utility - Preferences and Utility Preference Relations x r...

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Unformatted text preview: Preferences and Utility Preference Relations x r y likes Bundle x at least as much as Bundle y (weakly prefers) x r y strictly prefers x to y : weakly prefers x to y , but does not weakly prefer y to x x ~ y indifferent between x and y : weakly prefers x to y and weakly prefers y to x ( x r y and y r x ) Assumptions three assumptions about the properties of consumers preferences: completeness , transitivity , and more is better . Completeness consumers can rank all bundles for any two bundles x and y , the consumer either x r y or y r x Note: reflexivity : Any bundle x is always at least as preferred as itself: x r x Transitivity If x is at least as preferred as y , and y is at least as preferred as z , then x is at least as preferred as z : x r y and y r z x r z More is Better ( nonsatiation or monotonicity ) all else the same, more of a good is better than less of it a good is a commodity for which more is preferred to less, at least at some levels of consumption. a bad is something for which less is preferred to more, such as pollution Why We Believe More-Is-Better Holds appears to be true for most people if consumers can freely dispose of excess goods, consumers can be no worse off with extra goods we observe consumers buying goods only when this condition is met Preference Maps Indifference Curve Properties bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin there is an indifference curve through every possible bundle indifference curves cannot cross indifference curves slope downward indifference curves cannot be thick Application: Income Buys Happiness Do people become satiated? Using data from 131 countries, Stevenson and Wolfers (2008) find a strong positive relationship between average levels of self-reported feelings of happiness and income per capita within and across countries They find no evidence of a satiation point wealthy U.S. citizens were asked, How much wealth do you need to live comfortably? Those with a net worth of over $1 million said that they needed $2.4 million to live comfortably, those with at least $5 million needed $10.4 million, those with at least $10 million needed $18.1 million Question What would indifference curves look like if people become satiated (didnt want more goods)? Utility Functions relationship between utility measures and every possible bundle of goods a utility function U ( x ) represents a preference relation r if and only if: x y y U ( x ) > U ( y ) x y y U ( x ) < U ( y ) x ~ y U ( x ) = U ( y )....
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utility - Preferences and Utility Preference Relations x r...

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