[北大微观经济学课件]ch4 Utility.ppt

Chapter Four Utility 效用 Structure Utility function (效用函数） Definition Monotonic transformation （单调转换） Examples of utility functions and their indifference curves Marginal utility （边际效用） Marginal rate of substitution 边际替代率 MRS after monotonic transformation 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”). Utility Functions Utility is an ordinal (i.e. ordering) concept. [序数效用] 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. 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. 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. Utility Functions Indiff. Curves So the bundles (4,1) and (2,2) are in the indiff. curve with utility level U o 4 But the bundle (2,3) is in the indiff. curve with utility level U o 6. On an indifference curve diagram, this preference information looks as follows: Utility Functions Indiff. Curves Utility Functions Indiff. Curves Comparing more bundles will create a larger collection of all indifference curves and a better description of the consumer’s preferences. Utility Functions Indiff. Curves Utility Functions Indiff. Curves The collection of all indifference curves for a given preference relation is an indifference map. An indifference map is equivalent to a utility function; each is the other. Utility Functions There is no unique utility function representation of a preference relation. Suppose U(x1,x2) =