IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/17436.html
   My bibliography  Save this paper

The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Conceptual Foundations

Author

Listed:
  • Bitros, George C.

Abstract

It is ascertained that the theorem of proportionality, which maintains that replacement investment is a constant proportion of the outstanding capital stock, has several fundamental shortcomings. It derives from a model founded on assumptions that are highly restrictive and unlikely to hold in reality. It is alien to the thinking of researchers in industrial organization and other neighboring fields to economics that treat the durability of capital goods as a choice variable. It ignores several thorny conceptual and methodological issues and, perhaps most important, it may have restrained seriously the progress towards developing models based on more realistic approaches of production. However, despite its shortcomings, the theorem continues to dominate mainstream capital theory, most probably because of: a) its simplicity, and b) the lack of a model that might yield a better theorem in terms of standard criteria, like explanatory and predictive power, simplicity, fruitfulness, etc. For this reason attention is drawn to recent research which shows that a model centered on the heterogeneous structure of capital and the useful lives of its components is both feasible and exceedingly rich in theoretical and empirical implications.

Suggested Citation

  • Bitros, George C., 2009. "The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Conceptual Foundations," MPRA Paper 17436, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17436
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/17436/1/MPRA_paper_17436.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chirinko, Robert S, 1993. "Business Fixed Investment Spending: Modeling Strategies, Empirical Results, and Policy Implications," Journal of Economic Literature, American Economic Association, vol. 31(4), pages 1875-1911, December.
    2. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    3. Barro, Robert J, 1972. "Monopoly and Contrived Depreciation," Journal of Political Economy, University of Chicago Press, vol. 80(3), pages 598-602, May-June.
    4. Malcomson, James M., 1975. "Replacement and the rental value of capital equipment subject to obsolescence," Journal of Economic Theory, Elsevier, vol. 10(1), pages 24-41, February.
    5. Dueker Michael & Fischer Andreas & Dittmar Robert, 2007. "Stochastic Capital Depreciation and the Co-movement of Hours and Productivity," The B.E. Journal of Macroeconomics, De Gruyter, vol. 6(3), pages 1-24, January.
    6. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-384, December.
    7. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
    8. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 70(1), pages 65-94.
    9. Omar Licandro & Luis A. Puch, 2000. "Capital Utilization, Maintenance Costs and the Business Cycle," Annals of Economics and Statistics, GENES, issue 58, pages 143-164.
    10. Collard, F. & Kollintzas, T., 1998. ""d" Along the Business Cycle," Athens University of Economics and Business 93, Athens University of Economics and Business, Department of International and European Economic Studies.
    11. Whelan, Karl, 2007. "Embodiment, productivity, and the age distribution of capital," Journal of Macroeconomics, Elsevier, vol. 29(4), pages 724-740, December.
    12. Nickell, Stephen, 1975. "A closer look at replacement investment," Journal of Economic Theory, Elsevier, vol. 10(1), pages 54-88, February.
    13. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    14. Kamien, Morton I & Schwartz, Nancy L, 1974. "Product Durability under Monopoly and Competition," Econometrica, Econometric Society, vol. 42(2), pages 289-301, March.
    15. Gerald L. Thompson, 1968. "Optimal Maintenance Policy and Sale Date of a Machine," Management Science, INFORMS, vol. 14(9), pages 543-550, May.
    16. Winston, Gordon C, 1974. "The Theory of Capital Utilization and Idleness," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1301-1320, December.
    17. Beatriz Rumbos & Leonardo Auernheimer, 2001. "Endogenous capital utilization in a neoclassical growth model," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 29(2), pages 121-134, June.
    18. Dale W. Jorgenson, 1966. "The Embodiment Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 74, pages 1-1.
    19. Edward Miller, 1990. "Can A Perpetual Inventory Capital Stock Be Used For Production Function Parameter Estimation?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 36(1), pages 67-82, March.
    20. Cooley, Thomas F. & Greenwood, Jeremy & Yorukoglu, Mehmet, 1997. "The replacement problem," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 457-499, December.
    21. S. K. Bhattacharyya, 1965. "Capital Longevity and Economic Growth," Review of Economic Studies, Oxford University Press, vol. 32(1), pages 39-46.
    22. Robert M. Solow, 1962. "Substitution and Fixed Proportions in the Theory of Capital," Review of Economic Studies, Oxford University Press, vol. 29(3), pages 207-218.
    23. Joan Robinson, 1959. "Some Problems Of Definition And Measurement Of Capital," Oxford Economic Papers, Oxford University Press, vol. 11(2), pages 157-160.
    24. Paul A. Samuelson, 1966. "A Summing Up," The Quarterly Journal of Economics, Oxford University Press, vol. 80(4), pages 568-583.
    25. Epstein, L. & Denny, M., 1980. "Endogenous capital utilization in a short-run production model : Theory and an empiral application," Journal of Econometrics, Elsevier, vol. 12(2), pages 189-207, February.
    26. Solow, Robert M, 1997. "Is There a Core of Usable Macroeconomics We Should All Believe In?," American Economic Review, American Economic Association, vol. 87(2), pages 230-232, May.
    27. Joan Robinson, 1953. "The Production Function and the Theory of Capital," Review of Economic Studies, Oxford University Press, vol. 21(2), pages 81-106.
    28. Ricardo J. Caballero & Mohamad L. Hammour, 1996. "On the Timing and Efficiency of Creative Destruction," The Quarterly Journal of Economics, Oxford University Press, vol. 111(3), pages 805-852.
    29. Omar Licandro & Luis A. Puch & J. Ramón Ruiz-Tamarit, 2001. "Optimal growth under endogenous depreciation, capital utilization and maintenance costs," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 543-559, September.
    30. McHugh, Richard & Lane, Julia, 1987. "The Age of Capital, the Age of Utilized Capital, and Tests of the Embodiment Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 362-367, May.
    31. Bitros, George C. & Flytzanis, Elias, 2009. "Utilization and maintenance in a model with scrapping," European Journal of Operational Research, Elsevier, vol. 194(2), pages 551-573, April.
    32. R. M. Solow & J. Tobin & C. C. Weizsäcker & M. Yaari, 1971. "Neoclassical Growth with Fixed Factor Proportions," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 9, pages 68-102, Palgrave Macmillan.
    33. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    34. Boucekkine, Raouf & Martinez, Blanca, 2003. "Replacement, adoption and economic dynamics: lessons from a canonical creative destruction model," Structural Change and Economic Dynamics, Elsevier, vol. 14(3), pages 339-359, September.
    35. Swan, Peter L, 1977. "Product Durability under Monopoly and Competition: Comment," Econometrica, Econometric Society, vol. 45(1), pages 229-235, January.
    36. Swan, Peter L, 1972. "Optimum Durability, Second-Hand Markets, and Planned Obsolescence," Journal of Political Economy, University of Chicago Press, vol. 80(3), pages 575-585, May-June.
    37. Caballero, Ricardo J & Hammour, Mohamad L, 1994. "The Cleansing Effect of Recessions," American Economic Review, American Economic Association, vol. 84(5), pages 1350-1368, December.
    38. Brown, Murray & Chang, Winston W, 1976. "Capital Aggregation in a General Equilibrium Model of Production," Econometrica, Econometric Society, vol. 44(6), pages 1179-1200, November.
    39. Bitros, George C. & Hritonenko, Natali & Yatsenko, Yuri, 2007. "Investment, replacement and scrapping in a vintage capital model with embodied technological change," MPRA Paper 3619, University Library of Munich, Germany.
    40. Chatterjee, Santanu, 2005. "Capital utilization, economic growth and convergence," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2093-2124, December.
    41. Gylfason, Thorvaldur & Zoega, Gylfi, 2001. "Obsolescence," CEPR Discussion Papers 2833, C.E.P.R. Discussion Papers.
    42. Giovanni Dosi & Giorgio Fagiolo & Andrea Roventini, 2006. "An Evolutionary Model of Endogenous Business Cycles," Computational Economics, Springer;Society for Computational Economics, vol. 27(1), pages 3-34, February.
    43. Joan Robinson, 1975. "The Unimportance of Reswitching," The Quarterly Journal of Economics, Oxford University Press, vol. 89(1), pages 32-39.
    44. Merrick, John Jr., 1984. "The anticipated real interest rate, capital utilization and the cyclical pattern of real wages," Journal of Monetary Economics, Elsevier, vol. 13(1), pages 17-30, January.
    45. Ambler, Steve & Paquet, Alain, 1994. "Stochastic Depreciation and the Business Cycle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(1), pages 101-116, February.
    46. Hiroshi Kinokuni, 1999. "Repair Market Structure, Product Durability, and Monopoly," Australian Economic Papers, Wiley Blackwell, vol. 38(4), pages 343-353, December.
    47. repec:adr:anecst:y:2000:i:58 is not listed on IDEAS
    48. Parks, Richard W, 1979. "Durability, Maintenance and the Price of Used Assets," Economic Inquiry, Western Economic Association International, vol. 17(2), pages 197-217, April.
    49. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    50. Jeremy Bulow, 1986. "An Economic Theory of Planned Obsolescence," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 729-749.
    51. Leonardo Auernheimer, 1986. "Variable Depreciation and Some of Its Implications," Canadian Journal of Economics, Canadian Economics Association, vol. 19(1), pages 99-113, February.
    52. Dale W. Jorgenson, 1974. "The Economic Theory of Replacement and Depreciation," Palgrave Macmillan Books, in: Willy Sellekaerts (ed.), Econometrics and Economic Theory, chapter 10, pages 189-221, Palgrave Macmillan.
    53. repec:adr:anecst:y:2000:i:58:p:05 is not listed on IDEAS
    54. Hulten, Charles R. & Wykoff, Frank C., 1981. "The estimation of economic depreciation using vintage asset prices : An application of the Box-Cox power transformation," Journal of Econometrics, Elsevier, vol. 15(3), pages 367-396, April.
    55. Greenwood, Jeremy & Hercowitz, Zvi & Huffman, Gregory W, 1988. "Investment, Capacity Utilization, and the Real Business Cycle," American Economic Review, American Economic Association, vol. 78(3), pages 402-417, June.
    56. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
    57. Richard Schmalensee, 1974. "Market Structure, Durability, and Maintenance Effort," Review of Economic Studies, Oxford University Press, vol. 41(2), pages 277-287.
    58. R. E. Hall, 1968. "Technical Change and Capital from the Point of View of the Dual," Review of Economic Studies, Oxford University Press, vol. 35(1), pages 35-46.
    59. Paul A. Samuelson, 1962. "Parable and Realism in Capital Theory: The Surrogate Production Function," Review of Economic Studies, Oxford University Press, vol. 29(3), pages 193-206.
    60. Kinokuni, Hiroshi, 1999. "Repair Market Structure, Product Durability, and Monopoly," Australian Economic Papers, Wiley Blackwell, vol. 38(4), pages 343-353, December.
    61. Dueker, Michael & Fischer, Andreas M, 2002. "Fixing Swiss Potholes: The Importance of Improvements," CEPR Discussion Papers 3159, C.E.P.R. Discussion Papers.
    62. repec:adr:anecst:y:2000:i:58:p:06 is not listed on IDEAS
    63. E. Kleiman & T. Ophir, 1966. "The Durability of Durable Goods," Review of Economic Studies, Oxford University Press, vol. 33(2), pages 165-178.
    64. Paul Zarembka, 1975. "Capital Heterogeneity, Aggregation, and the Two-Sector Model," The Quarterly Journal of Economics, Oxford University Press, vol. 89(1), pages 103-114.
    65. Michael Waldman, 1993. "A New Perspective on Planned Obsolescence," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 273-283.
    66. Mann, Duncan P., 1992. "Durable goods monopoly and maintenance," International Journal of Industrial Organization, Elsevier, vol. 10(1), pages 65-79, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bitros, George C., 2010. "The Puzzle of the Replacement Ratio in the Context of Renewal Theory," MPRA Paper 19871, University Library of Munich, Germany.
    2. Bitros, George C., 2009. "The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Applicability," MPRA Paper 17821, University Library of Munich, Germany.

    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. 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.
    2. Dimitrios Koumparoulis, 2011. "The Proportionality Hypothesis in Capital Theory: an Assessment of the Literature," EuroEconomica, Danubius University of Galati, issue 27, pages 27-39, February.
    3. Martial Dupaigne, 2007. "Les variations choisies de l'utilisation du capital : une revue des implications macroéconomiques," Revue d'économie politique, Dalloz, vol. 117(2), pages 161-196.
    4. Cagri Saglam & Vladimir M. Veliov, 2008. "Role of Endogenous Vintage Specific Depreciation in the Optimal Behavior of Firms," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(3), pages 381-410, September.
    5. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona School of Economics.
    6. Fabrice Collard & Omar Licandro, 2020. "The neoclassical model and the welfare costs of selection," Discussion Papers 2020/03, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    7. Raouf, BOUCEKKINE & Blanca, MARTINEZ & Cagri, SAGLAM, 2006. "Capital Maintenance Vs Technology Adopton under Embodied Technical Progress," Discussion Papers (ECON - Département des Sciences Economiques) 2006030, Université catholique de Louvain, Département des Sciences Economiques.
    8. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    9. Adriano A. Rampini, 2019. "Financing Durable Assets," American Economic Review, American Economic Association, vol. 109(2), pages 664-701, February.
    10. Gregory E. Goering, 2007. "Durable‐Goods Monopoly With Maintenance," Bulletin of Economic Research, Wiley Blackwell, vol. 59(3), pages 231-246, July.
    11. Eleni Angelopoulou & Sarantis Kalyvitis, 2012. "Estimating the Euler Equation for Aggregate Investment with Endogenous Capital Depreciation," Southern Economic Journal, John Wiley & Sons, vol. 78(3), pages 1057-1078, January.
    12. Raouf BOUCEKKINE & Aude POMMERET, 2000. "Optimal Capital Accumulation, Energy Cost and the Nature of Technological Progress," LIDAM Discussion Papers IRES 2001023, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. Gamboa, Franklin & Maldonado, Wilfredo Leiva, 2014. "Feasibility and optimality of the initial capital stock in the Ramsey vintage capital model," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 40-45.
    14. Julián David Parada, 2008. "Tasa de depreciación endógena y crecimiento económico," Documentos de Trabajo 004594, Universidad del Rosario.
    15. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    16. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Journal of Economic Theory, Elsevier, vol. 88(1), pages 161-187, September.
    17. Bitros, George C. & Flytzanis, Elias, 2009. "Utilization and maintenance in a model with scrapping," European Journal of Operational Research, Elsevier, vol. 194(2), pages 551-573, April.
    18. Motamedi, N. & Reza Peyghami, M. & Hadizadeh, M., 2013. "A mixed integer nonlinear programming model for the optimal repair–replacement in the firm," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 366-371.
    19. Boucekkine, Raouf & Hritonenko, Natali & Yatsenko, Yuri, 2011. "Scarcity, regulation and endogenous technical progress," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 186-199, March.
    20. Hritonenko, Natali & Yatsenko, Yuri, 2010. "Technological innovations, economic renovation, and anticipation effects," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1064-1078, November.

    More about this item

    Keywords

    Capital longevity; replacement; depreciation; scrappage; maintenance; utilization; obsolescence.;
    All these keywords.

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

    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:17436. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.