ECONOMIC

Then, subtracting equation (4) from equation (3),lnY*i— InY* = (lnY s + ln(l-fk)) — "(mY + ln(l + k)) = lnYj — mYT (5)and S2(lnY*)=SHlnY). (6)Thus, a proportional tax on income or a proportional cash subsidy does not changerelative income inequality.Relative inequality decreases (increases) if the income of each observation isincreased (decreased) by the same dollar amount. A $100 per year grant to a poorfamily constitutes a larger percentage increase in income than an equal dollar grant toa wealthy family. Such a grant reduces the relative inequality of income.A progressive tax is one in which the higher the level of income, the larger theproportion of income paid in taxes. In a regressive tax a smaller proportion of incomeis paid in taxes as income increases. A progressive tax reduces, and a regressive taxincreases, relative income inequality (S 2 (lnY)).180