Optimality of the Friedman Rule in Economies with Money Demand by Firms

Motivated by the facts that firms hold about two thirds of M1 in industrialized economies, I study the optimality of the Friedman rule in economies with money demand by firms and different types of fiscal instruments. Money demand by firms is introduced in two ways: a cash-in-advance (CIA) constraint on wages and money in the production (MIP) function. In the case of a CIA constraint on wages, I show that the Friedman rule is not optimal when the government has access to only one distortionary tax to finance its expenditures. This is the case both in an economy with labor only and in one with labor and capital. Once a sufficiently rich menu of taxes is available to the fiscal authorities, the Friedman rule, then, may or may not be optimal. In contrast, in the case of MIP function, the optimal policy is to satiate the economy with real balances, even in the presence of distorting taxes on consumption and capital. That is, the Friedman rule is optimal. I also show that adding a working capital constraint on wages to a cash-andcredit goods model has no impact on the optimality of the Friedman rule and that it still remains optimal if preferences satisfy homotheticity and separability assumptions.