文档介绍：Advanced Economics (lecture 5: consumption theory II)
Ye Jianliang
CONTENT
WA and demand law
From preferences to utility
Utility maximization
Expenditure minimization
and demand law
Walrasian demand function x(p,w) satisfied WA if for any we have:
See the fig.
and demand law
Changing in price will change wealth too. But how can we tell the demand changing by price changing from wealth changing?
Given a changing from ,and people will not get worse that is
here wealth changing (compensation )
was called “Slutsky pensation” and “(Slutsky) compensated price changing”.
and demand law
Proposition5: x(p,w) satisfied WA if and only if: and when
,
indicates, , or that’s called “demand law ”, or “compensation demand law ”.
and demand law
Slutsky matrix (substitution matrix)
Substitution effects
is
Giffen good is necessary inferior good.
preferences to utility
Definition: is a utility function of preference , if
Can we always find a utility function of ?
Maybe
If X is finite, there always exist utility function.
Proposition1: only rational can be represented by a utility function. ( not )
Lexicographic preference: rational but no utility function exist.
preferences to utility
Continuity:
then ,or x upper contour sets
and lower contour sets are closure.
Proposition2:If is continuous, then exist a continuous utility function representing .
preferences to utility
Desirability: preference is desirable if
is monotone:
is local non-satiation: there is a
proposition3: is strong monotone, then it’s monotone; is monotone, it’s local non-satiation.
preferences to utility
Convexity: x upper contour sets are convex.
Decreasing in marginal rate of substitution.
people like variety.
Preferences are convex means utility function is quasi-concave.