Strategic Economic Growth With Decreasing Rates Of Time Preference In A Two-Agent Economy.

Abstract

This paper presents a two-agent economy, in which each agent has a consumption-dependent time
preference. The optimal dynamic paths of accumulation will tend to one of many possible steady states,
depending on the location of the initial capital level. The qualitative properties of this economic system
have been analyzed elsewhere (Tohmé and Dabús, 2000). It has been shown that the interaction between
the two agents may drag the poorest agent towards a higher steady state, getting her out of the potential
poverty trap in which she could fall in isolation.
We are interested now in studying specific functional forms of the joint production function, the utility
functions and the psychological discount rates. The goal is to characterize both the individual and joint
steady states in order to assess the advantages of interaction.
Following the lead of (Dockner and Nishimura, 2004) we will obtain the subgame perfect equilibria
of the economy seen as a two-person non-zero sum game. We will show that the non-linear convergence
path towards the steady state examined by Tohm´e and Dab´us also obtains in a closed-loop solution..