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Computing elasticities

The maker of a leading brand of low calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:
Q = - 5,200 - 42P + 20Px + 5.2I + 0.20A + 0.25M
(2002) (17.5) (6.2) (2.5) (0.09) (0.21)
R^2 = 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 supermarket is located = 5,500
A (in dollars)= Monthly advertising expenditure = 10,000
M = Number of microwave ovens sold in the SMSA in which the
supermarket is located = 5,000

Using the information, answer the following questions:
- Compute elasticities for each variable
How concerned do you think this company would be about the impact of a recession on its sales? Explain.
- Do you think that this firm should cut its price to increase its market share? Explain.
What proportion of the variation in sales is explained by the independent variables in the equations? How confident are you about this answer? Explain.

Solution Preview

Elasticity w.r.t to variable x is dQ/dx * x/Q
First calculate the value of Q for the given values of variables.
Q = - 5,200 - 42P + 20Px + 5.2I + 0.20A + 0.25M
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 supermarket is located = 5,500
A (in dollars)= Monthly advertising expenditure = 10,000
M = Number of microwave ovens sold in the SMSA in which the
supermarket is located = 5,000 ...

Solution Summary

Computing elasticities is achieved.

$2.19