中级微观经济学讲义5－收入效应和替代效应（更新）.pdf

Chapter 5
INCOME AND SUBSTITUTION
EFFECTS
By
WALTER NICHOLSON
Slides prepared by
Linda Ghent (Eastern Illinois University)
Modified by
Huihua NIE (Renmin Unversity of China)
1
Logic
: Preference----convex set, utility
function, indifference curve
: Maximization---- indifference
curve and budget constraint, indirect utility
function and expenditure function
: Comparative statics----
income and price, Px ->X and Py ->X
2
Demand Functions
• The optimal levels of x1 ,x2 ,…,xn can be
expressed as functions of all prices and
income, which is Marshall demand
function
• Prices and income are exogenous
x1* = d1( p1, p2,…, pn, I)
x* = x(px ,py ,I) y* = y(px ,py ,I)
How about comparative statics?
3
Homogeneity
• If we were to double all prices and
income, the optimal quantities demanded
will not change
– the budget constraint is unchanged
0
xi* = t di( p1, p2 ,…,pn, I)= di( tp1, tp2,…, tpn, tI)
• Individual demand functions are
homogeneous of degree zero in all prices
and income
4
Homogeneity
• With a Cobb-Douglas utility function
utility = U(x,y) =
the demand functions are
t I
x*  y* 
ptx py
• Note that a doubling of both prices and
income would leave x* and y*
unaffected
5
Changes in Income
• An increase in income will cause the
budget constraint out in a parallel
fashion given prices don’t change
• Since px/ py does not change, the MRS
will stay constant as the worker moves
to higher levels of satisfaction
6
Increase in I