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Production Under Uncertainty

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Handbook of Production Economics

Abstract

This chapter describes a formal model of a stochastic production technology. Alternative axioms and different structural restrictions are presented, and producer decision-making under uncertainty is examined. The presentation emphasizes the formal similarities between the stochastic production environment and more traditional models of a nonstochastic technology and producer behavior under certainty. The nonstochastic multiple-output technology is shown to be special case of the more general stochastic production structure.

My thanks to Spiro Stefanou for comments that considerably improved the presentation.

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Notes

  1. 1.

    Donald Rumsfeld famously said: “‘…there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know” (US Department of Defense, 2002).

  2. 2.

    Luenberger [30] coined the “shortage” terminology. Later building upon Luenberger [30], Chambers, Chung, and Färe [7] introduced the “directional distance” terminology to emphasize its similarities to and differences from distance function of the type studied by Shephard [? ]. See the chapter entitled “Distance Functions” by Chambers and Färe in this volume.

  3. 3.

    As it turns out, the Cobb-Douglas specification is actually not a viable candidate for characterizing a directional distance function. It fails to satisfy a key regularity property such functions must possess. This regularity condition, which is referred to as the translation property, is important from a technical perspective. But it is not crucial to our discussion of stochastic technologies and thus has been ignored.

  4. 4.

    As far as I am aware, Chambers and Quiggin [8] were the first to recognize that \(Z\left ( x\right ) \) for this particular specification took this shape.

  5. 5.

    Formally, gradients are replaced by subgradients at the kink. Visually, subgradients are represented by the infinity of hyperplanes tangent to \( Z\left ( x\right ) \) at the kink.

  6. 6.

    Most applications treat the case where S is infinite-dimensional and thus take ε to be an interval of the real line.

  7. 7.

    At this juncture, it would be a good exercise for you to revisit Fig. 9 and the associated intuitive discussion in an attempt to determine whether 1 is associated with more or less moisture than 2.

  8. 8.

    These conditions are easily relaxed. See, for example, Chambers and Quiggin ( [10,11,12], 2010), Chambers [6], and Chambers and Voica [13].

  9. 9.

    Although it is not discussed here, one can alternatively express the Fisher separation theorem in terms of a revenue function defined over discounted period 1 prices and x. That derivation, in turn, allows for a decomposition of present value maximizing supplies in terms of substitution and scale effects.

  10. 10.

    The reader is referred to Chambers and Quiggin [10] for a more detailed and thorough treatment of revenue-cost functions.

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Author information

Authors and Affiliations

  1. Department of Agricultural and Resource Economics, University of Maryland, College Park, MD, USA

    Robert G. Chambers

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  1. Robert G. Chambers
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Correspondence to Robert G. Chambers .

Editor information

Editors and Affiliations

  1. Department of Economics, University of Connecticut, Storrs, CT, USA

    Subhash C. Ray

  2. Department of Agricultural and Resource Economics, University of Maryland, College Park, MD, USA

    Robert G. Chambers

  3. Department of Economics, Binghamton University, Binghamton, NY, USA

    Subal C. Kumbhakar

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Chambers, R.G. (2022). Production Under Uncertainty. In: Ray, S.C., Chambers, R.G., Kumbhakar, S.C. (eds) Handbook of Production Economics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3455-8_6

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