IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/5254.html
   My bibliography  Save this paper

A Brief History of Production Functions

Author

Abstract

This paper gives an outline of evolution of the concept and econometrics of production function, which was one of the central apparatus of neo-classical economics. It shows how the famous Cobb-Douglas production function was indeed invented by von Thunen and Wicksell, how the CES production function was formulated, how the elasticity of substitution was made a variable and finally how Sato’s function incorporated biased technical changes. It covers almost all specifications proposed during 1950-1975, and further the LINEX production functions and incorporation of energy as an input. The paper in divided into (1) single product functions, (2) joint product functions, and (3) aggregate production functions. It also discusses the ‘capital controversy’ and its impacts.

Suggested Citation

  • Mishra, SK, 2007. "A Brief History of Production Functions," MPRA Paper 5254, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:5254
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/5254/1/MPRA_paper_5254.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. SK Mishra, 2007. "Estimation of Zellner-Revankar Production Function Revisited," Economics Bulletin, AccessEcon, vol. 3(14), pages 1-7.
    2. Richard E. Just & David Zilberman & Eithan Hochman, 1983. "Estimation of Multicrop Production Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 65(4), pages 770-780.
    3. Gronau, Reuben, 1977. "Leisure, Home Production, and Work-The Theory of the Allocation of Time Revisited," Journal of Political Economy, University of Chicago Press, vol. 85(6), pages 1099-1123, December.
    4. Sudhanshu Mishra, 2007. "Least squares estimation of joint production functions by the differential evolution method of global optimization," Economics Bulletin, AccessEcon, vol. 3(51), pages 1-13.
    5. Joan Robinson, 1953. "The Production Function and the Theory of Capital," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 21(2), pages 81-106.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
    8. Berndt, Ernst R & Wood, David O, 1979. "Engineering and Econometric Interpretations of Energy-Capital Complementarity," American Economic Review, American Economic Association, vol. 69(3), pages 342-354, June.
    9. Sato, Ryuzo, 1975. "The Most General Class of CES Functions," Econometrica, Econometric Society, vol. 43(5-6), pages 999-1003, Sept.-Nov.
    10. Shaikh, Anwar, 1974. "Laws of Production and Laws of Algebra: The Humbug Production Function," The Review of Economics and Statistics, MIT Press, vol. 56(1), pages 115-120, February.
    11. David Levhari & Paul A. Samuelson, 1966. "The Nonswitching Theorem is False," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(4), pages 518-519.
    12. Chetty, V Karuppan, 1969. "Econometrics of Joint Production: A Comment," Econometrica, Econometric Society, vol. 37(4), pages 731-731, October.
    13. Wibe, Soren A, 1984. "Engineering Production Functions: A Survey," Economica, London School of Economics and Political Science, vol. 51(204), pages 401-411, November.
    14. Hollis B. Chenery, 1949. "Engineering Production Functions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 63(4), pages 507-531.
    15. Graham, John W & Green, Carole A, 1984. "Estimating the Parameters of a Household Production Function with Joint Products," The Review of Economics and Statistics, MIT Press, vol. 66(2), pages 277-282, May.
    16. Chizmar, John F & Zak, Thomas A, 1983. "Modeling Multiple Outputs in Educational Production Functions," American Economic Review, American Economic Association, vol. 73(2), pages 17-22, May.
    17. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    18. Vinod, H. D., 1976. "Canonical ridge and econometrics of joint production," Journal of Econometrics, Elsevier, vol. 4(2), pages 147-166, May.
    19. Dietmar Lindenberger, 2003. "Service Production Functions," Journal of Economics, Springer, vol. 80(2), pages 127-142, October.
    20. Koopmans, Tjalling C, 1979. "Economics among the Sciences," American Economic Review, American Economic Association, vol. 69(1), pages 1-13, March.
    21. Kümmel, Reiner, 1982. "The impact of energy on industrial growth," Energy, Elsevier, vol. 7(2), pages 189-203.
    22. Stiglitz, Joseph E, 1974. "The Cambridge-Cambridge Controversy in the Theory of Capital: A View from New Haven: A Review Article," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 893-903, July/Aug..
    23. Yair Mundlak & Assaf Razin, 1971. "On Multistage Multiproduct Production Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(3), pages 491-499.
    24. Kurz,Heinz D. (ed.), 2000. "Critical Essays on Piero Sraffa's Legacy in Economics," Cambridge Books, Cambridge University Press, number 9780521580892.
    25. Pollak, Robert A & Wachter, Michael L, 1975. "The Relevance of the Household Production Function and Its Implications for the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 255-277, April.
    26. Paul A. Samuelson, 1962. "Parable and Realism in Capital Theory: The Surrogate Production Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(3), pages 193-206.
    27. Samuelson, Paul A, 1979. "Paul Douglas's Measurement of Production Functions and Marginal Productivities," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 923-939, October.
    28. George J. Stigler, 1952. "The Ricardian Theory of Value and Distribution," Journal of Political Economy, University of Chicago Press, vol. 60(3), pages 187-187.
    29. Lloyd, Peter J, 1969. "Elementary Geometric/Arithmetic Series and Early Production Theory," Journal of Political Economy, University of Chicago Press, vol. 77(1), pages 21-34, Jan./Feb..
    30. Rao, Potluri, 1969. "A Note on Econometrics of Joint Production," Econometrica, Econometric Society, vol. 37(4), pages 737-738, October.
    31. Harris, Donald J, 1973. "Capital, Distribution, and the Aggregate Production Function," American Economic Review, American Economic Association, vol. 63(1), pages 100-113, March.
    32. Mishra, SK, 2007. "Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves," MPRA Paper 4634, University Library of Munich, Germany.
    33. Avi J. Cohen, 2003. "Retrospectives: Whatever Happened to the Cambridge Capital Theory Controversies?," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 199-214, Winter.
    34. Fare, Rolf, 1986. " On the Existence and Equivalence of Three Joint Production Functions," Scandinavian Journal of Economics, Wiley Blackwell, vol. 88(4), pages 669-674.
    35. Vinod, Hrishikesh D, 1969. "Econometrics of Joint Production-A Reply," Econometrica, Econometric Society, vol. 37(4), pages 739-740, October.
    36. Harcourt,G. C., 1972. "Some Cambridge Controversies in the Theory of Capital," Cambridge Books, Cambridge University Press, number 9780521096720.
    37. Dhrymes, Phoebus J & Mitchell, B M, 1969. "Estimation of Joint Production Functions," Econometrica, Econometric Society, vol. 37(4), pages 732-736, October.
    38. A. Cohen & G. Harcourt., 2009. "Whatever Happened to the Cambridge Capital Theory Controversies?," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 8.
    39. Revankar, Nagesh S, 1971. "A Class of Variable Elasticity of Substitution Production Functions," Econometrica, Econometric Society, vol. 39(1), pages 61-71, January.
    40. Mishra, SK, 2006. "A Note on Numerical Estimation of Sato’s Two-Level CES Production Function," MPRA Paper 1019, University Library of Munich, Germany, revised 02 Dec 2006.
    41. repec:ebl:ecbull:v:3:y:2007:i:51:p:1-13 is not listed on IDEAS
    42. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(2), pages 201-218.
    43. Salvadori, Neri & Steedman, Ian, 1988. "Joint Production Analysis in a Sraffian Framework," Bulletin of Economic Research, Wiley Blackwell, vol. 40(3), pages 165-195, June.
    44. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7.
    45. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    46. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 291-299.
    47. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    48. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    49. Robert D. Weaver, 1983. "Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 65(1), pages 45-56.
    50. Sato, Ryuzo, 1970. "The Estimation of Biased Technical Progress and the Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(2), pages 179-208, June.
    51. Yair Mundlak, 1963. "Specification and Estimation of Multiproduct Production Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 45(2), pages 433-443.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudhanshu Mishra, 2007. "Least squares estimation of joint production functions by the differential evolution method of global optimization," Economics Bulletin, AccessEcon, vol. 3(51), pages 1-13.
    2. repec:ebl:ecbull:v:3:y:2007:i:51:p:1-13 is not listed on IDEAS
    3. Carlo Milana, 2019. "Solving the Reswitching Paradox in the Sraffian Theory of Capital," Applied Economics and Finance, Redfame publishing, vol. 6(6), pages 97-125, November.
    4. repec:hal:spmain:info:hdl:2441/62drs526639gbqbrni9v9kvsv5 is not listed on IDEAS
    5. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," Sciences Po publications info:hdl:2441/62drs526639, Sciences Po.
    6. Dennis O. Kundisch & Neeraj Mittal & Barrie R. Nault, 2014. "Research Commentary —Using Income Accounting as the Theoretical Basis for Measuring IT Productivity," Information Systems Research, INFORMS, vol. 25(3), pages 449-467, September.
    7. Nadia Garbellini, 2018. "Inequality in the 21st Century:A Critical Analysis of Piketty`s Work," Working Papers Series 69, Institute for New Economic Thinking.
    8. Jesus Felipe & John S.L. McCombie, 2013. "The Aggregate Production Function and the Measurement of Technical Change," Books, Edward Elgar Publishing, number 1975.
    9. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," Post-Print hal-03403639, HAL.
    10. Frédéric Reynès, 2017. "The Cobb-Douglas function as a flexible function. Analysing the substitution between capital, labor and energy," Documents de Travail de l'OFCE 2017-12, Observatoire Francais des Conjonctures Economiques (OFCE).
    11. Frédéric Reynès, 2011. "The cobb-douglas function as an approximation of other functions," Working Papers hal-01069515, HAL.
    12. repec:hal:spmain:info:hdl:2441/1cpd872l2j8lb968d53pu5f30q is not listed on IDEAS
    13. Jesus Felipe & F. Gerard Adams, 2005. ""A Theory of Production" The Estimation of the Cobb-Douglas Function: A Retrospective View," Eastern Economic Journal, Eastern Economic Association, vol. 31(3), pages 427-445, Summer.
    14. Frédéric Reynés, 2017. "The Cobb-Douglas function as a flexible function," Working Papers hal-03582829, HAL.
    15. G. C. Harcourt, 2015. "On the Cambridge, England, Critique of the Marginal Productivity Theory of Distribution," Review of Radical Political Economics, Union for Radical Political Economics, vol. 47(2), pages 243-255, June.
    16. George Bitros, 2010. "The theorem of proportionality in contemporary capital theory: An assessment of its conceptual foundations," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(4), pages 367-401, December.
    17. Frédéric Reynés, 2019. "The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities," SciencePo Working papers Main hal-03403639, HAL.
    18. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    19. Reynès, Frédéric, 2019. "The Cobb–Douglas function as a flexible function," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 11-17.
    20. Pillai N., Vijayamohanan & AM, Narayanan, 2019. "Energy Efficiency: A Sectoral Analysis for Kerala," MPRA Paper 101424, University Library of Munich, Germany.
    21. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    22. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09i29kgilc0 is not listed on IDEAS
    23. Frédéric Reynès, 2011. "The cobb-douglas function as an approximation of other functions," SciencePo Working papers Main hal-01069515, HAL.
    24. Harvey Gram & Geoffrey Harcourt, 2015. "Joan Robinson and MIT," Working Papers 9, City University of New York Graduate Center, Ph.D. Program in Economics.
    25. Yara Zeineddine, 2021. "Institutional Aspects of Capital in Joan Robinson's 'Rules of the Game': Rentier versus Entrepreneurs in Managerial Capitalism," Working Papers hal-03230146, HAL.
    26. Luigi L. Pasinetti, 2000. "Critique of the neoclassical theory of growth and distribution," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 53(215), pages 383-431.

    More about this item

    Keywords

    Production function; Cobb-Douglas; CES; Transcendental; translog; Zellner-Revankar; VES; Bruno; Kadiyala; Diewert; Kummel; Mundlak; Engineering production function; Multi-output; joint product; Data Envelopment; Household production function; Humbug production function; capital controversy; Cambridge controversy;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • B13 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Neoclassical through 1925 (Austrian, Marshallian, Walrasian, Wicksellian)

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:5254. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.