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

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Author Info
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)

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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.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 13 (1998)
Issue (Month): 2 ()
Pages: 101-127
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Handle: RePEc:jae:japmet:v:13:y:1998:i:2:p:101-127

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  1. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Estimation of Homothetic and Homothetically Separable Functions," STICERD - Econometrics Paper Series /2003/461, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  2. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Boston College Working Papers in Economics 585, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
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  3. 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. [Downloadable!]
  4. Hang Keun Ryu, 2003. "Choice of representation system for economic analysis," Applied Economics Letters, Taylor and Francis Journals, vol. 10(13), pages 863-866, October. [Downloadable!] (restricted)
  5. Gad Allon & Michael Beenstock & Steven Hackman & Ury Passy & Alex Shapiro, 2005. "Nonparametric estimation of concave production technologies by entropic methods," Econometrics 0512003, EconWPA. [Downloadable!]
  6. William E. Griffiths & Christopher J. O’Donnell, 2003. "Estimating Variable Returns to Scale Production Frontiers with Alternative Stochastic Assumptions," Department of Economics - Working Papers Series 872, The University of Melbourne. [Downloadable!]
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