The motor company Ford started its latest manufacturing facility for Ranger bakkies in Silverton, Tshane, Gauteng. The company employs some 6000 workers who all received a housing subsidy. Most of these workers bought newly erected houses in a township development near the factory.

You saw an opportunity in the market and started a security gate motor installation business in the are. The following relations describe the monthly demand and supply conditions for your business catering to new houses owners in the area:

Qd = 7,000 - 6P

Qs = -1,000 + 2P

Where Q = number of security gate motors expected to be installed each month

P = the price per motor installed

Required:

1. What are the equilibrium price and output levels?
2. Calculate the elasticity of demand at the equilibrium point.
3. What is the meaning of the elasticity value and what action can you take to increase your revenue?
4. What should happen in your market, apart from an adjustment in your price, to increase your demand (and sales)?
5. Suppose the South African economy has recovered after the COVID-19 pandemic and the demand for bakkies increases substantially. Ford has extended its plant and employs another 3,000 employees. A new development was launched in the area where most of the new workers bought their new houses. As a result, the demand for your security gate motors (to be installed) changes to Qd = 5,000 - 4P. At the same time a competitor also starts to install security gate motors. This causes your supply curve to change to

Qs = -740 + 3P. Calculate the new equilibrium quantity and price levels.

1. What will happen with your revenue per month after the changes have taken place and why?
2. When will you know that you will continue to stay in business over the short run after the introduction of the competitor.

Homebase (PTY) Ltd is the manufacturer of a robot vacuum cleaner, iRobot-H. It makes use of 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 24 months. From this equation the expected sales for the next 12 months can be estimated.

Q = 6,200 - 40P + 25Pc + 6.2Y + 0.3A + 0.20S

(2.002) (17.5) (6.2) (2.5) (0.09) (0.21) - Standard deviation (SEC) of each parameter

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 = $2,900
• Pc (in Rand) = Price of leading competitor's product = $3,500
• Y (in Rand) = Average per capita income in the country = $25,000
• A (in Rand) = Homebase's monthly advertising expenditure = $20,000
• 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:

1. Calculate the number of iRobot-H vacuum cleaners that Homebase (PTY) Ltd is expected to sell over the next 12 months.
2. What is the meaning of the variables -40P, + 6.2Y and 0.20S?
3. What is the meaning of the equation R² = 0.55?
4. Determine the t-values for P, Pc and Y, and discuss their significance.