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Economic Generality Versus Mathematical Genericity: Activity‐Level Indeterminacy And The Index Theorem In Constant Returns Production Economies

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  • Saverio M. Fratini

Abstract

When the mathematical concept of genericity was arrived at in economics, it was meant more or less as a synonym for generality. Referring to constant return production economies, we will argue that this is not always the case. In particular, the representation of technology that is mathematically generic is not at all general for economists. We will see that in cases that are economically general, but not mathematically generic, activity‐level indeterminacy may occur. In these cases, Kehoe's index theorem, a well‐known result of the application of the differentiable approach to production economies, becomes unusable.

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  • Saverio M. Fratini, 2008. "Economic Generality Versus Mathematical Genericity: Activity‐Level Indeterminacy And The Index Theorem In Constant Returns Production Economies," Metroeconomica, Wiley Blackwell, vol. 59(2), pages 266-275, May.
    • Handle: RePEc:bla:metroe:v:59:y:2008:i:2:p:266-275
    DOI: 10.1111/j.1467-999X.2007.00305.x
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    1. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
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    3. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-287, May.
    4. Kehoe, Timothy J., 1982. "Regular production economies," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 147-176, September.
    5. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(1), pages 119-147.
    6. Varian, Hal R, 1975. "A Third Remark on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 43(5-6), pages 985-986, Sept.-Nov.
    7. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-953, September.
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    Cited by:

    1. Saverio M. Fratini, 2019. "On The Second Stage Of The Cambridge Capital Controversy," Journal of Economic Surveys, Wiley Blackwell, vol. 33(4), pages 1073-1093, September.
    2. Fratini, Saverio M. & Levrero, Enrico Sergio, 2009. "A remark on the supposed equivalence between complete markets and perfect foresight hypothesis," MPRA Paper 15988, University Library of Munich, Germany.
    3. Fabio Petri, 2009. "On the Recent Debate on Capital Theory and General Equilibrium," Department of Economics University of Siena 568, Department of Economics, University of Siena.

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