SOME WELFARE PROBLEMS OF INTERTEMPORAL DECISION-MAKING,
PURDUE UNIV LAFAYETTE IND KRANNERT GRADUATE SCHOOL OF INDUSTRIAL ADMINISTRATION
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The paper is concerned with optimal decision-making over time. The tools of the Pontryagin maximum principle are used to investigate the case of water pollution. Two producers on a stream, one upstream from the other, are considered the upstream producer is assumed to be causing damage to the other. The first question considered is the optimal allocation of the water resource between the two. Taxation schemes to achieve the optimum solution are discussed and it is proposed that waste disposal be limited by legal restrictions. This should induce cooperation between the firms to finance a treatment plant. The result is that the upstream firm is able to produce at a higher level than the level corresponding to the restrictions on his waste and the downstream firm obtains water of a higher quality than the level corresponding to the restrictions. Thus both are better off when a jointly financed treatment plant is built. The model considered answers the questions of the optimal plant capacity over the time period and how much each firm should contribute to running the plant. Thus the paper extends the usual static analysis of optimal resource allocation and in addition considers optimal investment over time.
- Operations Research
- Water Pollution and Control