Chapter Four Utility
Chapter Four Utility
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
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 xxx〈U(x)>ux) Xx U(x)<U(x”) x~x〈Ux)=Ux”)
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
Utility Functions Utility is an ordinal (i.e. ordering) concep[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 is always non-minus
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 is always non-minus
Utility functions Indiff. Curves Consider the bundles (4, 1),(2, 3 ) and (22) Suppose(2,3)x(4,1)~(22) Assign to these bundles any numbers that preserve the preference ordering; eg.U(2,3)=6>U(4,1)=U(2,2)=4. Call these numbers utility levels
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
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 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=4 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:
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:
Utility Functions Indiff Curves 2 (2,3)x(2,2)~(4,1) U≡6 2 4 X
Utility Functions & Indiff. Curves U 6 U 4 (2,3) (2,2) ~ (4,1) x1 x2 p
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 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 2 U≡6 U≡4 U≡2 2 4 X
Utility Functions & Indiff. Curves U 6 U 4 U 2 x1 x2
