Abstract
Economies with infinitely many commodities fail to pass the standard equilibrium existence test with linear price systems. On the other hand, Peleg and Yaari [25], Aliprantis, Brown, and Burkinshaw [2], and Araujo and Monteiro [4] show that the existence of equilibrium in economies with infinitely many commodities is obtainable, under standard assumptions, with extended price systems (functions to the extended real line). All, however, assume that preferences are complete preorderings and satisfy some strict monotonicity assumption. We show that the same conclusion holds when preferences are neither monotone nor transitive. Our commodity spaces are L p , 1 ≤ p ≤ ∞, > and price systems are measurable functions. We also consider the space ca (S, J) (finite measures on (S, J) and extend the results to economies with commodity differentiation. Finally, we show that under the assumptions of Aliprantis, Brown, and Burkinshaw [2] their equilibrium extended price systems coincide with ours.
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Tourky, R. (1999). Remark on extended price equilibria. In: Alkan, A., Aliprantis, C.D., Yannelis, N.C. (eds) Current Trends in Economics. Studies in Economic Theory, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03750-8_29
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DOI: https://doi.org/10.1007/978-3-662-03750-8_29
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