Monetary Analysis In Continuous Time

Abstract

Discrete time methodologies have been developed to obtain the transitional dynamics of the major economic aggregates in a general equilibrium monetary model. To achieve explicit solutions, however, they rely on approximations whose implications as to the qualitative characteristics of the equilibrium have been ignored. Here, the general equilibrium of a frictionless stochastic monetary economy with technological and monetary shocks and a representative agent endowed with a Sidrausky utility function of general shape is obtained in continuous time. Assuming fairly general stochastic dynamics for the exogenous processes, the equilibrium paths of endogenous variables are derived without any approximation. The relationships between money, inflation, real wealth, investment and consumption, financial asset prices and nominal and real interest rates are exactly derived and some of them are shown to be strongly non-linear. Moreover, in a special case where the utility function is log separable and the stochastic features of the economy are simplified, complete closed form solutions are derived, again without approximation. Stochastic money never is super-neutral, regardless of the shape of the representative agent's utility function.