A general equilibrium model with financial frictions in which individuals may encounter unobservable investment opportunities is developed along the lines of Kiyotaki and Moore (2012). I study efficiency properties induced by money and monetary policy when financial frictions prevent optimal equilibrium allocations. By providing closed-form solutions to all prices, allocations, welfare, and, especially, the distribution of individuals with respect to assets, I show that the Friedman rule achieves maximal social welfare, independent of how tight the financial constraints may be. The same level of welfare would be induced by an omniscient central planner able to verify who has an investment opportunity.

We construct a microfounded model of money with Gul–Pesendorfer preferences. In each period, agents are tempted to spend all their money by the end of the period, and they suffer from the forgone utility that could have been obtained by adopting the tempting choice. We find that the Friedman rule may not be optimal. A positive nominal interest rate improves welfare because it reduces the real money balances and renders the temptation less attractive. The welfare gained by deviating from the rule is equivalent to 0.67% of consumption.

We formulate a central bank's problem of selecting an optimal long-run inflation rate as the choice of a distorting tax by a planner who wishes to maximize discounted stationary utility for a heterogeneous population of infinitely lived households in an economy with constant aggregate income and public information. Households are segmented into agents who store value in currency alone and agents who have access to both currency and loans. We show that the optimum inflation rate is positive, because inflation reduces the value of the outside option for credit agents and raises their debt limits.

The welfare cost of anticipated inflation is quantified in a matching model of money calibrated to 23 different OECD countries for several sample periods. In most economies, in the common period 1978–1998, a representative agent would give up only a fraction of 1% of consumption to avoid 10% inflation. The welfare cost of inflation varies across countries, from a fraction of 0.1% in Japan, to more than 2% in Australia, reaching 6% with bargaining. The model fits money demand data of several countries poorly, however. The fit generally improves with longer sample periods. The results are fairly robust to variations in choice of calibrated parameters and calibration targets.

A model is constructed in which trading partners are asymmetrically informed about future trading opportunities and spatial and informational frictions limit arbitrage between markets. These frictions create inefficiency relative to a full-information equilibrium, and the extent of this inefficiency is affected by monetary policy. A Friedman rule is optimal under a wide range of circumstances, including ones where segmented markets limit the extent of monetary policy intervention.

This paper modifies a Townsend turnpike model by letting agents stay at a location long enough to trade some consumption loans, but not long enough to support a Pareto-optimal allocation. Monetary equilibria exist that are nonoptimal in the absence of a scheme to pay interest on currency at a particular rate. Paying interest on currency at the optimal rate delivers a Pareto-optimal allocation, but a different one than the allocation for an associated nonmonetary centralized economy. The price level remains determinate under an optimal policy. We study the response of the model to “helicopter drops” of currency, steady increases in the money supply, and restrictions on private intermediation.

We study the money-in-the-utility-function model in which agents are heterogeneous in their initial wealth. We show that the Friedman rule is not optimal even if the government uses nonlinear income taxation for redistribution. A positive nominal interest rate raises social welfare because it relaxes the incentive compatibility constraint for highly endowed agents. Although the setup is close to that of da Costa and Werning [Journal of Political Economy (2008) 116, 82–112], who investigate skill heterogeneity, the role of the nominal interest rate in this paper here differs from the one in their model.

We study how discount window policy affects the frequency of banking crises, the level of investment, and the scope for indeterminacy of equilibrium. Previous work has shown that providing costless liquidity through a discount window has mixed effects in terms of these criteria: It prevents episodes of high liquidity demand from causing crises but can lead to indeterminacy of stationary equilibrium and to inefficiently low levels of investment. We show how offering discount window loans at an above-market interest rate can be unambiguously beneficial. Such a policy generates a unique stationary equilibrium. Banking crises occur with positive probability in this equilibrium and the level of investment is suboptimal, but a proper combination of discount window and monetary policies can make the welfare effects of these inefficiencies arbitrarily small. The near-optimal policies can be viewed as approximately implementing the Friedman rule.

This paper analyzes the optimal inflation tax in economies with structural imperfections in labor, commodity, and currency markets. The Friedman rule is a classic result in economics that claims that the optimal monetary policy is to set a zero nominal interest rate. This Ramsey equilibrium is robust in a wide range of environments without imperfections in input, output, or financial markets. In many developing countries, however, a large fraction of activity takes place in the “informal” sector. Roughly speaking, the informal sector is the untaxed and unregulated market sometimes referred to as the underground economy. We obtain three results. First, we show that when structural imperfections such as an informal sector exist, the optimal inflation tax is positive. Second, we show that structural imperfections introduce an important asymmetry in the welfare cost function. Third, we provide quantitative results.