MAXIMIZING STATIONARY UTILITY IN A CONSTANT TECHNOLOGY
YALE UNIV NEW HAVEN CT COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
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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 Ux1,x2,... Summation, t1 to tinfinity, of alpha superscriptt-1 ux sub t, Oalpha1, is maximized under given conditions of technology and population growth. Here xt is per capita consumption in period t, and ux 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 Ux1, x2, x3,... Vx1, Ux2, x3,.... One obtains 1 by Vx, U ux alpha U. The natural generalization of alpha in 1 to stationary utility is the function 2a alphax the partial derivative of Vx,U with respect to U subscript U Ux,x,x,.... In this paper we study the maximization of 2 under production assumptions.
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