The demand for roses.* Table 7.6 gives quarterly data on these variables:
Y = quantity of roses sold, dozens
X2 = average wholesale price of roses, $/dozen
X3 = average wholesale price of carnations, $/dozen
X4 = average weekly family disposable income, $/week
X5 = the trend variable taking values of 1, 2, and so on, for the period 1971-III to 1975-II in the Detroit metropolitan area
You are asked to consider the following demand functions:
Yt = α1 + α2 X2t + α3 X3t + α4 X4t + α5 X5t + ut
ln Yt = β1 + β2 ln X2t + β3 ln X3t + β4 ln X4t + β5 X5t + ut
a. Estimate the parameters of the linear model and interpret the results.
b. Estimate the parameters of the log-linear model and interpret the results.
c. β2 , β3 , and β4 give, respectively, the own-price, cross-price, and income elasticities of demand. What are their a priori signs? Do the results con- cur with the a priori expectations?
TABLE 7.6
Year and
|
quarter
|
Y
|
X2
|
X3
|
X4
|
X5
|
|
1971-III
|
11,484
|
2.26
|
3.49
|
158.11
|
1
|
|
-IV
|
9,348
|
2.54
|
2.85
|
173.36
|
2
|
|
1972-I
|
8,429
|
3.07
|
4.06
|
165.26
|
3
|
|
-II
|
10,079
|
2.91
|
3.64
|
172.92
|
4
|
|
-III
|
9,240
|
2.73
|
3.21
|
178.46
|
5
|
|
-IV
|
8,862
|
2.77
|
3.66
|
198.62
|
6
|
|
1973-I
|
6,216
|
3.59
|
3.76
|
186.28
|
7
|
|
-II
|
8,253
|
3.23
|
3.49
|
188.98
|
8
|
|
-III
|
8,038
|
2.60
|
3.13
|
180.49
|
9
|
|
-IV
|
7,476
|
2.89
|
3.20
|
183.33
|
10
|
|
1974-I
|
5,911
|
3.77
|
3.65
|
181.87
|
11
|
|
-II
|
7,950
|
3.64
|
3.60
|
185.00
|
12
|
|
-III
|
6,134
|
2.82
|
2.94
|
184.00
|
13
|
|
-IV
|
5,868
|
2.96
|
3.12
|
188.20
|
14
|
|
1975-I
|
3,160
|
4.24
|
3.58
|
175.67
|
15
|
|
-II
|
5,872
|
3.69
|
3.53
|
188.00
|
16
|
d. How would you compute the own-price, cross-price, and income elas- ticities for the linear model?
e. On the basis of your analysis, which model, if either, would you choose and why?