Recursive utility and optimal capital accumulation. I: Existence
type: Item
instance of: scholarly article
title: Recursive utility and optimal capital accumulation. I: Existence
zbMATH Open document ID: 0679.90014
DOI: 10.1016/0022-0531(89)90104-X
author: Robert A. Becker
author: John H. III Boyd
author: Bom Yong Sung
published in: Journal of Economic Theory
publication date: 1989-01-01T00:00:00Z
review text: This paper demonstrates existence of optimal capital accumulation paths when the planner's preferences are represented by a recursive objective functional. Time preference is flexible. Mathematically, the problem is as follows: \[ \max imize\quad \int^{\infty}_{0}L(t,k,\dot k)\exp (\int^{\infty}_{0}R(s,k,\dot k)ds)dt, \] s.t. k: \({\mathbb{R}}_+\to {\mathbb{R}}^ m\) is an absolutely continuous function; \(\dot k\in G(t,k)\) a.e.; \(0\leq k(0)\leq x\), where L: \(\Omega \to {\mathbb{R}}_+\) and R: \(\Omega\) \(\to {\mathbb{R}}\) are continuous on \(\Omega\) and convex in k, which are the felicity function and the discounting function of the economy respectively; \(\Omega \subset {\mathbb{R}}\times {\mathbb{R}}^ m\times {\mathbb{R}}^ m\) is the technology set of the economy and \(G(t,k)=\{y: (t,k,y)\in \Omega \}\) is the investment correspondence, which is compact-convex- valued and upper semicontinuous in t. Existence of optimal paths is addressed via the classical Weierstrass theorem. An improved version of a lemma due to Varaiya proves compactness of the feasible set for the compact-open topology. A monotonicity argument is combined with a powerful theorem of Cesari to demonstrate upper semicontinuity.
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 4114349
zbMATH Keywords: recursive utility
zbMATH Keywords: existence of optimal capital accumulation paths
zbMATH Keywords: Weierstrass theorem
zbMATH Keywords: upper semicontinuity
MaRDI profile type: Publication
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full work available at URL: 0022-0531(89)90104-x
OpenAlex ID: W1965517468
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