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Заменимость И Дополнительность Товаров В Терминах Функций Полезности

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  • Данилов В.И.

Abstract

В работе рассматривается задача характеризации функций полезности, порождающих валово-заменимый спрос. Пусть f - вогнутая функция полезности некоторого потребителя, выраженная в денежной форме. Это значит, что его спрос при цене p формируется как задача максимизации чистой полезности f(x)?p(x). Такая функция называется ВЗ-функцией, если увеличение цены любого товара приводит к повышению спроса на оставшиеся товары. В работе доказано, что f является ВЗ-функцией тогда и только тогда: когда двойственная по Фенхелю функция f* супермодулярна. Как следствие устанавливается субмодулярность любой ВЗ-функции. В работе устанавливается также правило вычисления производной для свертки нескольких вогнутых функций.

Suggested Citation

  • Данилов В.И., 2015. "Заменимость И Дополнительность Товаров В Терминах Функций Полезности," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 51(4), pages 25-36, октябрь.
    • Handle: RePEc:scn:cememm:v:51:y:2015:i:4:p:25-36
    Note: Москва
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    References listed on IDEAS

    as
    1. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
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