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The Cambridge capital controversies: contributions from the complex plane

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  • Michael Osborne
  • Ian Davidson

Abstract

This article takes a fresh look at reswitching. When two production techniques are compared, reswitching occurs when one technique is more viable than the other at a high interest rate, switches to being less viable at a lower rate, and reswitches to being more viable again at even lower rates. For some, reswitching undermines the foundations of neoclassical economics because it belies the idea of a monotonic relationship between relative capital values and factor price. The reswitching equation is an nth degree polynomial having n roots, implying the existence of n interest rates. Conventional analysis uses one interest rate but ignores the others. We argue that the others should not be ignored because all rates are determined simultaneously, and when one rate shifts, all rates shift. We demonstrate that the Samuelson reswitching model possesses a ‘dual’ expression containing every interest rate, the rates being compressed into a composite, interest-rate variable, thereby establishing a role for interest rates previously thought lacking in use and meaning. The relationship between this composite interest rate and capital value does not exhibit reswitching. The notion of a composite interest rate has implications for economics beyond reswitching.

Suggested Citation

  • Michael Osborne & Ian Davidson, 2016. "The Cambridge capital controversies: contributions from the complex plane," Review of Political Economy, Taylor & Francis Journals, vol. 28(2), pages 251-269, April.
  • Handle: RePEc:taf:revpoe:v:28:y:2016:i:2:p:251-269
    DOI: 10.1080/09538259.2015.1129751
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    References listed on IDEAS

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    1. 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.
    2. David Levhari & Paul A. Samuelson, 1966. "The Nonswitching Theorem is False," The Quarterly Journal of Economics, Oxford University Press, vol. 80(4), pages 518-519.
    3. Dorfman, Robert, 1981. "The Meaning of Internal Rates of Return," Journal of Finance, American Finance Association, vol. 36(5), pages 1011-1021, December.
    4. Zonghie Han & Bertram Schefold, 2006. "An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory," Cambridge Journal of Economics, Oxford University Press, vol. 30(5), pages 737-765, September.
    5. David Levhari, 1965. "A Nonsubstitution Theorem and Switching of Techniques," The Quarterly Journal of Economics, Oxford University Press, vol. 79(1), pages 98-105.
    6. Harcourt,G. C., 1972. "Some Cambridge Controversies in the Theory of Capital," Cambridge Books, Cambridge University Press, number 9780521096720.
    7. Michio Morishima, 1966. "Refutation of the Nonswitching Theorem," The Quarterly Journal of Economics, Oxford University Press, vol. 80(4), pages 520-525.
    8. N. Cachanosky & P. Lewin, 2014. "Roundaboutness is Not a Mysterious Concept: A Financial Application to Capital Theory," Review of Political Economy, Taylor & Francis Journals, vol. 26(4), pages 648-665, October.
    9. P. Garegnani, 1966. "Switching of Techniques," The Quarterly Journal of Economics, Oxford University Press, vol. 80(4), pages 554-567.
    10. Michael Bruno & Edwin Burmeister & Eytan Sheshinski, 1966. "The Nature and Implications of the Reswitching of Techniques," The Quarterly Journal of Economics, Oxford University Press, vol. 80(4), pages 526-553.
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    1. repec:taf:revpoe:v:29:y:2017:i:3:p:440-453 is not listed on IDEAS
    2. repec:jpe:journl:1477 is not listed on IDEAS

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