Price elasticity of demand (PED) shows the relationship between price and quantity demanded and provides a precise calculation of the effect of a change in price on quantity demanded.
We can use this equation to calculate the
effect of price changes on quantity demanded, and on the
revenue received by firms before and after any
price change.
For example, if the price of a daily newspaper increases from £1.00 to £1.20p, and the daily sales falls from 500,000 to 250,000, the PED will be:
There are three ‘types’ of revenue:
Study the patterns of numbers and see if you can analyse the relationships between the three measures of revenue – then answer the following:
.
For example, if the price of a daily newspaper increases from £1.00 to £1.20p, and the daily sales falls from 500,000 to 250,000, the PED will be:
 50% / + 20%
= () 2.5
The negative sign indicates
that P and Q are inversely related,
which we would expect for most price/demand relationships.
This is significant because the newspaper supplier can calculate or
estimate how revenue will be affected by the change in price. In
this case, revenue at £1.00 is £500,000 (£1 x 500,000) but falls to
£300,000 after the price rise (£1.20 x 250,000).
PED can also be:
The range of responses
The degree of response of quantity demanded to a change in price can vary considerably. The key benchmark for measuring elasticity is whether the coefficient is greater or less than proportionate. If quantity demanded changes proportionately, then the value of PED is 1, which is called ‘unit elasticity’.PED can also be:

Less than one, which means PED is
inelastic.

Greater than one, which is
elastic.

Zero (0), which is
perfectly inelastic.

Infinite (∞), which is
perfectly elastic.
PED along a linear demand
curve
PED on a linear demand curve will fall
continuously as the curve slopes downwards, moving from left to
right. PED = 1 at the midpoint of a linear demand curve.
PED and revenue
There is a precise mathematical connection between PED and a firm’s revenue.There are three ‘types’ of revenue:

Total revenue (TR), which is found by
multiplying price by quantity sold (P x Q).

Average revenue (AR), which is found by dividing
total revenue by quantity sold (TR/Q).
Consider these figures and calculate Total, Marginal and
Average Revenue.

Marginal revenue (MR), which is defined as the
revenue from selling one extra unit. This is calculated by finding
the change in TR from selling one more unit.
PRICE (£) Qd TR MR AR 10 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10
Study the patterns of numbers and see if you can analyse the relationships between the three measures of revenue – then answer the following:

How are price and average revenue connected?

What happens to total revenue as output
increases?

What is the connection between total revenue and
marginal revenue?

How are marginal revenue and average
revenue connected?
Observations
When TR is at a maximum, MR = zero, and PED = 1 Price and AR are identical, because AR = TR/Q, which is P x Q/Q, and cancel out the Qs to get P.
 A curve plotting AR (=P) against Q is also a firm’s demand curve.
 TR increases, reaches a peak and decreases.
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