Economic Theory

, Volume 40, Issue 3, pp 457–471 | Cite as

Non-convex aggregate technology and optimal economic growth

Research Article

Abstract

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state toward which the convergence of the optimal path is monotone and asymptotic. When the discount rate is in some intermediate range, we will find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, we show that the optimal paths monotonically converge to one single appropriate equilibrium steady state. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range. In this range, we give conditions under which the above critical value might not exist, and the economy attains one steady state in finite time, then stays at the other steady state afterward.

Keywords

Nonconvex aggregate technology Poverty trap Multiple equilibria Dynamic convergence 

JEL Classification

C61 D90 O41 Q20 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Département d’économiqueUniversité Laval, Cité UniversitaireSainte-FoyCanada
  2. 2.PSE, Université Paris 1, CNRSParisFrance
  3. 3.GREQAM and EUREQUAUniversité Paris 1ParisFrance

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