Stochastic inequalities based on Cobb-Douglas utility functions

摘要

Consumer theory studies how individuals make choices given the prices of goods, budgetconstraints and their preferences. The preferences of a consumer are represented by a utilitymeasure. One of the most important examples of utility mappings is given by the Cobb-Douglasfunctions. Frequently the quantities of goods involved in the selection problem are random insteadof deterministic. Motivated by the need to compare the preferences and investments of aconsumer when the quantities of goods are random and the utility belongs to the Cobb-Douglasfamily, a new stochastic order is introduced. The order is analyzed in detail, providing characterizations,conditions which lead to the order and properties derived from the order. Specialemphasis is placed on the antisymmetric property of the new ordering. The proposed stochasticorder weakens the concave order.