Express the estimated demand equation in logarithms is x a

Question

1. The following log-linear demand curve for a price-setting firm is estimated using the ordinary least squares method:

Q = aP^bM^cP^d_R

where Q and P are the quantity and price respectively for good X, M is consumer income, and P_R is the price of good R.

The estimation results are presented below:

DEPENDENT VARIABLE:	LNQ	R-SQUARE	F-RATIO	P-VALUE ON F
OBSERVATIONS:	64	0.8464	110.25	0.0001
		PARAMETER	STANDARD
VARIABLE		ESTIMATE	ERROR	T-RATIO	P-VALUE
INTERCEPT		5.65	3.20	1.77	0.0825
LNP		-1.02	0.59	-1.73	0.0890
LNM		0.45	0.22	2.05	0.0452
LNPR		-2.0	0.75	-2.67	0.0098

a. Express the estimated demand equation in logarithms.

b. Is X a normal or an inferior good? And how are goods X and R related? Explain.

c. Which of the parameter estimates are statistically significant at the 5 percent level?

d. Estimate the own-price elasticity for good X, the cross-price elasticity for goods X and R, and the income elasticity for good X.

e. Holding all other things constant, if household income were to fall by 22%, what would we expect to happen to quantity demanded? Explain.

f. Holding all other things constant, if own price were to increase by 22%, what would we expect to happen to quantity demanded? Explain.

g. Holding all other things constant, if the price of R were to fall by 8%, what would we expect to happen to quantity demanded? Explain.

2. The British Columbia Tourist Association distributes pamphlets, maps, and other tourist-related information to people who call a toll-free number and request information. The marketing manager decided to develop a multiple regression model to predict the number of calls that will be received in the coming week. A random sample of 20 weeks is selected.

a. Specify a suitable multiple regression equation to estimate with the data.

b. What percentage of the total variation in the number of calls is explained by the regression model?

c. Is the overall multiple regression equation statistically significant? Explain.

d. Which, if any, of the independent variables is statistically significant? Test using a significance level of 0.05.

3. Assume you've just been assigned to a project to determine the future demand for natural gas in a rapidly growing community where the population is expanding because of the influx of several large employers. The community is in a geographical area with four distinct seasons that are characterized by cold snowy winters and hot summers.  The population in the community is mostly middle class with larger than average families.  There is an existing utilities structure with adequate supplies of natural gas as well as other competing energy services.  You can assume that all the factors of a general demand function, Q_d = f (P, M, P_R, T, P_e, N), as described in your text, beginning on page 39, have been considered. 

1. Describe five additional factors that you consider most significant for forecasting the demand for natural gas over the next 4 years.  (Keep in mind the data must be quantifiable, you will have to identify a process for collecting the information over an appropriate time period, and the data must be relevant as a factor in accurately determining the demand for natural gas.) FACTORS AFFECTING SUPPLY SHOULD NOT BE CONSIDERED.

2. Briefly outline the processes you would use in gathering and analyzing these five additional factors for forecasting the demand curve for natural gas.

3. Provide appropriate feedback for your peers to convince them on the: (i) importance, and (ii) the feasibilty of getting measurable definition and data, (so that some meaningful discussion can take place), of the factors and the processes described above.