Elasticity

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:

- 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).

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 co-efficient 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:

1. Total revenue (TR), which is found by multiplying price by quantity sold (P x Q).
   
2. 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.
   
3. 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

   
   

Answer
Study the patterns of numbers and see if you can analyse the relationships between the three measures of revenue – then answer the following:

1. How are price and average revenue connected?
   
2. What happens to total revenue as output increases?
   
3. What is the connection between total revenue and marginal revenue?
   
4. How are marginal revenue and average revenue connected?
   

Observations

When TR is at a maximum, MR = zero, and PED = 1.

1. Price and AR are identical, because AR = TR/Q, which is P x Q/Q, and cancel out the Qs to get P.
2. A curve plotting AR (=P) against Q is also a firm’s demand curve.
3. TR increases, reaches a peak and decreases.

Why does a firm want to know PED?

There are several reasons why firms gather information about the PED of its products. A firm will know much more about its internal operations and product costs than it will about its external environment. Therefore, gathering data on how consumers respond to changes in price can help reduce risk and uncertainly. More specifically, knowledge of PED can help the firm forecast its sales and set its price.

Sales forecasting

The firm can forecast the impact of a change in price on its sales volume, and sales revenue (total revenue, TR). For example, if PED for a product is (-) 2, a 10% reduction in price (say, from £10 to £9) will lead to a 20% increase in sales (say from 1000 to 1200). In this case, revenue will rise from £10,000 to £10,800.

Pricing policy

Knowing PED helps the firm decide whether to raise or lower price, or whether to price discriminate. Price discrimination is a policy of charging consumers different prices for the same product. If demand is elastic, revenue is gained by reducing price, but if demand is inelastic, revenue is gained by raising price.

Non-pricing policy

When PED is highly elastic, the firm can use advertising and other promotional techniques to reduce elasticity.