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What is the price elasticity of demand given the demand for meals at a local restaurant?

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1. Using data covering May 1998 to October 2000 a student attempted to estimate the demand for meals at a local restaurant. The data included the average price per meal (p), the number of customers (q), and advertising expenditures (a). The following model in levels and logs was estimated:

Q = b0 + b1p + b2a + b3s + b4T

The s variable measures seasonality, but requires some explanation in this application. The town the restaurant is in is small, but enjoys big crowds during sporting events held at the local university. The university also does not have many summer programs so student population is very small during the summer months. For these reasons, the grad student set the season variable equal to one during the regular school months and zero in the summer months and December - the times when there are few students in the town. The trend variable (T) captures any time trend and takes the value one for the first month of the data, two for second, and so on. The regression results are as follows:

Dependent Variable: Number of Customers - Levels
F-ratio = 19.354 R2 = .7559

Variable Estimate Standard Error t-ratio
Intercept 8790.42 1716.78 5.12
Price (p) -505.92 168.45 -3.00
Advertising (a) .824 .593 1.39
Season (s) 966.142 178.37 5.41
Trend (T) 25.86 11.07 2.335

Dependent Variable: Number of Customers - LOGS
F-ratio = 23.994 R2 = .7993

Variable Estimate Standard Error t-ratio
Intercept 10.018 0.823 12.177
Ln Price -0.995 0.316 -3.15
Ln Advertising 0.097 0.062 1.575
Season (s) 0.199 0.032 6.212
Trend (T) 0.005 0.002 2.539
Means of Variables: Customers = 5026.73, Price = $10.42 and Ads = $602.20

a. What is the price elasticity of demand?
b. Is the restaurant's advertising program effective?
c. If you were the manager of the restaurant, would you change the advertising budget?
d. Is the business in this restaurant stable over time?
e. Is business slower during the months when students are gone from the area?

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Solution Preview

a. The price elasticity of demand is -0.995.
b. No, the restaurant's advertising program is not effective because if we look at the t-ratio of advertising we can find that the hypothesis of using advertisement as one of the component variable in the equation has been ...

Solution Summary

This solution provides five answers for the price elasticity of demand problems in an attached Word document in 200 words with calculations.