04s - 2011/3/3 Utility Functions 4 A preference relation...

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2011/3/3 1 4 Utility 2 Utility Functions A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function. Continuity means that small changes to a consumption bundle cause only small changes to the preference level. 3 Utility Functions A utility function U(x) represents a preference relation if and only if: x’ x” U(x’) > U(x”) x’ x” U(x’) < U(x”) x’ x” U(x’) = U(x”). ~ f p p 4 Utility Functions Utility is an ordinal (i.e. ordering) concept. E.g . if U(x) = 6 and U(y) = 2 then bundle x is strictly preferred to bundle y. But x is not preferred three times as much as is y.
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2011/3/3 2 5 Utility Functions & Indiff. Curves Consider the bundles (4,1), (2,3) and (2,2). Suppose (2,3) (4,1) (2,2). Assign to these bundles any numbers that preserve the preference ordering; e.g. U(2,3) = 6 > U(4,1) = U(2,2) = 4. Call these numbers utility levels. p 6 Utility Functions & Indiff. Curves An indifference curve contains equally preferred bundles. Equal preference same utility level. Therefore, all bundles in an indifference curve have the same utility level. 7 Utility Functions & Indiff. Curves So the bundles (4,1) and (2,2) are in the indiff. curve with utility level U   But the bundle (2,3) is in the indiff. curve with utility level U 6. On an indifference curve diagram, this preference information looks as follows: 8 Utility Functions & Indiff. Curves U 6 U 4 (2,3) (2,2) (4,1) x 1 x 2
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2011/3/3 3 9 Utility Functions & Indiff. Curves Another way to visualize this same information is to plot the utility level on a vertical axis. 10 U(2,3) = 6 U(2,2) = 4 U(4,1) = 4 Utility Functions & Indiff. Curves x 1 x 2 Utility 11
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This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Dee during the Spring '10 term at Andhra University.

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04s - 2011/3/3 Utility Functions 4 A preference relation...

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