Question

(2) As soon as you became the director of marketing at the maker of a leading brand of low-calorie microwavable food, you requested a group of designated staff members to estimate a product demand. The team leader submitted to you a report containing the following estimated demand equation for its product using data from 26 supermarkets around the country for the month of June 2020:

Q = - 5200 - 42P + 20PX + 5.2I + .20A + .25M

          R-square = 0. 55   n = 26

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 competitior's product = 600; I (in dollars) = Per capita income of the standard metropolitan statistical area 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 this information, answer the following questions: You must explain each question in detail and must show the formula used.

a. Compute the own price elasticity of demand.

b. How concerned do you think this company would be about the impact of a recession on its sales? Explain.

c. Do you think that this firm should cut its price to increase its market share? Explain.

d. What proportion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer? Explain.

Answer 1

Plugging in given values,

Q =  - 5200 - 42 x 500 + 20 x 600 + 5.2 x 5,500 + 0.2 x 10,000 + 0.25 x 5,000

Q = - 5200 - 21,000 + 12,000 + 28,600 + 2,000 + 1,250

Q = 17,650

(a)

Own price Elasticity (Ed) = (dQ/dP) x (P/Q) = - 42 x (500 / 17,650) = - 1.19

(b)

Income elasticity = (dQ/dI) x (I/Q) = 5.2 x (5,500 / 17,650) = 1.62

Since income elasticity > 1, this is a normal and luxury good. So a decrease in income due to a recession will decrease demand of the good, which is matter of concern.

(c)

Since |Ed| > 1, demand is elastic and a price cut will increase revenue. So the price cut is justified.

(d)

55% of the variation in sales is explained by the independent variables, which is the value of R² (= 0.55 = 55%). Since this is a low value, goodness of fit is weak and poor.