Based on 21 months of past data, Ziggy's Drive-In has determined that the demand for its hamburgers is given by the following equation:
Q = 205.2 - 200P + 100PC + 0.5Y + 23.0A
(110.9) (35.65) (49.5) (0.117) (8.712) (standard errors)
R2 = 0.74 SEE = 18.9
where Q = number of hamburgers sold per month, in thousands
P = price of Ziggy's hamburgers, in dollars
PC = price of hamburgers for Ziggy's major competitor, in dollars
Y = income per capita in the surrounding community, thousands of dollars
A = advertising expenditures during the previous month, thousands of dollars
Currently, Ziggy charges $1.00 for its hamburgers, while its closest competitor charges $1.20. Income per capita is $20,000, while advertising was $5,000 in the preceding month.
a. Evaluate the overall explanatory power of the regression model. Use a 0.05 level of significance. State all your hypotheses and explain your results. Do not use rules of thumb. Note: You will need to calculate the F statistic to answer this question.
b. Which of the independent variables, if any, appear to be statistically significant at the 0.05 level in explaining sales? State all your hypotheses and explain your results. Do not use rules of thumb.
c. What proportion of the total variation in sales is explained by the independent variables in this regression equation? How does your answer change if you adjust your answer based on the number of observations relative to the number of variables in this equation?
d. Derive a 95% confidence interval for current sales at the present values of each variable. Do not use rules of thumb.
2. A multiplicative demand function of the form: Qd = aPb1Yb2Pob3 is estimated using cross-sectional data and 224 observations. The regression results were as follows:
Constant (a) Price
(P) Income
(Y) Price of other good (Po)
Coefficient 0.02248 -0.2243 1.3458 0.1034
Standard Error 0.01885 0.0563 0.5012 0.8145
a. How should the coefficients be interpreted in this equation? Explain.
b. What is the quantity demanded if price is $10, income is $9000, and price of the other good is $15? Show your calculations.
c Is demand elastic or inelastic? How can you tell? What impact would a price increase have on total revenue? on total profit? Explain.
d How are these two goods related? Should the firm be concerned about a change in the price of the other good? Explain.
e. Is this product a luxury, necessity, or inferior good? Explain.