consumer could conceivably consume. The consumer's utility function ranks each package in the consumption set. If the consumer strictly prefers x to y or is indifferent between them, then . For example, suppose a consumer's consumption set is X = {nothing, 1 apple,1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}, and his utility function is u(nothing) = 0, u(1 apple) = 1, u(1 orange) = 2, u(1 apple and 1 orange) = 5, u(2 apples) = 2 and u(2 oranges) = 4. Then this consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges. In micro-economic models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives a consumption set of , and each package is a vector containing the amounts of each commodity. For the example, there are two commodities: apples and oranges. If we say apples is the first commodity, and oranges the second, then the consumption set is and u(0, 0) = 0, u(1, 0) = 1, u(0, 1) = 2, u(1, 1) = 5, u(2, 0) = 2, u(0, 2) = 4 as before. Note that for u to be a utility function on X, however, it must be defined for every package in X, so now the function needs to be defined for fractional apples and oranges too. One function that would fit these numbers is Preferences have three main properties: Completeness Assume an individual has two choices, A and B. By ranking the two choices, one and only one of the following relationships is true: an individual strictly prefers A (A>B); an individual strictly prefers B (B>A); an individual is indifferent between A and B (A=B). Either a ≥ b OR b ≥ a (OR both) for all (a,b) Transitivity Individuals’ preferences are consistent over bundles. If an individual prefers bundle A to bundle B, and prefers bundle B to bundle C, then it can be assumed that the individual prefers bundle A to bundle C. (If a ≥ b and b ≥ c, then a ≥ c for all (a,b,c)). Non-Satiation (Monotone Preferences) All else being constant, individuals always prefer more of positive goods rather than negative goods, vice versa. In terms of the indifferent curves, individuals will always prefer bundles that are on a higher indifference curve. In other words, all else