To begin this problem, specify the regression equation and match it with the additional data you are given in Step 3. After you have matched the regression equation with the additional data, calculate the elasticity for each variable. Consider the following scenario: The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its producer using data from 26 supermarkets around the country for the month of April:
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Q =
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-5,200 -
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42P +
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20Px +
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5.2I +
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0.20A +
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0.25M
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Standard Errors
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(2.002)
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(17.5)
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(6.2)
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(2.5)
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(0.09)
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(0.21)
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R2 = 0.55
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n = 26
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F = 4.88
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Assume the following values for the independent variables:
Q = Quantity sold per month
P (in cents) = Price of the product = 500. (Note: No need to convert to dollars.)
Px (in cents) = Price of leading competitor's product = 600 (Note: No need to convert to dollars.)
I (in dollars) = Per capita income of the Standard Metropolitan Statistical Area (SMSA) in which the supermarket is located = 5,500 (Note: No need to convert to cents.)
A (in dollars) = Monthly advertising expenditure = 10,000. (Note: No need to convert to cents.)
M = Number of microwave ovens sold in the SMSA in which the supermarket is located = 5,000
Using this information, answer the following:
1. Compute the elasticity for each variable.
2. How concerned do you think this company would be about the impact of a recession on its sales? Explain.
3. Do you think that this firm should cut its price to increase its market share? Explain.
4. What proportion of the variation in sales is explained by the independent variables in the equations? How confident are you about this answer? Explain.