A measure of the size of the effect on demand of a change in selling price is called the price
elasticity of demand.
Price elasticity of demand (PED) =
% change in demand
% change in price
A high PED means that the demand is very sensitive to changes in price, or
elastic
.
A low PED means that the demand is not very sensitive to changes in price, or
inelastic
.
E
XAMPLE
3
Using the figures from example 2, calculate the price elasticity of demand
if the current selling price is $16 per unit
if the current selling price is $15 per unit
27
June 2014 Examinations
Paper F5
PRICING
Chapter 7

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6
Optimal pricing – equations
In section 4, we were presented with the price/demand relationship as a table, and used these
figures to calculate the optimum level of selling price from those available.
In principle, it would be possible to have an equation relating the selling price to the demand, and
to then solve the problem algebraically.
6.1
Price/demand equation
In the exam you could be asked to derive the price/demand equation yourself from information
given, or alternatively you could be given the equation. If you were asked to derive the equation
yourself, then it would always be on the basis that the relationship was linear (as is the case in
example 2, from inspection).
($)P
Q (units)
The equation would therefore be of the form:
P = a – bQ
where
P = selling price
Q = quantity demanded at that price
a = theoretical maximum price (if the price is set at ‘a’ or above, then the demand will
be zero)
b = the change in price required to change demand by 1 unit (the gradient of the line)
E
XAMPLE
4
A company sells an article at $12 per unit and has a demand of 16,000 units at this price.
If the selling price were to be increased by $1 per unit, it is estimated that demand will fall by 2,500 units.
On the assumption that the price/demand relationship is linear, derive the equation relating the sell-
ing price to the demand.
June 2014 Examinations
Paper F5
PRICING
Chapter 7
28

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6.2
Optimal selling price
Having identified the price/demand relationship, it is easy to derive the equation for the revenue
at any level – the total revenue will be equal to PQ.
We could then show on a graph the total revenue and total costs for any level of demand. It would
be of this sort of shape:
($)
(units)
Our objective is to maximise profit. We can do this by calculating the Marginal Revenue and
Marginal Cost, and using the fact that the profit is maximised when the two are equal.
E
XAMPLE
5
A company currently has a demand for one of its products of 2000 units at a selling price of $30 per unit.

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