chapter 6 demand - wordpress.com fileproperties of demand functions comparative statics analysis of...
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![Page 1: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/1.jpg)
Chapter 6
Demand
![Page 2: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/2.jpg)
Properties of Demand Functions
Comparative statics analysis of
ordinary demand functions -- the
study of how ordinary demands
x1*(p1,p2,y) and x2*(p1,p2,y) change as
prices p1, p2 and income y change.
![Page 3: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/3.jpg)
Own-Price Changes
How does x1*(p1,p2,y) change as p1
changes, holding p2 and y constant?
Suppose only p1 increases, from p1’to p1’’ and then to p1’’’.
![Page 4: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/4.jpg)
x1
x2
p1 = p1’
Fixed p2 and y.
p1x1 + p2x2 = y
Own-Price Changes
![Page 5: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/5.jpg)
Own-Price Changes
x1
x2
p1= p1’’
p1 = p1’
Fixed p2 and y.
p1x1 + p2x2 = y
![Page 6: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/6.jpg)
Own-Price Changes
x1
x2
p1= p1’’p1=
p1’’’
Fixed p2 and y.
p1 = p1’
p1x1 + p2x2 = y
![Page 7: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/7.jpg)
Own-Price ChangesFixed p2 and y.
![Page 8: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/8.jpg)
x1*(p1’)
Own-Price Changes
p1 = p1’
Fixed p2 and y.
![Page 9: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/9.jpg)
x1*(p1’)
p1
x1*(p1’)
p1’
x1*
Own-Price ChangesFixed p2 and y.
p1 = p1’
![Page 10: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/10.jpg)
x1*(p1’)
p1
x1*(p1’)
p1’
p1 = p1’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 11: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/11.jpg)
x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)
p1’
p1 = p1’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 12: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/12.jpg)
x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)
x1*(p1’’)
p1’
p1’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 13: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/13.jpg)
x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)
x1*(p1’’)
p1’
p1’’
p1 = p1’’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 14: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/14.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)
x1*(p1’’)
p1’
p1’’
p1 = p1’’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 15: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/15.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)x1*(p1’’’)
x1*(p1’’)
p1’
p1’’
p1’’’
x1*
Own-Price ChangesFixed p2 and y.
![Page 16: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/16.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)x1*(p1’’’)
x1*(p1’’)
p1’
p1’’
p1’’’
x1*
Own-Price Changes Ordinary
demand curve
for commodity 1Fixed p2 and y.
![Page 17: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/17.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)x1*(p1’’’)
x1*(p1’’)
p1’
p1’’
p1’’’
x1*
Own-Price Changes Ordinary
demand curve
for commodity 1Fixed p2 and y.
![Page 18: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/18.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
p1
x1*(p1’)x1*(p1’’’)
x1*(p1’’)
p1’
p1’’
p1’’’
x1*
Own-Price Changes Ordinary
demand curve
for commodity 1
p1 price
offer
curve
Fixed p2 and y.
![Page 19: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/19.jpg)
Own-Price Changes
The curve containing all the utility-
maximizing bundles traced out as p1
changes, with p2 and y constant, is
the p1- price offer curve.
The plot of the x1-coordinate of the
p1- price offer curve against p1 is the
ordinary demand curve for
commodity 1.
![Page 20: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/20.jpg)
Own-Price Changes
What does a p1 price-offer curve look
like for Cobb-Douglas preferences?
![Page 21: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/21.jpg)
Own-Price Changes
What does a p1 price-offer curve look
like for Cobb-Douglas preferences?
Take
Then the ordinary demand functions
for commodities 1 and 2 are
U x x x xa b( , ) .1 2 1 2
![Page 22: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/22.jpg)
Own-Price Changes
x p p ya
a b
y
p1 1 2
1
*( , , )
x p p yb
a b
y
p2 1 2
2
*( , , ) .
and
Notice that x2* does not vary with p1 so the
p1 price offer curve is
![Page 23: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/23.jpg)
Own-Price Changes
x p p ya
a b
y
p1 1 2
1
*( , , )
x p p yb
a b
y
p2 1 2
2
*( , , ) .
and
Notice that x2* does not vary with p1 so the
p1 price offer curve is flat
![Page 24: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/24.jpg)
Own-Price Changes
x p p ya
a b
y
p1 1 2
1
*( , , )
x p p yb
a b
y
p2 1 2
2
*( , , ) .
and
Notice that x2* does not vary with p1 so the
p1 price offer curve is flat and the ordinary
demand curve for commodity 1 is a
![Page 25: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/25.jpg)
Own-Price Changes
x p p ya
a b
y
p1 1 2
1
*( , , )
x p p yb
a b
y
p2 1 2
2
*( , , ) .
and
Notice that x2* does not vary with p1 so the
p1 price offer curve is flat and the ordinary
demand curve for commodity 1 is a
rectangular hyperbola.
![Page 26: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/26.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
x2
x1
Own-Price ChangesFixed p2 and y.
x
by
a b p
2
2
*
( )
xay
a b p1
1
*
( )
![Page 27: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/27.jpg)
x1*(p1’’’) x1*(p1’)
x1*(p1’’)
x2
x1
p1
x1*
Own-Price Changes Ordinary
demand curve
for commodity 1
is
Fixed p2 and y.
x
by
a b p
2
2
*
( )
xay
a b p1
1
*
( )
xay
a b p1
1
*
( )
![Page 28: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/28.jpg)
Own-Price Changes
What does a p1 price-offer curve look
like for a perfect-complements utility
function?
![Page 29: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/29.jpg)
Own-Price Changes
What does a p1 price-offer curve look
like for a perfect-complements utility
function?
U x x x x( , ) min , .1 2 1 2
Then the ordinary demand functions
for commodities 1 and 2 are
![Page 30: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/30.jpg)
Own-Price Changes
x p p y x p p yy
p p1 1 2 2 1 2
1 2
* *( , , ) ( , , ) .
![Page 31: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/31.jpg)
Own-Price Changes
x p p y x p p yy
p p1 1 2 2 1 2
1 2
* *( , , ) ( , , ) .
With p2 and y fixed, higher p1 causes
smaller x1* and x2*.
![Page 32: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/32.jpg)
Own-Price Changes
x p p y x p p yy
p p1 1 2 2 1 2
1 2
* *( , , ) ( , , ) .
With p2 and y fixed, higher p1 causes
smaller x1* and x2*.
p x xy
p1 1 2
2
0 , .* *
As
![Page 33: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/33.jpg)
Own-Price Changes
x p p y x p p yy
p p1 1 2 2 1 2
1 2
* *( , , ) ( , , ) .
With p2 and y fixed, higher p1 causes
smaller x1* and x2*.
p x xy
p1 1 2
2
0 , .* *
As
p x x1 1 2 0 , .* *
As
![Page 34: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/34.jpg)
Fixed p2 and y.
Own-Price Changes
x1
x2
![Page 35: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/35.jpg)
p1
x1*
Fixed p2 and y.
x
y
p p
2
1 2
*
xy
p p1
1 2
*
Own-Price Changes
x1
x2
p1’
xy
p p1
1 2
* ’
p1 = p1’
’
’
y/p2
![Page 36: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/36.jpg)
p1
x1*
Fixed p2 and y.
x
y
p p
2
1 2
*
xy
p p1
1 2
*
Own-Price Changes
x1
x2
p1’
p1’’
p1 = p1’’
’’x
y
p p1
1 2
* ’’
’’
y/p2
![Page 37: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/37.jpg)
p1
x1*
Fixed p2 and y.
x
y
p p
2
1 2
*
xy
p p1
1 2
*
Own-Price Changes
x1
x2
p1’
p1’’
p1’’’
xy
p p1
1 2
*
p1 = p1’’’
’’’’’’
’’’
y/p2
![Page 38: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/38.jpg)
p1
x1*
Ordinary
demand curve
for commodity 1
is
Fixed p2 and y.
x
y
p p
2
1 2
*
xy
p p1
1 2
*
xy
p p1
1 2
*.
Own-Price Changes
x1
x2
p1’
p1’’
p1’’’
y
p2
y/p2
![Page 39: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/39.jpg)
Own-Price Changes
What does a p1 price-offer curve look
like for a perfect-substitutes utility
function?
U x x x x( , ) .1 2 1 2
Then the ordinary demand functions
for commodities 1 and 2 are
![Page 40: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/40.jpg)
Own-Price Changes
x p p yif p p
y p if p p1 1 2
1 2
1 1 2
0*( , , )
,
/ ,
x p p yif p p
y p if p p2 1 2
1 2
2 1 2
0*( , , )
,
/ , .
and
![Page 41: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/41.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
Fixed p2 and y.
x2 0*
xy
p1
1
*
p1 = p1’ < p2
’
![Page 42: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/42.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
x2 0*
xy
p1
1
*
p1’
p1 = p1’ < p2
’
xy
p1
1
* ’
![Page 43: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/43.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
p1’
p1 = p1’’ = p2
![Page 44: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/44.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
p1’
p1 = p1’’ = p2
![Page 45: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/45.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
x2 0*
xy
p1
1
*
p1’
p1 = p1’’ = p2
’’
x1 0*
xy
p2
2
*
![Page 46: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/46.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
x2 0*
xy
p1
2
*
p1’
p1 = p1’’ = p2
x1 0*
xy
p2
2
*
0 12
xy
p
*
p2 = p1’’
![Page 47: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/47.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
xy
p2
2
*
x1 0*
p1’
p1’’’
x1 0*
p2 = p1’’
![Page 48: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/48.jpg)
Fixed p2 and y.
Own-Price Changes
x2
x1
p1
x1*
Fixed p2 and y.
p1’
p2 = p1’’
p1’’’
xy
p1
1
*
0 12
xy
p
*
y
p2
p1 price
offer
curve
Ordinary
demand curve
for commodity 1
![Page 49: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/49.jpg)
Own-Price Changes
Usually we ask “Given the price for
commodity 1 what is the quantity
demanded of commodity 1?”
But we could also ask the inverse
question “At what price for
commodity 1 would a given quantity
of commodity 1 be demanded?”
![Page 50: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/50.jpg)
Own-Price Changes
p1
x1*
p1’
Given p1’, what quantity is
demanded of commodity 1?
![Page 51: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/51.jpg)
Own-Price Changes
p1
x1*
p1’
Given p1’, what quantity is
demanded of commodity 1?
Answer: x1’ units.
x1’
![Page 52: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/52.jpg)
Own-Price Changes
p1
x1*x1’
Given p1’, what quantity is
demanded of commodity 1?
Answer: x1’ units.
The inverse question is:
Given x1’ units are
demanded, what is the
price of
commodity 1?
![Page 53: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/53.jpg)
Own-Price Changes
p1
x1*
p1’
x1’
Given p1’, what quantity is
demanded of commodity 1?
Answer: x1’ units.
The inverse question is:
Given x1’ units are
demanded, what is the
price of
commodity 1?
Answer: p1’
![Page 54: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/54.jpg)
Own-Price Changes
Taking quantity demanded as given
and then asking what must be price
describes the inverse demand
function of a commodity.
![Page 55: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/55.jpg)
Own-Price Changes
A Cobb-Douglas example:
xay
a b p1
1
*
( )
is the ordinary demand function and
pay
a b x1
1
( )
*
is the inverse demand function.
![Page 56: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/56.jpg)
Own-Price Changes
A perfect-complements example:
xy
p p1
1 2
*
is the ordinary demand function and
py
xp1
1
2 *
is the inverse demand function.
![Page 57: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/57.jpg)
Income Changes
How does the value of x1*(p1,p2,y)
change as y changes, holding both
p1 and p2 constant?
![Page 58: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/58.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
![Page 59: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/59.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
![Page 60: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/60.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
![Page 61: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/61.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
![Page 62: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/62.jpg)
Income Changes
A plot of quantity demanded against
income is called an Engel curve.
![Page 63: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/63.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
![Page 64: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/64.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
x1*
y
x1’’’x1’’
x1’
y’y’’y’’’
![Page 65: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/65.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
x1*
y
x1’’’x1’’
x1’
y’y’’y’’’
Engel
curve;
good 1
![Page 66: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/66.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve x2*
y
x2’’’x2’’
x2’
y’y’’y’’’
![Page 67: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/67.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve x2*
y
x2’’’x2’’
x2’
y’y’’y’’’
Engel
curve;
good 2
![Page 68: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/68.jpg)
Income ChangesFixed p1 and p2.
y’ < y’’ < y’’’
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
x1*
x2*
y
y
x1’’’x1’’
x1’
x2’’’x2’’
x2’
y’y’’y’’’
y’y’’y’’’
Engel
curve;
good 2
Engel
curve;
good 1
![Page 69: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/69.jpg)
Income Changes and Cobb-
Douglas Preferences
An example of computing the
equations of Engel curves; the Cobb-
Douglas case.
The ordinary demand equations are
U x x x xa b( , ) .1 2 1 2
xay
a b px
by
a b p1
12
2
* *
( );
( ).
![Page 70: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/70.jpg)
Income Changes and Cobb-
Douglas Preferences
xay
a b px
by
a b p1
12
2
* *
( );
( ).
Rearranged to isolate y, these are:
ya b p
ax
ya b p
bx
( )
( )
*
*
11
22
Engel curve for good 1
Engel curve for good 2
![Page 71: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/71.jpg)
Income Changes and Cobb-
Douglas Preferencesy
yx1*
x2*
ya b p
ax
( ) *11
Engel curve
for good 1
ya b p
bx
( ) *22
Engel curve
for good 2
![Page 72: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/72.jpg)
Income Changes and Perfectly-
Complementary Preferences
Another example of computing the
equations of Engel curves; the
perfectly-complementary case.
The ordinary demand equations are
x xy
p p1 2
1 2
* *.
U x x x x( , ) min , .1 2 1 2
![Page 73: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/73.jpg)
Income Changes and Perfectly-
Complementary Preferences
Rearranged to isolate y, these are:
y p p x
y p p x
( )
( )
*
*
1 2 1
1 2 2
Engel curve for good 1
x xy
p p1 2
1 2
* *.
Engel curve for good 2
![Page 74: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/74.jpg)
Fixed p1 and p2.
Income Changes
x1
x2
![Page 75: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/75.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
Fixed p1 and p2.
![Page 76: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/76.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
Fixed p1 and p2.
![Page 77: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/77.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
x1’’x1’
x2’’’x2’’x2’
x1’’’
Fixed p1 and p2.
![Page 78: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/78.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
x1’’x1’
x2’’’x2’’x2’
x1’’’ x1*
y
y’y’’y’’’
Engel
curve;
good 1
x1’’’x1’’
x1’
Fixed p1 and p2.
![Page 79: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/79.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
x1’’x1’
x2’’’x2’’x2’
x1’’’
x2*
y
x2’’’x2’’
x2’
y’y’’y’’’
Engel
curve;
good 2Fixed p1 and p2.
![Page 80: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/80.jpg)
Income Changes
x1
x2
y’ < y’’ < y’’’
x1’’x1’
x2’’’x2’’x2’
x1’’’ x1*
x2*
y
y x2’’’x2’’
x2’
y’y’’y’’’
y’y’’y’’’
Engel
curve;
good 2
Engel
curve;
good 1
x1’’’x1’’
x1’
Fixed p1 and p2.
![Page 81: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/81.jpg)
Income Changes
x1*
x2*
y
y x2’’’x2’’
x2’
y’y’’y’’’
y’y’’y’’’
x1’’’x1’’
x1’
y p p x ( )*
1 2 2
y p p x ( )*
1 2 1
Engel
curve;
good 2
Engel
curve;
good 1
Fixed p1 and p2.
![Page 82: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/82.jpg)
Income Changes and Perfectly-
Substitutable Preferences
Another example of computing the
equations of Engel curves; the
perfectly-substitution case.
The ordinary demand equations are
U x x x x( , ) .1 2 1 2
![Page 83: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/83.jpg)
Income Changes and Perfectly-
Substitutable Preferences
x p p yif p p
y p if p p1 1 2
1 2
1 1 2
0*( , , )
,
/ ,
x p p yif p p
y p if p p2 1 2
1 2
2 1 2
0*( , , )
,
/ , .
![Page 84: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/84.jpg)
Income Changes and Perfectly-
Substitutable Preferences
x p p yif p p
y p if p p1 1 2
1 2
1 1 2
0*( , , )
,
/ ,
x p p yif p p
y p if p p2 1 2
1 2
2 1 2
0*( , , )
,
/ , .
Suppose p1 < p2. Then
![Page 85: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/85.jpg)
Income Changes and Perfectly-
Substitutable Preferences
x p p yif p p
y p if p p1 1 2
1 2
1 1 2
0*( , , )
,
/ ,
x p p yif p p
y p if p p2 1 2
1 2
2 1 2
0*( , , )
,
/ , .
Suppose p1 < p2. Then xy
p1
1
* x2 0* and
![Page 86: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/86.jpg)
Income Changes and Perfectly-
Substitutable Preferences
x p p yif p p
y p if p p1 1 2
1 2
1 1 2
0*( , , )
,
/ ,
x p p yif p p
y p if p p2 1 2
1 2
2 1 2
0*( , , )
,
/ , .
Suppose p1 < p2. Then xy
p1
1
* x2 0* and
x2 0*
.y p x 1 1*
and
![Page 87: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/87.jpg)
Income Changes and Perfectly-
Substitutable Preferences
x2 0*
.y p x 1 1
*
y y
x1* x2*0
Engel curve
for good 1
Engel curve
for good 2
![Page 88: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/88.jpg)
Income Changes
In every example so far the Engel
curves have all been straight lines?
Q: Is this true in general?
A: No. Engel curves are straight
lines if the consumer’s preferences
are homothetic.
![Page 89: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/89.jpg)
Homotheticity
A consumer’s preferences are
homothetic if and only if
for every k > 0.
That is, the consumer’s MRS is the
same anywhere on a straight line
drawn from the origin.
(x1,x2) (y1,y2) (kx1,kx2) (ky1,ky2)pp
![Page 90: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/90.jpg)
Income Effects -- A
Nonhomothetic Example
Quasilinear preferences are not
homothetic.
For example,
U x x f x x( , ) ( ) .1 2 1 2
U x x x x( , ) .1 2 1 2
![Page 91: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/91.jpg)
Quasi-linear Indifference Curvesx2
x1
Each curve is a vertically shifted
copy of the others.
Each curve intersects
both axes.
![Page 92: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/92.jpg)
Income Changes; Quasilinear
Utilityx2
x1
x1~
![Page 93: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/93.jpg)
Income Changes; Quasilinear
Utilityx2
x1
x1~
x1*
y
x1~
Engel
curve
for
good 1
![Page 94: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/94.jpg)
Income Changes; Quasilinear
Utilityx2
x1
x1~
x2*
y Engel
curve
for
good 2
![Page 95: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/95.jpg)
Income Changes; Quasilinear
Utilityx2
x1
x1~
x1*
x2*y
y
x1~
Engel
curve
for
good 2
Engel
curve
for
good 1
![Page 96: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/96.jpg)
Income Effects
A good for which quantity demanded
rises with income is called normal.
Therefore a normal good’s Engel
curve is positively sloped.
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Income Effects
A good for which quantity demanded
falls as income increases is called
income inferior.
Therefore an income inferior good’s
Engel curve is negatively sloped.
![Page 98: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/98.jpg)
Income Changes; Goods
1 & 2 Normal
x1’’’x1’’
x1’
x2’’’x2’’x2’
Income
offer curve
x1*
x2*
y
y
x1’’’x1’’
x1’
x2’’’x2’’
x2’
y’y’’y’’’
y’y’’y’’’
Engel
curve;
good 2
Engel
curve;
good 1
![Page 99: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/99.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
![Page 100: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/100.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
![Page 101: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/101.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
![Page 102: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/102.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
![Page 103: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/103.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
![Page 104: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/104.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1
Income
offer curve
![Page 105: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/105.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1x1*
yEngel curve
for good 1
![Page 106: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/106.jpg)
Income Changes; Good 2 Is Normal,
Good 1 Becomes Income Inferior
x2
x1x1*
x2*
y
y
Engel curve
for good 2
Engel curve
for good 1
![Page 107: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/107.jpg)
Ordinary Goods
A good is called ordinary if the
quantity demanded of it always
increases as its own price decreases.
![Page 108: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/108.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2
![Page 109: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/109.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2
p1 price
offer
curve
![Page 110: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/110.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2
p1 price
offer
curve
x1*
Downward-sloping
demand curve
Good 1 is
ordinary
p1
![Page 111: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/111.jpg)
Giffen Goods
If, for some values of its own price,
the quantity demanded of a good
rises as its own-price increases then
the good is called Giffen.
![Page 112: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/112.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2
![Page 113: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/113.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2 p1 price offer
curve
![Page 114: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/114.jpg)
Ordinary GoodsFixed p2 and y.
x1
x2 p1 price offer
curve
x1*
Demand curve has
a positively
sloped part
Good 1 is
Giffen
p1
![Page 115: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/115.jpg)
Cross-Price Effects
If an increase in p2
– increases demand for commodity 1
then commodity 1 is a gross
substitute for commodity 2.
– reduces demand for commodity 1
then commodity 1 is a gross
complement for commodity 2.
![Page 116: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/116.jpg)
Cross-Price Effects
A perfect-complements example:
xy
p p1
1 2
*
x
p
y
p p
1
2 1 22
0*
.
so
Therefore commodity 2 is a gross
complement for commodity 1.
![Page 117: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/117.jpg)
Cross-Price Effects
p1
x1*
p1’
p1’’
p1’’’
y
p2’
Increase the price of
good 2 from p2’ to p2’’and
![Page 118: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/118.jpg)
Cross-Price Effects
p1
x1*
p1’
p1’’
p1’’’
y
p2’’
Increase the price of
good 2 from p2’ to p2’’and the demand curve
for good 1 shifts inwards
-- good 2 is a
complement for good 1.
![Page 119: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/119.jpg)
Cross-Price Effects
A Cobb- Douglas example:
xby
a b p2
2
*
( )
so
![Page 120: Chapter 6 Demand - WordPress.com fileProperties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,y)](https://reader030.vdocument.in/reader030/viewer/2022040218/5e0fe218f428393541440c3a/html5/thumbnails/120.jpg)
Cross-Price Effects
A Cobb- Douglas example:
xby
a b p2
2
*
( )
x
p2
1
0*
.
so
Therefore commodity 1 is neither a gross
complement nor a gross substitute for
commodity 2.