Problem 1
The maker of a leading brand of low-calorie microwavable food estimates the following demand equation for its product using data from 26 supermarkets around the country for the month of April.
Q = - 5200 - 42P + 20PX + 5.2I + .20A + .25M
(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)
R2 = 0.55 n = 26 F = 4.88
Assume the following values for the independent variables:
Q = Quantity sold per month
P (in cents) = Price of the product = 500
PX (in cents) = Price of leading competitor's product = 600
I (in dollars) = Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = 5,500
A (in dollars) = Monthly advertising expenditures = 10,000
M = Number of microwave ovens sold in the SMSA in which the
supermarkets are located = 5,000
Using this information, answer the following questions:
a. Compute elasticities for each variable.
b. How concerned do you think this company would be about the impact of a recession on its sales? Explain. (Hint: Interpret income elasticity coefficient.)
c. Do you think that this firm should cut its price to increase its market share? Explain. (Hint: Refer to the price elasticity of demand.)
d. What portion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer? Explain. (Hint: Interpret R2 and F.)
Problem 2
You have the following data for the last 12 months' sales for the PRQ Corporation (in thousands of dollars):
January 500 July 610
February 520 August 620
March 520 September 580
April 510 October 550
May 530 November 510
June 580 December 480
a. Calculate a 3-month centered moving average.
b. Use this moving average to forecast sales for January of next year.
c. If you were asked to forecast January and February sales for next year, would you be confident of your forecast using the preceding moving averages? Why or why not?