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In our incomplete markets economy households choose portfolios consisting of risky (uninsurable) capital and money. Money is a bubble, it has positive value even though it yields no payoff. The market outcome is constrained Pareto inefficient due to a pecuniary externality. Each individual agent takes the real interest rate as given, while in the aggregate it is driven by the economic growth rate, which in turn depends on individual portfolio decisions. Higher inflation due to higher money growth lowers the real interest rate on money and tilts the portfolio choice towards physical capital investment. Modest inflation boosts growth rate and welfare.

This paper computes the steady-state optimal rate of inflation assuming two different sticky-price specifications, Calvo (1983) and Taylor (1980), in a model with monopolistic competition. The optimal rate of inflation in steady state is always positive. This result is robust to changes in the degree of price stickiness. In both cases of staggered prices, the optimal rate of inflation is approximately equal to the ratio between the rate of discount and the Dixit-Stiglitz elasticity. ; Asier Aguilera-Bravo gratefully acknowledges financial support from Fundación Banco Sabadell, Fundación Bancaria Caja Navarra and Universidad Pública de Navarra. Miguel Casares would like to acknowledge financial support from the Spanish government (research project ECO2015-64330-P).

In central theories of monetary non-neutrality the Ramsey optimal inflation rate varies between the negative of the real interest rate and zero. This paper explores how the interaction of nominal wage and search and matching frictions affect the policy prescription. We show that adding the combination of such frictions to the canonical monetary model can generate an optimal inflation rate that is significantly positive. Specifically, for a standard U.S. calibration, we find a Ramsey optimal inflation rate of 1.11 percent per year.

The Friedman rule states that steady-state welfare is maximized when there is deflation at the real rate of interest. Recent work by Khan et al (2003) uses a richer model but still finds deflation optimal. In an otherwise standard new Keynesian model we show that, if households have hyperbolic discounting, small positive rates of inflation can be optimal. In our baseline calibration, the optimal rate of inflation is 2.1% and remains positive across a wide range of calibrations.

The Friedman rule states that steady-state welfare is maximized when there is deflation at the real rate of interest. Recent work by Khan et al. (2003) uses a richer model but still finds deflation optimal. In an otherwise standard new Keynesian model we show that, if households have hyperbolic discounting, small positive rates of inflation can be optimal. In our baseline calibration, the optimal rate of inflation is 2.1% and remains positive across a wide range of calibrations.