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Homework answers / question archive / 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

Economics

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.

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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