max{0, t(y − a)}. Income in the economy is distributed with a cumulative distribution F with density f. Therefore, if we denote the total amount of resources collected by the tax system with R(t; a), we obtain R(t; a) = tφ(a), where Note that It is assumed that the government must raise a total amount of resources equal to an exogenously specified amount which does not enter the utility of the agents. Therefore, the government’s budget constraint then requires and this equation can be used