Page 393 - PM Integrated Workbook 2018-19

Answers

Chapter 5

Example 1

Find the linear relationship between price (P) and the quantity demanded (Q),
i.e. find the straight-line demand equation, in relation to the following sales and
demand data:

Selling price of $200 = sales of 1,000 units per month.

Selling price of $220 = sales of 950 units per month.

(a) Use this equation to predict the quantity demanded per month if the
selling price is $300.

Step 1: Find the gradient, b

The question provides us with two selling prices and the respective level
of demand at these selling prices. Therefore, we can begin by calculating
the gradient of the straight line, b.

b (gradient) = change in price/change in quantity

b = (220 – 200)/(950 – 1,000) = – 0.4

Step 2: Calculate the intersect, a

Once the gradient is known the intersect can be found using either of the
selling prices and demand levels given in the question.

For example:

Price (P) = 200 when 1000 units (Q) are sold, and substituting – 0.4 for b:

200 = a – (0.4 × 1,000)

200 = a – 400

a = 200 + 400 = 600

Step 3: Straight-line demand equation

So the equation is: P = 600 – 0.4Q.

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