Utility_course - Chapter Four Utility Utility Central...

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Unformatted text preview: Chapter Four Utility Utility Central concept in economics. Idea is to measure happiness or satisfaction Traced back to utilitarianism Neo-classical interpretation Preferences - A Reminder x y: x is strictly preferred to y. x y: x and y are equally preferred. x y: x is preferred to y. p ~ f Utility Functions Utility functions are numerical functions by which we represent preferences. A function U(x) represents a preference relation if and only if: x x U(x) >= U(x) ~ f ~ f Utility Function A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function . Continuity means that small changes in the bundles lead to small changes in the preference level. Utility Functions Utility is an ordinal (i.e. ordering) concept. Example: 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 . Utility Functions & Indiff. Curves Consider the bundles (4,1), (2,3) and (2,2). Suppose (2,3) (4,1) (2,2). Say U(2,3) = 6 > U(4,1) = U(2,2) = 4. Call these numbers utility levels . p Utility Functions & Indiff. Curves An indifference curve contains all equally preferred bundles. Therefore, an indifference curve contains all the bundles that have the same utility level. Utility Functions & Indiff. Curves So the bundles (4,1) and (2,2) are in the indiff. curve with utility level U 4 But the bundle (2,3) is in the indiff. curve with utility level U 6. On an indifference curve diagram, it looks as follows: Utility Functions & Indiff. Curves U 6 U 4 (2,3) (2,2) (4,1) x 1 x 2 p Utility Functions & Indiff. Curves Another way to visualize this same information is to plot the utility level on a vertical axis....
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Utility_course - Chapter Four Utility Utility Central...

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