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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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- Fall '10