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On Endogenous Competitive Business Cycles

Jean-Michel Grandmont

Abstract

This paper develops an example in which persistent deterministic business cycles appear in a purely endogenous fashion under laissez-faire. These cycles are not attributable to exogenous "shocks" nor to any variation of policy since there are none in the model. Markets clear in the Walrasian sense at every date, and traders have perfect foresight along the cycles. The origin of these cycles is the potential conflict between the wealth effect and the intertemporal substitution effect that are associated with real interest rate movements. Business cycles appear in particular when the degree of concavity of a trader's utility function is sufficiently higher for old agents than for younger ones. The techniques employed to study the occurrence and the stability of such business cycles are borrowed partly from recent mathematical theories that have been constructed by using the notion of the "bifurcation" of a dynamical system in order to explain the emergence of cycles and the transition to turbulent ("chaotic") behavior in physical, biological, or ecological systems. The equilibrium level of output is shown to be negatively related to the equilibrium level of the real interest rate. A similar relation exists (but in the opposite direction) between equilibrium real money balances and real interest rates. These relations hold both in the long run, i.e. along business cycles, and in the short run, i.e. on the transition path, and whether movements of the real interest rate are anticipated or not. The basic ingredient there is the condition that older agents have a higher marginal propensity to consume leisure. Monetary policy by means of nominal interests payments is shown to be extremely effective. A permanent change of the rate of growth of the money supply by these means is superneutral. Yet, there exists a very simple deterministic countercyclical policy that enables monetary authorities to stabilize completely business cycles and to force the economy back to the unique (Golden rule) stationary state. Due to the nonlinearity of the model such a policy affects not only the variances of real equilibrium magnitudes but also their means.