Theories of optimal production in a planned economy have usually assumed that the tas system can allow the government to achieve any desired redistribution of property. ^ On the other hand, some recent discussions of public investment criteria have tended to ignore taxation as a complementary method of controlling the economy. ^ Although lump sum transfers of the kind required for full optimality' are not feasible today, commodity and income taxes can certainly be used to increase welfare. ^ We shall therefore examine the maximization of social welfare using * The authors are at Massachusetts Institute o
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