Rubinstein2005-page58 - k Given this special interpretation...

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October 21, 2005 12:18 master Sheet number 56 Page number 40 LECTURE 4 Consumer Preferences The Consumer’s World Up to this point we have dealt with the basic economic model of rational choice. In this lecture we will discuss a special case of the rational man paradigm: the consumer . A consumer is an economic agent who makes choices between available combinations of com- modities. As usual, we have a certain image in mind: a person goes to the marketplace with money in hand and comes back with a bundle of commodities. As before, we will begin with a discussion of consumer preferences and utility, and only then discuss consumer choice. Our Frst step is to move from an abstract treatment of the set X to a more detailed structure. We take X to be < K + ={ x = ( x 1 , ... , x K ) | for all k , x k 0 } . An element of X is called a bundle. A bundle x is interpreted as a com- bination of K commodities where x k is the quantity of commodity
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Unformatted text preview: k . Given this special interpretation of X , we impose some conditions on the preferences in addition to those assumed for preferences in general. The additional three conditions use the structure of the space X : monotonicity uses the orderings on the axis (the ability to compare bundles by the amount of any particular commodity); continuity uses the topological structure (the ability to talk about closeness); convexity uses the algebraic structure (the ability to speak of the sum of two bundles and the multiplication of a bundle by a scalar). Monotonicity Monotonicity is a property that gives commodities the meaning of “goods.” It is the condition that more is better. Increasing the amount of some commodities cannot hurt, and increasing the amount of all commodities is strictly desired. ±ormally,...
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