Regularity of a general equilibrium in a model with infinite past and future

Abstract

We develop easy-to-verify conditions to assure that a comparative statics exercise in a dynamic general equilibrium model is feasible, i.e., the implicit function theorem is applicable. Consider an equilibrium equation, ϒ(k,E)=k of a model where an equilibrium variable (k) is a continuous bounded function of time, real line, and the policy parameter (E) is a locally integrable function of time. The key conditions are time invariance of ϒ and the requirement that the Fourier transform of the derivative of ϒ with respect to k does not return unity. Further, in a general constant-returns-to-scale production and homogeneous life-time-utility overlapping generations model we show that the first condition is satisfied at a balanced growth equilibrium and the second condition is satisfied for “almost all” policies that give rise to such equilibria.