When we say that individual x has utility function u

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When we say that individual X has utility function u( ) all we are saying is that this individual's u(.) –all we are saying is that this individual s preferences can be represented by function u(.) Saying that bundle A gives 10 units of utility does not have any significance, except if we also know that bundle B is worth 12 (8) units of utility. Then it implies that bundle A is worse (better) than B. Utility Ordinal Utility Function Places market baskets in the order of most preferred to least preferred, but it does not indicate how much one market basket is preferred to another If we take utility function u(.) and transform it using an increasing function f() into function v(x,y,z)=f(u(x,y,z)) then v(.)and u(.) are equivalent, i.e. reflect the same preferences. Utility Function If I am always indifferent between 1 can of Coke and 1 coke Pepsi, then my preferences for Coke and Pepsi can be represented by a utility function u(C,P)=C+P where C and P are the numbers of cans of Coke and Pepsi that I consume. But these preferences are also represented by utility function u(C,P)=5C+5P, but not by a utility function u(C,P)=2C+6P. Ordinal Utility Although we numerically rank baskets and indifference curves, numbers are ONLY for ranking A utility of 4 is not necessarily twice as good as a utility of 2 If buying 1 pair of tennis sneakers makes you happier than buying 2 shirts, then we say that the sneakers give you more utility than 2 shirts Indifference Curves and Utility Function An Indifference curve at level u is a collection of all such points (x 1 ,..,x n ) that satisfy u(x 1 ,..,x n )=u. This gives an easy way to draw indifference curves. • Take any points (x x ) and (y y ) s t Take any points (x 1 ,..,x n ) and (y 1 ,..,y n ) s.t. individual i likes the first of them better than the second. Then: (x 1 ,..,x n ) is on a higher indifference curve than (y 1 ,..,y n ) and u(x 1 ,..,x n ) > u(y 1 ,..,y n )
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