Heterogeneity, monetary policy, Mirrleesian taxes, and the Friedman rule

We consider an overlapping-generations economy with money rationalized through a cash-in-advance constraint and heterogeneous agents subject to nonlinear taxation of labor income and linear taxation of commodity purchases. Some agents are more productive and more financially connected than others leading to their earning more income and requiring a proportionately smaller cash reserve to mediate their expenditures. We show that a nonlinear income tax can always fully neutralize the redistributive implications of who gets the extra money. On the other hand, with differences in financial connectedness, the tax policy cannot neutralize the redistributive implications of the monetary growth rate. Nevertheless the Friedman rule is found to be often desirable as a corner solution without having to impose arbitrary restrictions on the structure of agents' preferences. At the same time, the differences in connectedness may result in the violation of the Friedman rule.