Question 2 [27]

You are the owner of Bushveld Pizzas (Pty) Ltd in the new mall at Hazy View in Mpumalanga.

After your first year, you decided to do some research to determine what your expected weekly

sales (quantity demanded) will be in order to plan your cash flow. Your research consists of

three components:

A: From your till slips you gathered and captured the following data:

Every time you increased or reduced the average price of your pizzas by 10%, your

sales decreased or increased by 30%.

Irrespective of an increase or decrease in the price of your pizzas, sales on Fridays

were 500 units more compared to every other day of the week.

Every time that your only competitor in the mall, Greasy Hamburgers (Pty) Ltd,

increased (reduced) the price of its double hamburgers by 10%, your sales increased

(decreased) by 20%.

B. Every week you spend R1 000 on advertisements by placing flyers under the windscreen

wipers of the parked vehicles in the parking area of the mall. You realised that your sales

dropped by 10% during the weeks that you did not complete, but increased by 10% if you did

this again the following week.

C. From the answers to a questionnaire that you asked customers to fill in at the shop you

established that they increased their spending on pizzas by 0.05% per week for each 1%

increase in their disposable income. From their answers you also gathered that the average

weekly income of your customers is R6 000 per household.

You asked one of your part-time waitresses, who is a student in economics, to put a regression

analysis of the data you gathered.

She found the following:

R2 = 0.65, n = 252, the standard deviation (SEC) for your price (P) = 1.5, that of income

(Y) = 0.02 and that of advertising (A) = 0.06. The t-value for the price of the competitor (Pc) = 4.

The current average price for a pizza is R90.00 and for a double Hamburger it is R80.00.

Required:

2.1. Determine the equation for expected pizza sales (Q). (3)

2.2. Calculate the expected weekly sales. (2)

2.3. Calculate the elasticities for the independent variables. (9)

2.4. What is the meaning of the elasticity values for P, Pc and Y? (3)

2.5. What is the meaning of R2 = 0.65 and n = 252? (2)

2.6. Calculate the t-values for the price of a pizza (P), income (Y) and advertising (A) and

explain their meaning. (6)

2.7. Calculate the standard deviation (SEC) for the price of a hamburger (Pc). (2)

Question 3 [19]

Dash Engineering Ltd is planning a new factory. Dash's chief executive officer (CEO) instructed

the planning team that production efficiency in the long term is the single most important

criterion when the potential capacity levels are considered. Manufacturing cost is a critical

driver of competitiveness in the industry, and the CEO made it very clear that achieving

economies of scale in the production process is non-negotiable.

The planning team prepared the following production and cost information associated with

different production capacity levels:

Production

capacity level

Total output

Long-run total

cost (LRTC)

I 10 000 50 000

II 25 000 90 000

III 62 500 120 000

IV 156 000 150 000

V 359 000 200 000

VI 683 000 260 000

VII 1 161 000 390 000

VIII 1 741 000 585 000

IX 2 089 000 877 500

X 2 298 000 1 320 000

Required:

3.1. Calculate the long-run marginal cost per unit and long-run average cost for each

capacity level for the CEO and present your answers in table format. (10)

3.2. From the information prepared in 3.1,organise second table based on production

capacity levels