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A note on the Drèze’s criterion for large capitalist firms


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  • Jean-Marc Bonnisseau


  • Oussama Lachiri



The paper extends the Drèze's Criterion [Investment under private ownership : optimality, equilibrium and stability, in «Allocation under Uncertainty ; Equilibrium and Optimality», Wiley, New York, 1974, p.129] for firms to non-smooth and non-convex technologies and to non-ordered preferences for the consumers. Technically, the proofs follow the lines of Guesnerie [Pareto Optimality in Non-convex Economies, in Econometrica, 43, p. 1-31, (1975)]. Using recent tools of non-smooth analysis, we exhibit the first-order-necessary conditions for constrained Pareto optimal allocations. The Drèze's criterion for firms is recovered, but the profit maximization is replaced by a first-order- necessary condition for optimality, together with other relations between state prices and consumptions. A new stock-market equilibrium is formalized. We show that stock holders buy nothing but stocks of a firm that maximize his expected profit with respect to his own shadow price.

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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04120.

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Length: 19 pages
Date of creation: Jan 2004
Date of revision:
Handle: RePEc:mse:wpsorb:b04120

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Keywords: Stock market; non-smooth analysis; present value; market value.;

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  1. Dierker, E. & Dierker, H. & Grodal, B., 1999. "Incomplete Markets and the Firm," Papers 9902, Washington St. Louis - School of Business and Political Economy.
  2. Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., . "Generic inefficiency of stock market equilibrium when markets are incomplete," CORE Discussion Papers RP -916, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Cornet, B., 1986. "The second welfare theorem in nonconvex economies," CORE Discussion Papers 1986030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Grossman, Sanford J & Hart, Oliver D, 1979. "A Theory of Competitive Equilibrium in Stock Market Economies," Econometrica, Econometric Society, vol. 47(2), pages 293-329, March.
  5. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
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