Perfect Equilibrium with Incomplete Financial Markets: An Elementary Exposition

  • David Cass
Part of the International Economic Association Series book series (IEA)

Abstract

Value and Capital is a real masterpiece, clearly and forcefully demon strating the importance of treating time explicitly, and thus recognis ing that economic plans made today unavoidably depend on beliefs about potential opportunities available tomorrow. Hicks focused his analysis on price uncertainty, starting from the position that, even in the absence of more fundamental sources of uncertainty, there is no convincing rationale for assuming either that individuals’ future price expectations will be identical, or if they were, that individuals’ future plans (based on these expectations) will be coordinated. In other words, self-fulfilling expectations, or perfect foresight, or—in Hicks’s own term—perfect equilibrium is unlikely even under the best of circumstances. But then why not a full range of current markets for trading forward, obviating the need for individuals to guess the potential course of future prices? Because in fact there is also fundamental uncertainty in the economic environment. In Hicks’s own words:

Thirdly, even if price expectations are consistent, still people may foresee their own wants incorrectly, or make wrong estimates of the results of the technical processes of production….Generally, then, it is uncertainty of the future, and the desire to keep one’s hands free to meet that uncertainty, which limit the extent of forward trading under capitalism; the ultimate cause why the first two kinds of disequilibrium cannot be met more efficiently reduces itself to the unavoidable presence of the third and fourth kinds.1

Keywords

Dition Librium Rium Defend Allo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow, K. J. (1964) ‘The Role of Securities in the Optimal Allocation of Risk-Bearing,’ Review of Economic Studies, vol. 31, pp. 91–6.CrossRefGoogle Scholar
  2. Balasko, Y. and Cass, D. (1989) ‘The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets,’ Econometrica, vol. 57, pp. 135–62.CrossRefGoogle Scholar
  3. Cass, D. (1984) ‘Competitive Equilibrium with Incomplete Financial Mar kets,’ CARESS Working Paper, University of Pennsylvania.Google Scholar
  4. Cass, D. (1989) ‘Sunspots and Incomplete Financial Markets: The Leading Example,’ in G. Feiwel (ed.) The Economics of Imperfect Competition: Joan Robinson and Beyond, (London: Macmillan).Google Scholar
  5. Chae, S. (1988) ‘Existence of Competitive Equilibrium with Incomplete Markets,’ Journal of Economic Theory, vol. 44, pp. 179–88.CrossRefGoogle Scholar
  6. Debreu, G. (1959) Theory of Value (New York: Wiley), ch. 7.Google Scholar
  7. Diamond, P. (1967) ‘The Role of a Stock Market in a General Equilibrium Model with Technological Uncertainty,’ American Economic Review, vol. 57, pp. 759–76.Google Scholar
  8. Duffie, D. (1987) ‘Stochastic Equilibria with Incomplete Financial Markets,’ Journal of Economic Theory, vol. 41, pp. 405–16.CrossRefGoogle Scholar
  9. Duffie, D. and Shafer, W. (1985) ‘Equilibrium in Incomplete Markets: I. A Basic Model of Generic Existence,’ Journal of Mathematical Economics, vol. 14, pp. 285–300.CrossRefGoogle Scholar
  10. Duffie, D. and Shafer, W. (1986) ‘Equilibrium in Incomplete Markets: II. Generic Existence in Stochastic Economies,’ Journal of Mathematical Economics, vol. 15, pp. 199–216.CrossRefGoogle Scholar
  11. Duffie, D. and Shafer, W. (1987) ‘Equilibrium and the Role of the Firm in Incomplete Markets,’ working paper, Graduate School of Business, Stanford University.Google Scholar
  12. Geanakoplos, J., Magill, M., Quinzii, M. and Dreze, J. (1990) ‘Generic Inefficiency of Stock Market Equilibrium when Markets are Incomplete,’ Journal of Mathematical Economics, vol. 19, pp. 113–51.CrossRefGoogle Scholar
  13. Geanakoplos, J. and Mas-Colell, A. (1989) ‘Real Indeterminacy with Financial Assets,’ Journal of Economic Theory, vol. 47, pp. 22–38.CrossRefGoogle Scholar
  14. Geanakoplos, J. and Polemarchakis, H. (1986) ‘Existence, Regularity and Constrained Suboptimality of Competitive Allocations when the Asset Market is Incomplete,’ in W. P. Heller, R. M. Starr and D. A. Starrett (eds) Uncertainty, Information and Communication, Essays in Honor of Kenneth J. Arrow, Volume III (Cambridge: Cambridge University Press).Google Scholar
  15. Geanakoplos, J. and Shafer, W. (1990) ‘Solving Systems of Simultaneous Equations in Economics,’ Journal of Mathematical Economics, vol. 19, pp. 69–93.CrossRefGoogle Scholar
  16. Grossman, S. J. (1977) ‘A Characterization of the Optimality of Equilibrium in Incomplete Markets,’ Journal of Economic Theory, vol. 15, pp. 1–15.CrossRefGoogle Scholar
  17. Grossman, S. J. and Hart, O. (1979) ‘A Theory of Competitive Equilibrium in Stock Market Economies,’ Econometrica, vol. 47, pp. 293–330.CrossRefGoogle Scholar
  18. Hart, O. D. (1975) ‘On the Optimality of Equilibrium when the Market Structure is Incomplete,’ Journal of Economic Theory, vol. 11, pp. 418–43.CrossRefGoogle Scholar
  19. Hicks, J. R. (1946) Value and Capital (Oxford: Clarendon Press) (2nd edition).Google Scholar
  20. Hirsch, M. D., Magill, M. and Mas-Colell, A. (1990) ‘A Geometric Ap proach to a Class of Existence Problems,’ Journal of Mathematical Econ omics, vol. 19, pp. 95–106.CrossRefGoogle Scholar
  21. Husseini, S., Lasry, J. -M. and Magill, M. (1990) ‘Existence of Equilibrium with Incomplete Markets,’ Journal of Mathematical Economics, vol. 19, pp. 39–67.CrossRefGoogle Scholar
  22. Magill, M. J. P. and Shafer, W. J. (1990) ‘Characterization of Generically Complete Real Asset Structures,’ Journal of Mathematical Economics, vol. 19, pp. 167–94.CrossRefGoogle Scholar
  23. McManus, D. (1986) ‘Regular Options Equilibria,’ CARESS Working Paper, University of Pennsylvania.Google Scholar
  24. Polemarchakis, H. M. (1988) ‘Portfolio Choice, Exchange Rates and In determinacy,’ Journal of Economic Theory, vol. 46, pp. 414–21.CrossRefGoogle Scholar
  25. Polemarchakis, H. M. and Ku, B.-I. (1990) ‘Options and Equilibrium,’ Journal of Mathematical Economics, vol. 19, pp. 107–12.CrossRefGoogle Scholar
  26. Radner, R. (1972) ‘Existence of Equilibrium Plans, Prices and Price Expec tations in a Sequence of Markets,’ Econometrica, vol. 40, pp. 289–303.CrossRefGoogle Scholar
  27. Repullo, R. (1986) ‘On the Generic Existence of Radner Equilibria when there are as Many Securities as States of Nature,’ Economic Letters, vol. 21, pp. 101–5.CrossRefGoogle Scholar
  28. Stiglitz, J. E. (1982) ‘The Inefficiency of Stock Market Equilibrium,’ Review of Economic Studies, vol. 49, pp. 241–61.CrossRefGoogle Scholar
  29. Werner, J. (1985) ‘Equilibrium in Economies with Incomplete Financial Markets,’ Journal of Economic Theory, vol. 36, pp. 110–19.CrossRefGoogle Scholar
  30. Werner, J. (1986) ‘Asset Prices and Real Indeterminacy in Equilibrium with Financial Markets,’ working paper, University of Bonn.Google Scholar
  31. Werner, J. (1990) ‘Structure of Financial Markets and Real Indeterminacy of Equilibria,’ Journal of Mathematical Economics, vol. 19, pp. 217–232.CrossRefGoogle Scholar
  32. Younès, Y. (1986) ‘Competitive Equilibrium for Incomplete Market Struc tures,’ CARESS Working Paper, University of Pennsylvania.Google Scholar

Copyright information

© International Economic Association 1991

Authors and Affiliations

  • David Cass
    • 1
  1. 1.University of PennsylvaniaUSA

Personalised recommendations