The demand for roses. The following table 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:

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 concur with the a priori expectations?
d. How would you compute the own-price, cross-price, and income elasticities for the linear model?
e. On the basis of your analysis, which model, if either, would you choose and why?

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Year and Quarter X2 Хз X4 X5 2.26 1971-II| 11,484 9,348 3.49 158.11 -IV 2.54 2.85 173.36 2 1972-I 8,429 10,079 9,240 8,862 3.07 4.06 165.26 3 3.64 2.91 172.92 -II 2.73 3.21 178.46 5 3.66 198.62 -IV 2.77 6. 3.76 1973-1 6,216 8,253 8,038 7,476 3.59 186.28 3.23 3.49 188.98 3.13 180.49 2.60 2.89 183.33 -IV 3.20 10 1974-I 5,911 7,950 6,134 5,868 3.77 3.65 181.87 11 3.64 3.60 185.00 12 -II 2.82 2.94 184.00 13 -IV 2.96 3.12 188.20 14 1975–I 3,160 5,872 4.24 3.58 175.67 15 3.53 -|| 3.69 188.00 16 Y; = a1 + a2X21 +azX3 + ¤4X4 + as X5t + u; In Y, = B1 + B2 InX2 + B3 In X34 + B4 In X4, + B5 X51 + u;