Koopmans recursive preferences and income convergence

Abstract Stiglitz (Econometrica 37 (1969) 382) shows income convergence in a many-agent Solow growth model with integrated capital markets (ICM). The many-agent Ramsey model (MARM) without ICM also gives income convergence. With a MARM, equal discount rates, and ICM, convergence of incomes (as opposed to product per capita) cannot occur. These results depend upon fixed saving propensities (Stiglitz) or separable additive preferences (Ramsey). Non-convergence of incomes is shown when preferences are identical Koopmans separable (KS). Endogenous discount rates may violate KS. A model for that case is developed when, even under favourable assumptions, oscillations or chaotic dynamics may result.