Question

Homebase (Pty) Ltd is the manufacturer of a robot vacuum cleaner,

iRobot-H. It uses built-in cameras and sensors to find its way around a home without fuss. It has different cleaning modes and advanced features such as the ability to produce maps of where it has cleaned and for how long. It really takes the drudge out of vacuum-cleaning homes. The company sells this product through 55 independent retail stores across the country. Homebase's marketing research team developed the demand equation below for iRobot-H, based on its average retail sales over the last 18 months. Q = 5 200 - 42P + 20PC + 5.2Y + 0.2A + 0.25S

(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)

R2 = 0.55 n = 55 F = 4.88

The following are the independent variables and their current values:

Q = quantity sold per month (sales)

P (in rand) = Price of iRobot-H = R2 900

PC (in rand) = Price of leading competitor's product = R3 200

Y (in rand) = Average per capita income in the country = R25 000

A (in rand) = Homebase's monthly advertising expenditure = R20 000

S (in units) = Number of robot vacuum cleaners sold across the country = 7 000 F (critical value) = 3.38 at 5% level of significance

Required: Show all calculations and relevant formulas.

2.1. What is the meaning of the parameters -42P, 20PC and 5.2Y? (3)

2.2. Calculate the elasticities for the price of iRobot-H (P), the product of the leading competitor (PC), average income (Y) and advertising expenditure (A). (8)

2.3. What will happen to the revenue of the company if Homebase decides to increase its price, given that all other factors remain the same? (2)

2.4 How significant are the independent variables in total and individually to explain the total sales that Homebase can expect to make? (12)

2.5. Assume that the following changes take place in the market for iRobot-H vacuum cleaners: The price (P) of iRobot drops to R2 500, the price of the competitor increases to R3 300 and the average per capita income of the country increases to R28 000.

2.5.1. Calculate the new quantity of vacuum cleaners that iRobot-H can expect to sell. (1)

2.5.2. Calculate the arch elasticity of demand, cross price elasticity of demand and income elasticity of demand for iRobot-H vacuum cleaners.