Linear exchange economies with a continuum of agents
The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called "regular" endowment where it is known.
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Volume (Year): 3 (2001)
Issue (Month): 4 ()
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- Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
- Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
- Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
- Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
- Bonnisseau, J.M. & Joffre, A., 1994. "Equilibrium Manifold for Linear Exchange Economies," Papiers d'Economie MathÃ©matique et Applications 94.87, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Dierker, Hildegard, 1975. "Equilibria and core of large economies," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 155-169.
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