Question

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

a) Calculate the quantity using the given values for the independent variables.

b) Calculate the total revenue at this quantity.

c) What proportion of the variation in sales is explained by the independent variables?

d) Calculate the price elasticity of demand. Hint: Use the point elasticity method described on page 72. A numeric example is demonstrated in the second paragraph on that page.

e) Based on the price elasticity of demand, do you think that this firm should cut its price to increase its market share? Why or why not?

f) Compute the income elasticity.

g) Based on the income elasticity of demand, do you think that this company would be extremely concerned about the impact of a recession on its sales? Why or why not?

Answer 1

Q = -5,200 – 42P + 20Px + 5.2l + 0.20A + 0.25M

Given: P (in cents) = 500

Px (in cents)= 600

I (in dollars) = 5,500

A (in dollars) = 10,000

M = 5,000

a) Calculation of Q with given values:

Q= -5,200 – 42(500) + 20(600) + 5.2(5500) + 0.20(10000) + 0.25(5000)

Q= -5200-21000+12000+28600+2000+1250= 17650

b) Total revenue= Price of the product x Quantity

Total revenue= 500 x 17650= 8,825,000

c) R2= 0.55 (Given)

It is a coefficient of determination which explains the proportion of variation in dependent variable explained by the explanatory variables.

Here R2= 0.55 implies that 55% of the variation in sales is explained by the independent variables.

d) Price elasticity of demand= dQ/dP x P/Q

Here dQ/dP= Differentiation of Q with respect to P

Q = -5,200 – 42P + 20Px + 5.2l + 0.20A + 0.25M

dQ/dP= -42

Price elasticity of demand= -42 x 500/17650= -1.19