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 , comparison of plans according to average fitnesses of the populations produced; for example, |
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The specification of how goods can be transformed into each other is called the technology of the model and the specification of how goods are transformed to satisfaction is called the utility function. Given this structure and some initial bundle of goods, the problem of optimal development is to decide at each point of time how much to invest and how much to consume in order to maximize utility summed over time in some suitable way.
Gale in "A Mathematical Theory of Optimal Economic Development"
Bull. AMS 74, 2 (p. 207) |
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One of the most important formulations of mathematical economics is the von Neumann technology. This technology can be presented (following David Gale 1968) in terms of a finite set of goods and a finite set of activities,where each activity transforms some goods into others. If the goods are indexed, then the goods available to the economy at any given time can be presented as a vector where the ith component gives the amount of the ith good. In the same way, the input to the jth activity and the resultant output can be given by a pair of vectors Wjand  where the ith component of Wjspecifies the amount of the ith good required by the activity, while the ith component of specifies the amount produced. An activity can be operated at various levels of effort so that, for instance, if the amount of input of each required good is doubled then the amount of output will be doubled. More generally, if the level of effort for activity j is cj then the pair  specifies the input and output of the activity. If a mixture of activities is allowed, the overall technology can be specified as the set of pairs |
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where W and W' are matrices having the vectors Wj and as their respective jth columns, each c is a vector having the level of the jth activity as its jth component, and Q designates the set of admissible activity mixes (corresponding to the real constraints limiting the total activity at any time). A program for utilizing the technology is given by a sequence of activities  satisfying the intuitive "local" requirement that the total amount of each good required as input for the activities at time |
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