Optimal Growth with Variable Rate of Time Preference

In this paper we develop 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 here that the instantaneous discount rate of the representative household is negatively related to its current consumption. With this assumption, we analyze the long run dynamic behaviour of the economy. 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. We derive a set of sufficient conditions for stability and instability in this context. We also show the possible existence of a poverty trap such that if an economy starts with a per capita income below a certain critical minimum value, then it optimally chooses a consumption-accumulation path such that it faces economic retrogression over time.