How does interest rate policy affect inflation? A simple general equilibrium model with the interest rate as the policy instrument

This paper analyses the connection between the assumptions often made on the utility functions of economic agents when general equilibrium is considered. Concretely, we analyse the effect of certain assumptions regarding the elasticity of marginal utility for both the existence of equilibrium and, assuming equilibrium exists, for the effect that raising the nominal interest rate has on the equilibrium inflation rate. Typical macroeconomic wisdom states that an increase in the interest rate will decrease inflation, and this seems to have been the basis for real-life macroeconomic policy in several countries. However, this wisdom is based on models in which the money supply, and not the interest rate, is the policy instrument. Using a very simple general equilibrium model of intertemporal consumption, this paper finds sufficient conditions for the negative relationship to hold (and for it not to hold) in the short run, when monetary policy is characterised by a given nominal interest rate. Above all, it is shown how the relative risk aversion characteristics that are assumed of the economic agents are important.