Question

The following is the linear specification of demand for a good, where there are only two of these businesses in the area and the number of buyers, N, of the good did not change during the specified time period.

                           Q = a + bPRICE + cINCOME + dSubPrice + eComPrice

where

                Q = sales of the good for firm 1

                PRICE = price of the good for firm 1

                INCOME = average annual household income in the area

                SubPrice = price of the substitute good for firm 1

                ComPrice = price of the complementary good for firm 1

The estimation of the above equation yielded the following output.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.977477
R Square	0.955462
Adjusted R Square	0.946085
Standard Error	42.41123
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	4	733155.8	183289	101.9001	1.47E-12
Residual	19	34175.53	1798.712
Total	23	767331.3
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1183.802	506.298	2.338154	0.030467	124.1086	2243.496	124.1086	2243.496
PRICE	-213.422	13.48632	-15.8251	2.14E-12	-241.649	-185.195	-241.649	-185.195
INCOME	0.091088	0.01241	7.339957	5.88E-07	0.065114	0.117063	0.065114	0.117063
SubPrice	101.3029	38.74776	2.614418	0.017052	20.20286	182.4029	20.20286	182.4029
ComPrice	71.8448	27.0997	2.651129	0.015763	15.12447	128.5651	15.12447	128.5651

What is the interpretation of coefficients b, c, d, and e?

What percent of the total variation in the good’s sales is explained by the model? From where did you get this information?

If PRICE = INCOME = SubPrice = ComPrice = 0, what is the value of SALES? Show all of your work.

What value do you predict SALES will take if PRICE = $9.05, INCOME = $26,614, SubPrice = $10.12 and ComPrice =$1.15?

Using the information in 8, compute price elasticity of demand, income elasticity of demand, and the two cross-price elasticities of demand.

What do the elasticities in 8 indicate about elasticity of demand for the good, the impact of income on the sale of the good and the type of good, the impact of the cross-price elasticity of SubPrice on the sale of the good, and the cross-price elasticity of ComPrice on the good?

               

Answer 1

b = -213.42. The b coefficient stands for the price in the above-mentioned regression question. A negative sign indicates that the sales of the good are inversely related to the price. So the higher the price of the commodity, the lesser the sale of the commodity. In this case, the sale of the goods will fall by 213.42 percentage.

c = 0.09. The c coefficient stands for income in the above-mentioned regression question. It has a positive sign indicating a direct relationship between the sales of the good of the firm 1 and the income of the natives. With a hike of income of 9 percent, there will also a one unit increase in sales of the good

d = 101.30. The d coefficient stands for the substitute goods in the above-mentioned regression question. It has a positive sign indicating a direct relationship between the sales of the good of the firm 1 and the substitute goods. With the increase in the price of the substitute goods, there will be an increase in the sales of the goods of firm 1.

e = 71.85. The e coefficient stands for the complementary goods in the above-mentioned regression question. It has a positive sign indicating a direct relationship between the sales of the good of the firm 1 and the complementary goods. With a 72 percent increase in the demand for complementary goods, there will 1 unit increase in sales of goods produced by form 1.

95 percent of the total variation in the good’s sales is explained by the model. R square of the model explains the variation.

Price = Income = Subsitute = Complemnatry = 0, then

Sales of goods = Constant = 1183.80

Sales of goods = 1183.80 - 213.42 * 9.05 + 0.09*26,614 + 101.30*10.12 + 71.85 * 1.15 = 2755.39 = 2755 units