The optimal price of money

One of the basic monetary policy issues facing the monopolist supplier of currency is what price to charge for its use. The price paid for the use of currency, by households or firms, is the foregone interest on less liquid, but riskless, assets such as short-term government bonds. Thus, the question of what price to charge for the use of currency is identified with the question of what is the optimal nominal interest rate. According to Friedman (1969), monetary policy ought to be conducted so that the resulting nominal interest on short-term, less liquid assets is zero. The argument for the Friedman rule is very simple: Since the cost of supplying money is negligible, the price charged for its use should also be very close to zero. The first best argument of Friedman (1969) was challenged by Phelps (1973) on the basis that a positive nominal interest rate generates tax revenues for the government. According to Phelps (1973), since the alternative sources of revenue also create distortions, liquidity should be taxed like any other good. This public finance argument motivated a literature on the optimal inflation tax in a second-best environment, where the government is constrained to finance exogenous government expenditures by recourse to distortionary taxes. Somewhat surprisingly, the recent literature on the optimal inflation tax has argued that, even in a second-best environment, it is optimal not to use the inflation tax, so that the Friedman rule is still optimal. Why is this the case? Why shouldn’t liquidity be taxed like any other good, as argued by Phelps (1973)? In this article, I review some of the results obtained in the literature on the optimality of the Friedman rule. I base the analysis on Correia and Teles (1996, 1999) and De Fiore and Teles (2003), which have built on work by Kimbrough (1986), Guidotti and Végh (1993), and Chari, Christiano, and Kehoe (1996), among others. I start by analyzing a simple environment where liquidity services are modeled as a final good, so that agents gain utility from consumption, leisure, and real balances, measured by the stock of money deflated by the price level. This is the context in which the argument of Phelps (1973) was made. According to Phelps, an application of the Ramsey (1927) principles of taxation of final goods, would mean that tax distortions should be distributed across goods, including liquidity services. Since the public finance principles, such as Ramsey (1927), were applied to costly goods, I allow for the possibility that money is costly to supply. I assume that the utility function satisfies the conditions for uniform taxation of final goods, established by Atkinson and Stiglitz (1972). In that case it is optimal to tax money, at the same proportionate rate as the consumption good. Thus, the price charged for the use of money, the nominal interest rate, int, should be equal to the cost of producing real balances, c, marked up by the optimal common tax rate, τ*, on real balances and consumption,