ON OPTIMAL DEVELOPMENT PROGRAMS WHEN FUTURE UTILITY IS DISCOUNTED.
OPERATIONS RESEARCH CENTER UNIV OF CALIF BERKELEY
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An economy with n goods and a constant supply of labor is considered. Goods are produced from labor and other goods by a specified set of activities. Given an initial supply of goods, we consider all possible production programs in discrete time from the present through infinity. With each program is associated a utility sequence measuring the satisfaction of the activity in each time period. Future utility is discounted at a positive rate, delta. A program is said to be optimal if the sum of the discounted utility sequence is maximized in the set of such sequences. Optimal programs exist in a wide class of economies. This paper considers the long-run behavior of optimal programs. It is shown that every economy has at least one optimal program which is stationary over time and that such programs are characterized by an infinite sequence of prices which are stationary up to the discount factor delta. Three examples are given to show that 1 the optimal stationary program need not be unique, 2 there may exist optimal programs which do not converge to any stationary program, and 3 this may be true for all but one initial supply. These results are discussed relative to the undiscounted case. Author
- Economics and Cost Analysis
- Operations Research