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Cost, Revenue, and Profit Function Estimates

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Handbook of Production Economics

Abstract

This chapter reviews the ways in which cost, revenue, and profit functions are used to identify and characterize an underlying technology. It concentrates on the more widely used functional forms to motivate various issues in the flexibility of various parametric functions, in the imposition of regularity conditions, in the use of non-parametric estimation of models, and in standard econometric models used to estimate the parameters of these different functional characterizations of an underlying technology. The modeling scenarios we consider also allow allocative and technical distortions and address how such distortions may be modeled empirically in the specification and estimation of the dual functional representations of the underlying primal technology.

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Notes

  1. 1.

    For more details on the issues discussed in this section, see Chapter 2 (Production Theory: Dual Approach) of Sickles and Zelenyuk [110] whose notation we adopt here.

  2. 2.

    A weaker continuity condition is that C(y, w) is continuous in w and lower semi-continuous in y.

  3. 3.

    See Caves et al. [19] for a discussion multi-output cost functions. See also Röller [100] for another study that consider multi-output cost functions.

  4. 4.

    See Wales [117] for another example in the utility function context.

  5. 5.

    For another application of constrained optimization method to a flexible (i.e., globally flexible Fourier) cost function, see Feng and Serletis [31].

  6. 6.

    See Kleit and Terrell [58] as an application of Bayesian approach for flexible cost functions.

  7. 7.

    See Kumbhakar and Lovell [65] for details.

  8. 8.

    A weaker continuity condition is that R(x, p) is continuous in p and upper semi-continuous in x.

  9. 9.

    Bos and Koetter [17] propose an alternative approach to overcome this issue. For observations where the profit is positive, they keep the left-hand-side variable as lnπ, and for those observations where the profit is negative, they replace the left-hand-side variable with 0. They also add an indicator variable to the right-hand side. This indicator variable equals 0 when the profit is positive and equals ln|π−| when the profit is negative. This method has the advantage that it uses all sample points for the estimations. However, when measuring inefficiency, the logarithmic scale breaks down for negative profits. Hence, the interpretation of inefficiency estimates for the observations with negative profits deviates from the standard interpretation. Koetter et al. [59] exemplify a study that uses this approach.

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Authors and Affiliations

  1. Department of Economics and Finance, University of Texas Rio Grande Valley, Edinburg, TX, USA

    Levent Kutlu

  2. Department of Economics, Rice University, Houston, TX, USA

    Robin C. Sickles

  3. Enterprise Model Risk, Freddie Mac, McLean, VA, USA

    Shasha Liu

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  1. Levent Kutlu
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  2. Shasha Liu
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  3. Robin C. Sickles
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Correspondence to Robin C. Sickles .

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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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Kutlu, L., Liu, S., Sickles, R.C. (2022). Cost, Revenue, and Profit Function Estimates. 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_12

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