A simple monetary growth model with variable rates of time preference

This paper constructs a simple optimal monetary growth model in which an endogenous and variable rate of time preference provides a rational foundation for a Tobin-effect in a system where otherwise strong neoclassical assumptions (e.g., perfect foresight, an infinite planning horizon, and continuous marketclearing) are maintained. Changes in the proportional rate ofgrowth of the nominal money supply affect both the rate of time preference (ñ) and the equilibrium capital—labour ratio. The impact effect of a fall in ñ (less impatience), and the induced capital accumulation that goes with it, drives the result. Proper transformation rules for two-state variablecontrol problems and curvature and simulation results for the rate of time preference function are also established. The latter in particular provides a reasonable and easily understood foundationfor simple systems in which the rate of time preference depends on an index of futureconsumption, and provides a counter-argument to well-known criticisms (e.g., Blanchard andFischer (1989) and Barro and Sali-i-Martin (1995)) of Epstein—Uzawa rate of time preference functions. All results are obtained in an analytically simple way, using standard techniques.