Geoscience Reference
In-Depth Information
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
Under 25
25 - 34
35 - 44
45 - 54
55 - 64
Over 64
2003=100
2010-2003
2020-2010
2030-2020
Fig. 11.3
Consumption growth by households of different ages (2003
¼
100)
ln
CU
ð
;
P
Þ¼
ð
1
U
Þ
ln
AP
ðÞþ
U
ln
BP
ðÞ
ð
11
:
1
Þ
X
k
α
k
ln
P
k
þ
2
X
k
X
1
ʳ
kj
ln
P
k
ln
P
j
and
where ln
AP
ðÞ¼α
0
þ
j
ðÞþʲ
0
Y
k
P
ʲ
k
k
ln
BP
ðÞ¼
ln
AP
To derive price elasticities that reflect both own price effects and cross price
effects, the
K
-good expenditure function is expressed in terms of a “two-good
economy” producing
i
and
i.
3
ln
CU
ð
;
P
Þ¼
ð
1
U
Þ
ln
AP
ðÞþ
U
ln
bP
ðÞ
ð
11
:
2
Þ
where
2
ʳ
ii
ln
P
i
ln
P
i
þ ʳ
ii
ln
P
i
ln
P
i
ln
A
1
ln
AP
ðÞ¼α
0
þ α
i
ln
P
i
þ α
i
ln
P
i
þ
þʳ
ii
ln
P
i
ln
P
i
þ ʳ
ii
lnP
i
ln
P
i
ðÞþʲ
0
P
ʲ
i
P
ʲ
i
and ln
BP
ðÞ¼
ln
AP
ðÞþ
ln
BP
ðÞ¼
ln
AP
i
3
This approach is also helpful to preserve degree of freedom in a small sample, since it can save
k-2
degrees of
freedom in the estimation. And the expenditure function changes from
X
C
¼
P
k
Q
k
for
k
goods to C
¼
P
i
Q
i
+P
i
Q
i
for good
i
and
i
.
k
