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Alternative functional forms for production, cost and returns to scale functions

Author

Listed:
  • Arnold Zellner

    (Graduate School of Business, University of Chicago, Chicago, IL 60637, USA)

  • Hang Ryu

    (Seoul Institute of Economic Research, 16 Eul Chi Ro 2 Ka, Choong Ku, Seoul, Korea)

Abstract

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.

Suggested Citation

  • Arnold Zellner & Hang Ryu, 1998. "Alternative functional forms for production, cost and returns to scale functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 101-127.
  • Handle: RePEc:jae:japmet:v:13:y:1998:i:2:p:101-127
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    Cited by:

    1. Bella, Giovanni & Mattana, Paolo, 2014. "Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 69-79.
    2. Urga, Giovanni & Walters, Chris, 2003. "Dynamic translog and linear logit models: a factor demand analysis of interfuel substitution in US industrial energy demand," Energy Economics, Elsevier, vol. 25(1), pages 1-21, January.
    3. Arthur S. Gow, 2003. "Microeconomic Modeling And Analysis Of Commodity Chemical Production In A Simple Plant," New York Economic Review, New York State Economics Association (NYSEA), vol. 34(1), pages 3-20.
    4. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," CeMMAP working papers CWP14/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    6. Griffiths, William E. & O'Donnell, Christopher J., 2005. "Estimating variable returns to scale production frontiers with alternative stochastic assumptions," Journal of Econometrics, Elsevier, vol. 126(2), pages 385-409, June.
    7. Gad Allon & Michael Beenstock & Steven Hackman & Ury Passy & Alexander Shapiro, 2007. "Nonparametric estimation of concave production technologies by entropic methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 795-816.
    8. Wong, Tsz-Nga & Yip, Chong K., 2010. "Indeterminacy and the elasticity of substitution in one-sector models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 623-635, April.
    9. Hang Ryu, 2009. "Economic assumptions and choice of functional forms: comparison of top down and bottom up approaches," Journal of Productivity Analysis, Springer, vol. 32(1), pages 55-62, August.
    10. Holzner, Christian & Launov, Andrey, 2010. "Search equilibrium and social and private returns to education," European Economic Review, Elsevier, vol. 54(1), pages 39-59, January.
    11. Thomsen, Thomas, 2000. "Short cuts to dynamic factor demand modelling," Journal of Econometrics, Elsevier, vol. 97(1), pages 1-23, July.
    12. Ryu, Hang Keun, 2011. "Subjective model selection rules versus passive model selection rules," Economic Modelling, Elsevier, vol. 28(1), pages 459-472.
    13. Andrey Launov & Christian Holzner, 2005. "Search Equilibrium, Production Parameters and Social Returns to Education: Theory and Estimation," 2005 Meeting Papers 604, Society for Economic Dynamics.
    14. Ryu, Hang Keun, 2011. "Subjective model selection rules versus passive model selection rules," Economic Modelling, Elsevier, vol. 28(1-2), pages 459-472, January.
    15. Sauer, J.F., 2005. "“Efficiency Flooding”: Black-Box Frontiers and Policy Implications," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 2(1), pages 17-52.
    16. Seo, Young-Joon & Park, Jin Suk, 2016. "The estimation of minimum efficient scale of the port industry," Transport Policy, Elsevier, vol. 49(C), pages 168-175.
    17. Alejandro Ramírez Vigoya, 2015. "Ajuste de una función de producción al sector financiero en Colombia," REVISTA FACULTAD DE CIENCIAS ECONÓMICAS, UNIVERSIDAD MILITAR NUEVA GRANADA, vol. 0(1), pages 141-156, June.
    18. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    19. Hang Keun Ryu, 2003. "Choice of representation system for economic analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 10(13), pages 863-866.

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