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

*Alexander Gorokhovsky* and
*Anna Rubinchik* ()

*Journal of Mathematical Economics*, 2018, vol. 74, issue C, 35-45

**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.

**Keywords:** Overlapping generations; Implicit function theorem; Determinacy; Time-invariance; Comparative statics (search for similar items in EconPapers)

**Date:** 2018

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

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:74:y:2018:i:c:p:35-45

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