummy-variable techniques to estimate elasticities of 1.4-2.2 for a selected group of states. These estimates of state income-tax elasticities have not gone unnoticed by public officials. When Maryland adopted a new income-tax law in 1967, the State's Board of Revenue Estimates issued a set of revenue forecasts that showed an annual growth rate of approximately 15 per cent, compared to a growth rate of about 10 per cent in aggregate personal income. The implicit elasticity estimate of 1.5 was well within the range of estimates made for Maryland and other states with similar tax laws. Experience with the tax in calendar years 19671969, however, has shown the actual incomeelasticity of revenues to be much closer to 1.0, although actual collections appear to be very sensitive to the rate of price inflation and variations in collections procedures. These observations underlie the model presented below.

[This paper presents a general formalism for calculating the effect of taxes on income distribution, and the resultant effect on income inequality. We first derive a closed form expression for income inequality (defined from a Lorenz curve) in terms of the income density function. By way of illustration, we use this expression to calculate the effect of a proportional and a lump sum tax on income inequality in a simple exponential income distribution. The results show that the effect of a lump sum tax imposed after a proportional tax is a function of the proportional tax rate, even though the proportional tax itself does not change inequality.]