Optimal growth with decreasing marginal impatience

Abstract This paper analyses the long run dynamics of a continuous time infinite horizon optimal growth model with identical households where the households’ rate of time preference is endogenously determined. However, unlike the existing literature, we assume that households have decreasing marginal impatience , i.e., the instantaneous discount rate is negatively related to the current consumption. With this assumption we analyse the stability and uniqueness of the long run equilibrium. We show that contrary to the general belief, a negative relationship between the instantaneous discount rate and the household's current consumption does not necessarily result in instability of the dynamic system. However, even a stable system may be characterized by multiple equilibria so that the initial condition becomes important in determining the long run behaviour of the economy. We derive a set of sufficient conditions for stability and uniqueness in this context.