Recursive preferences and balanced growth (original) (raw)

Global equilibrium dynamics with stationary recursive preferences

Journal of Economic Behavior & Organization, 1987

We study the global dynamics of capital accumulation for a general two-sector model which is not necessarily convex and where preferences of an infinitely-lived agent are stationary but not additively separable. We obtain monotonicity and convergence results for capital under 'normality' assumptions on preferences and factor intensity assumptions on technology. We then derive results on oscillatory dynamics under alternative factor-intensity conditions or under the assumption of inferiority of 'future utilities'. Finally, in an exchange model with two agents we show that utilities will be monotonic or oscillatory depending on the normality or inferiority of the preferences.

Recursive utility and optimal growth with bounded or unbounded returns

Journal of Economic Theory, 2005

In this paper we propose a unifying approach to the study of recursive economic problems. Postulating an aggregator function as the fundamental expression of tastes, we explore conditions under which a utility function can be constructed. We also modify the usual dynamic programming arguments to include this class of models. We show that Bellman's equation still holds, so many results known for the additively separable case can be generalized for this general description of preferences. Our approach is general, allowing for both bounded and unbounded (above/below) returns. Many recursive economic models, including the standard examples studied in the literature, are particular cases of our setting.

Economic Growth with Interacting Heterogeneous Agents

This paper presents a variation in the literature of optimal growth with varying time preferences. To introduce heterogeneity among agents, our model considers two agents, which differ in their initial endowments and therefore in their degrees of impatience. Assuming that the agents share the yields of a single productive unit, non-monotone paths for the total capital in the economy can be obtained. This arises as a result of the "cross-over effects" between the individual capital paths. On the other hand, the decreasing rates of time preferences implies that an optimal dynamic path of the economy will tend to one of many possible steady states, depending on the location of the initial endowments.

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

2007

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).

Equilibria of a stationary economy with recursive preferences

Journal of Optimization Theory and Applications, 1991

We consider an intertemporal stationary economy in discrete time, where agents have recursive preferences. Using dynamic programming, we show that equilibrium consumption trajectories from a capital stock are interior Pareto optima and are characterized by a strictly positive parameter in △n−1, the set of agents' initial weights. We then exhibit prices that support the Pareto optima and use the Negishi method to characterize the parameters corresponding to equilibria. Finally, we prove the existence of equilibria and show that the number of regular equilibria is odd.

Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience

Dynamic Games and Applications, 2018

We study the interaction between strategy, heterogeneity and growth in a two-agent model of capital accumulation. Preferences are represented by recursive utility functions with decreasing marginal impatience. The stationary equilibria of this dynamic game are analyzed under two alternative information structures: one in which agents precommit to future actions, and another one where agents use Markovian strategies. In both cases, we develop sufficient conditions to prove the existence of equilibria and characterize their stability properties. The precommitment case is characterized by monotone convergence, but Markovian equilibria may exhibit nonmonotonic paths, even in the long-run.

Economic Growth in a Two-Agent Economy

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. One of the main results of this model arises in comparison with single-agent models. More precisely, one possible instance of the model consists of a case in which the two agents are such that without interaction one would become “rich” and the other “poor”. However, since they share a single production unit, a potential poverty trap may become averted.

The determinacy of equilibrium in economies of overlapping generations

Economic Theory, 2006

Equilibrium paths in an economy of overlapping generations are determinate. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, nonstorable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the lifespan of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however the indeterminacy vanishes as the number of periods in the lifespan of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the lifespan of individuals, and, in continuous time, it is infinite; however these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that origi...