Utility_course

# Utility_course - Chapter Four Utility Utility ย Central...

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

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