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Optimal allocation of a fixed production under price uncertainty

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  • Inmaculada Rodríguez-Puerta
  • Alberto Álvarez-López

Abstract

In this paper, we consider a model of production allocation in the context of the theory of the firm under uncertainty. This is the case of a firm that has just produced a known amount of an output and can allocate it to two possible ends: one with a certain price, the other with an uncertain price. We first establish conditions to determine whether the firm will make use of both ends or of only one of them. In particular, we find a limit value for the certain price (which we call the frontier price) below which the firm decides to allocate the total amount of production to the uncertain end. We then study comparative-static effects on the optimal output allocated to each end, and also on the frontier price. Finally, we analyze an application concerning the middleman who buys the firm’s output in the certain end. This is a pricing problem: namely obtaining the price in the certain end that the middleman must offer to the producer in order to attain a desired amount of output. In two specific cases, we also provide closed-form expressions for the optimal allocation to both ends and for the frontier price. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Inmaculada Rodríguez-Puerta & Alberto Álvarez-López, 2016. "Optimal allocation of a fixed production under price uncertainty," Annals of Operations Research, Springer, vol. 237(1), pages 121-142, February.
    • Handle: RePEc:spr:annopr:v:237:y:2016:i:1:p:121-142:10.1007/s10479-014-1702-7
    DOI: 10.1007/s10479-014-1702-7
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