MAXIMIZING STATIONARY UTILITY IN A CONSTANT TECHNOLOGY
Abstract
This paper is concerned with a problem in the optimal control of a nonstochastic process over time. It can also be looked on as a problem in convex programming in a space of infinite sequences of real numbers. The literature on optimal economic growth contains several papers in which a utility function of the form (1) U(x1,x2,...) = Summation, t=1 to t=infinity, of alpha (superscript(t-1)) u(x sub t), O<alpha<1, is maximized under given conditions of technology and population growth. Here xt is per capita consumption in period t, and u(x) is a strictly concave, increasing, single-period utility function. Alpha is called a discount factor. A generalization of (1) has been proposed under the name stationary utility, and is definable by a recursive relation (2) U(x1, x2, x3,...) = V(x1, U(x2, x3,...)). One obtains (1) by V(x, U) = u(x) + alpha U. The natural generalization of alpha in (1) to stationary utility is the function (2a) alpha(x) = (the partial derivative of V(x,U) with respect to U) subscript U = U(x,x,x,...). In this paper we study the maximization of (2) under production assumptions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 14, 1967
- Accession Number
- AD0655627
Entities
People
- Richard Beals
- Tjalling C. Koopmans
Organizations
- Yale University