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An economy is considered that has n goods and k types of labor, each of which is growing at the same constant rate. Goods are produced from labor and other goods by a set of specified activities. Given an initial supply of goods and amounts of labor, all possible production programs running from the present time to infinity through discrete time periods are considered. With each program is associated a utility sequence measuring the satisfaction achieved by the program at each period of time. A program is optimal if its utility sequence overtakes all other such sequences. The paper is devoted to proving the existence of optimal programs for a wide class of economies and to deriving the properties of such programs. In particular it is shown that the optimal program approaches a certain balanced program. Essential use is made of the existence of an infinite sequence of optimal prices with respect to which the optimal program is one which maximizes the sum of profit and utility at each time period. (Author)
Douglas Gale (Sun,) studied this question.