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Demand
Consumer Demand
Consumer’s demand functions:
mppxx ,, 2111
mppxx ,, 2122
Changes in Income Given Prices
Normal Goods
Both goods 1 and 2 are normal
2x
1x
X
Y 0,, 211
m
mppx
0,, 212
m
mppx
An Inferior Good
Good 1 is normal.Good 2 is inferior:
2x
1x
X Y0
,, 212
m
mppx
Income Offer and Engel Curves
m
1x1x
2x Income Offer Curve Engel Curve
Cobb-Douglas
Demand function for good 1:
Demand function for good 2:
2x
1x
*2x
*1x
11
p
mcx
2
2 1p
mcx
Cobb Douglas
Income Offer Curve: Engel Curve:
2x
1x
m
1x
c
p1
Perfect Substitutes
2x
1x
1
2
1
p
p
*1x
Demand function for good 1:
if
if
if
21 pp 11 / pmx
11 /,0 pmx
01 x 21 pp
21 pp
Perfect Substitutes (with )
2x
1x
m
1x
Income Offer Curve:
21 pp
Engel Curve:
1p
Perfect Complements
Optimal choice:
Budget line:
Demand function for goods 1 and 2:
*1x
*2x
1x
2x12 xx
12 xx
mxpxp 2211
2121
pp
mxx
Perfect Complements
Income Offer Curve: Engel Curve:2x
1x 1x
m
21 pp
Homothetic Preferences
Consumer’s preferences only depend on the ratio of the two goods:
If Then, for
Example: Cobb-Douglas, Perfect substitutes, Perfect Complements.Properties: straight income offer curve and Engel curve.
),(~),( 2121 yyxx
),(~),( 2121 tytyxtxt0t
Luxury Good
m
1x
Necessary Good
m
1x
Changes in Prices
Fix income and price of one good and change price of the other.
Ordinary Goods
Price of good 1 decreases.
Demand for good 1 increases.
2x
1x
YX
Giffen Goods
Price of good 1 decreases.
Demand for good 1 decreases.
2x
1x
X
Y
Price Offer and Demand Curves
Price Offer Curve: Demand Curve:
2x
1x
1p
1x
Perfect Complements
Price Offer Curve: Demand Curve:2x
1x
1p
1x
Substitutes
Good 1 is a substitute for good 2 when:
0
,,
2
211
p
mppx
Complements
Good 1 is a complement to good 2:
0
,,
2
211
p
mppx
Inverse Demand Function
Consider a demand function
The inverse demand function is
Cobb-Douglas example:
mppxx ,, 2111
111 xpp
11
p
mcx
11
x
mcp
Inverse Demand Curve
Inverse Demand Curve
1p
1x
Optimal choice:
Suppose:
(composite good)
Rearrange:
12 p
MRSp
p
2
1
MRSp 1
