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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
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 + 5.2l + 0.20A + 0.25M
(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 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, compute the income elasticity.
Expert Solution
Step one: substitute the values of variables in the demand equation to obtain quantity demanded
The demand equation is given as:
Q = -5,200 - 42P + 20Px + 5.2l + 0.20A + 0.25M
But
P = 500
PX = 600
I = 5,500
A = 10,000
M = 5,000
Hence, QD= - 5200 ? 42(500) + 20(600) + 5.2(5500) + 0.20(10000) + 0.25(5000) = 17,650 units
Step: Use the QD to work out the income elasticity
Income Elasticity (IE)
Income elasticity formula is given as:
IE = (change in quantity/change in income) * (income / quantity)
Where;
(Change in quantity/change in income) = 5.2 (obtained by differentiating Quantity demanded with respect to income)
Income = 5500
Quantity = 17650
Hence, IE = 5.2 *(5500/17650) = 1.6204
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