A. Using the marketing data from the 15 test markets shown above, estimate the parameters of the linear empirical demand function:
1. Using the appropriate tests, Evaluate the significance of the regression as a whole and the significance of the individual parameters at 5% level of significance. (show all your steps and procedure).
If any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again.
a. Your final estimated linear demand function for Liquid Ozarka is
b. What percentage of the variation in sales of Liquid Ozarka is explained by your estimated demand function?
2. The marketing consultants describe a “typical” market as one in which the price of Liquid Ozarka is $3.50 per gallon, average household income is $45,000, the price of rival bottled water is $3 per gallon, and the population is 75,000.
Answer the following questions for this “typical” market scenario.
a. What is the estimated elasticity of demand for Liquid Ozarka? Is demand elastic or inelastic? What would be the percentage change in price required to increase sales of Liquid Ozarka by 10 percent?
b. What is the estimated income elasticity of demand? Is Liquid Ozarka a normal or inferior good? A 6 percent increase in average household income would be predicted to cause what percentage change in sales of Liquid Ozarka?
c. What is the estimated cross-price elasticity of demand for Liquid Ozarka with respect to changes in price of its rival brand of bottled water? Does the estimated cross-price elasticity have the expected algebraic sign? Why or why not? If the price of the rival brand of water rises by 8 percent, what is the estimated percentage change in sales of Liquid Ozarka?
B. Using the marketing data from the preceding 15 test markets, estimate the parameters for the log-linear empirical demand function:
1. Using the P-Values, if any of the parameter estimates are not significant at the 2 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again.
c. Your final estimated log-linear demand function for Liquid Ozarka is
2. Does a log-linear specification work better than a linear specification of demand for Liquid Ozarka? Explain by comparing F-ratios, R2s, and t-ratios (or p-values).
3. Using the estimated log-linear demand function, compute the price, income, and cross-price elasticity of demand. How do they compare to the estimated elasticity for the linear demand specification?
4. What is the estimated quantity demand based on the values of explanatory variables given above?