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The geometry of global production and factor price equalisation

Author

Listed:
  • Ivar Ekeland

    (Canada Research Chair in Mathematical Economics - UBC - University of British Columbia)

  • Roger Guesnerie

    (CDF - Collège de France - CdF - Collège de France, PJSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a production economy where commodities are partitioned into irreproducible factors and reproducible goods, and the production technologies have constant returns to scale. We examine the geometry of the efficient frontier of the global production set and derive theorems of nonsubstitution type. We complement the geometric viewpoint by an algebraic characterization of the efficient frontier, that put emphasis on the "factors values" of goods. We analyse the connections between the prices of goods and the prices of factors. In particular, we show that if the number of goods is at least twice as large as the number of factors, then, generically, the prices of goods uniquely determine the prices of factors.

Suggested Citation

  • Ivar Ekeland & Roger Guesnerie, 2006. "The geometry of global production and factor price equalisation," PSE Working Papers halshs-00589105, HAL.
  • Handle: RePEc:hal:psewpa:halshs-00589105
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00589105
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    References listed on IDEAS

    as
    1. Kubler, F. & Chiappori, P. -A. & Ekeland, I. & Polemarchakis, H. M., 2002. "The Identification of Preferences from Equilibrium Prices under Uncertainty," Journal of Economic Theory, Elsevier, vol. 102(2), pages 403-420, February.
    2. Kevin H. O'Rourke & Jeffrey G. Williamson, 1999. "The Heckscher-Ohlin Model Between 1400 and 2000: When It Explained Factor Price Convergence, When It Did Not, and Why," NBER Working Papers 7411, National Bureau of Economic Research, Inc.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    5. Jones, Ronald W & Scheinkman, Jose A, 1977. "The Relevance of the Two-Sector Production Model in Trade Theory," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 909-935, October.
    6. Kehoe, Timothy J., 1982. "Regular production economies," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 147-176, September.
    7. Travis, William P, 1972. "Production, Trade, and Protection When There are Many Commodities and Two Factors," American Economic Review, American Economic Association, vol. 62(1), pages 87-106, March.
    8. Ethier, Wilfred J., 1984. "Higher dimensional issues in trade theory," Handbook of International Economics,in: R. W. Jones & P. B. Kenen (ed.), Handbook of International Economics, edition 1, volume 1, chapter 3, pages 131-184 Elsevier.
    9. Kehoe, Timothy J, 1983. "Regularity and Index Theory for Economies with Smooth Production Technologies," Econometrica, Econometric Society, vol. 51(4), pages 895-917, July.
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    11. Pierre-André Chiappori & Ivar Ekeland & Felix Kübler & Heracles M. Polemarchakis, 1999. "The Identification of Preferences from Equilibrium Prices," Working Papers hal-00598229, HAL.
    12. Neary, J Peter, 1985. "Two-by-Two International Trade Theory with Many Goods and Factors," Econometrica, Econometric Society, vol. 53(5), pages 1233-1247, September.
    13. Richard B. Freeman, 1995. "Are Your Wages Set in Beijing?," Journal of Economic Perspectives, American Economic Association, vol. 9(3), pages 15-32, Summer.
    14. Bidard, Christian, 1990. "An Algorithmic Theory of the Choice of Techniques," Econometrica, Econometric Society, vol. 58(4), pages 839-859, July.
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