We apply duality methods of linear and convex programming to the problems of operation and rental valuation of facilities for conversion and storage of cyclically priced goods, e.g., energy. Both problems are approached by shadow-pricing the stock (which is a purely intermediate commodity); and if the given market price p for the final good is a continuous function of time, then the stock's shadow price function ψ is shown to be unique (and continuous). Therefore, despite being perfect Allen–Hicks complements, the plant's capacities have definite and separate marginal values, which are expressed in terms of ψ (and p ). In particular, the unit reservoir rent equals the total positive variation of ψ over the cycle. The optimal storage policy is also given in terms of ψ and p . The marginal capacity values are used to determine the optimum investment. The framework can accommodate related storage problems (such as hydroelectric generation).
Journal of Economic Dynamics and Control – Elsevier
Published: Nov 1, 2002
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