Price elasticity of demand
Author: Geoff Riley Last updated: Sunday 23 September, 2012
Price elasticity of demand measures the responsiveness of demand after a change in price
The formula for calculating the co-efficient of elasticity of demand is:
Percentage change in quantity demanded divided by the percentage change in price
Since changes in price and quantity usually move in opposite directions, usually we do not bother to
put in the minus sign. We are more concerned with the co-efficient of elasticity of demand.
Example: Demand for rail services
At peak times, the demand for rail transport becomes inelastic – and higher prices are charged by rail
companies who can then achieve higher revenues and profits
Values for price elasticity of demand
1. If Ped = 0 demand is perfectly inelastic - demand does not change at all when the price
changes – the demand curve will be vertical.
2. If Ped is between 0 and 1 (i.e. the % change in demand from A to B is smaller than the
percentage change in price), then demand is inelastic.
3. If Ped = 1 (i.e. the % change in demand is exactly the same as the % change in price), then
demand isunit elastic. A 15% rise in price would lead to a 15% contraction in demand leaving
total spending the same at each price level.
4. If Ped > 1, then demand responds more than proportionately to a change in price i.e. demand
is elastic. For example if a 10% increase in the price of a good leads to a 30% drop in demand.
The price elasticity of demand for this price change is –3
Factors affecting price elasticity of demand

The number of close substitutes – the more close substitutes there are in the market, the more
elastic is demand because consumers find it easy to switch

The cost of switching between products – there may be costs involved in switching. In this
case, demand tends to be inelastic. For example, mobile phone service providers may insist on
a12 month contract.

The degree of necessity or whether the good is a luxury – necessities tend to have an inelastic
demand whereas luxuries tend to have a more elastic demand.

The proportion of a consumer’s income allocated to spending on the good – products that take
up a high % of income will have a more elastic demand

The time period allowed following a price change – demand is more price elastic, the longer
that consumers have to respond to a price change. They have more time to search for cheaper
substitutes and switch their spending.

Whether the good is subject to habitual consumption – consumers become less sensitive to the
price of the good of they buy something out of habit (it has become the default choice).

Peak and off-peak demand - demand is price inelastic at peak times and more elastic at offpeak times – this is particularly the case for transport services.

The breadth of definition of a good or service – if a good is broadly defined, i.e. the demand
for petrol or meat, demand is often inelastic. But specific brands of petrol or beef are likely to
be more elastic following a price change.
Demand curves with different price elasticity of demand
Elasticity of demand and total revenue for a producer / supplier
The relationship between elasticity of demand and a firm’s total revenue is an important one.

When demand is inelastic – a rise in price leads to a rise in total revenue – a 20% rise in price
might cause demand to contract by only 5% (Ped = -0.25)

When demand is elastic – a fall in price leads to a rise in total revenue - for example a 10% fall
in price might cause demand to expand by only 25% (Ped = +2.5)
Peak and Off-Peak Demand and Prices
Why are prices for package holidays more expensive during school holiday weeks? Why are rail fares
more expensive at peak times? During peak demand periods, market demand is higher and also more
price inelastic. This allows producers to sell their products for higher prices and make increased
profits.
The table below gives an example of the relationships between prices; quantity demanded and total
revenue. As price falls, the total revenue initially increases, in our example the maximum revenue
occurs at a price of £12 per unit when 520 units are sold giving total revenue of £6240.
Price
Quantity
Total Revenue
Marginal Revenue
£ per unit
Units
£s
£s
20
200
4000
18
280
5040
13
16
360
5760
9
14
440
6160
5
12
520
6240
1
10
600
6000
-3
8
680
5440
-7
6
760
4560
-11
Consider the elasticity of demand of a price change from £20 per unit to £18 per unit. The % change
in demand is 40% following a 10% change in price – giving an elasticity of demand of -4 (i.e. highly
elastic).
In this situation when demand is price elastic, a fall in price leads to higher total consumer spending /
producer revenue
Consider a price change further down the estimated demand curve – from £10 per unit to £8 per unit.
The % change in demand = 13.3% following a 20% fall in price – giving a co-efficient of elasticity of –
0.665 (i.e. inelastic). A fall in price when demand is price inelastic leads to a reduction in total
revenue.
Change in the market
What happens to total revenue?
Ped is inelastic and a firm raises its price.
Total revenue increases
Ped is elastic and a firm lowers its price.
Total revenue increases
Ped is elastic and a firm raises price.
Total revenue decreases
Ped is -1.5 and the firm raises price by 4%
Total revenue decreases
Ped is -0.4 and the firm raises price by 30%
Total revenue increases
Ped is -0.2 and the firm lowers price by 20%
Total revenue decreases
Ped is -4.0 and the firm lowers price by 15%
Total revenue increases
Elasticity of demand and indirect taxation
Many products are subject to indirect taxes. Good examples include the duty on cigarettes (cigarette
taxes in the UK are among the highest in Europe) alcohol and fuel. Here we consider the effects of
indirect taxes on costs and the importance of elasticity of demand in determining the effects of a tax
on price and quantity.
A tax increases the costs of a business causing an inward shift in supply. The vertical distance
between the pre-tax and the post-tax supply curve shows the tax per unit. With an indirect tax, the
supplier may be able to pass on some or all of this tax to the consumer by raising price. This is
known as shifting the burden of the tax and this depends on the elasticity of demand and supply.
Consider the two charts above.

In the left hand diagram, the demand curve is drawn as price elastic. The producer must
absorb the majority of the tax itself (i.e. accept a lower profit margin on each unit sold). When
demand is elastic, the effect of a tax is still to raise the price – but we see a bigger fall
in equilibrium quantity. Output has fallen from Q to Q1 due to a contraction in demand.

In the right hand diagram, demand is drawn as price inelastic (i.e. Ped <1 over most of the
range of this demand curve) and therefore the producer is able to pass on most of the tax to
the consumer through a higher price without losing too much in the way of sales. The price
rises from P1 to P2 – but a large rise in price leads only to a small contraction in demand from
Q1 to Q2.
Example: Will price cuts work for Sony?
Sony is cutting the price of its PlayStation 3 gaming console by nearly a fifth, hoping to jump-start
sales of a five-year old device losing ground to Microsoft's Xbox. The price tag on the 160 GB version
has fallen to £200 in the UK and from €299 to €249 in Europe
News reports, Aug 2011.
The usefulness of price elasticity for producers
Firms can use PED estimates to predict:

The effect of a change in price on the total revenue & expenditure on a product.

The price volatility in a market following changes in supply – this is important for commodity
producers who suffer big price and revenue shifts from one time period to another.

The effect of a change in an indirect tax on price and quantity demanded and also whether the
business is able to pass on some or all of the tax onto the consumer.

Information on the PED can be used by a business as part of a policy of price discrimination.
This is where a supplier decides to charge different prices for the same product to different
segments of the market e.g. peak and off peak rail travel or prices charged by many of our
domestic and international airlines.

Usually a business will charge a higher price to consumers whose demand for the product is
price inelastic
Price elasticity of demand and changing market prices
The price elasticity of demand will influence the effects of shifts in supply on price and quantity in a
market. This is illustrated in the next two diagrams.
In the left hand diagram below we have drawn a highly elastic demand curve. We see an outward shift
of supply – which leads to a large rise in equilibrium price and quantity and only a relatively small
change in the market price.
In the right hand diagram, a similar increase in supply is drawn together with an inelastic demand
curve. Here the effect is more on the price. There is a sharp fall in the price and only a relatively small
expansion in the equilibrium quantity.
PRICE ELASTICITY
Price Elasticity of Demand – the responsiveness of quantity demanded to changes in price.
Price elasticity of demand =
Cross elasticity of demand =
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑑𝑒𝑚𝑎𝑛𝑑𝑒𝑑
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑑𝑒𝑚𝑎𝑛𝑑𝑒𝑑 𝑔𝑜𝑜𝑑 𝑎
Price elasticity of supply =
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒 𝑔𝑜𝑜𝑑 𝑏
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒
Values for price elasticity of demand
5. If Ped = 0 demand is perfectly inelastic - demand does not change at all when the price changes – the
demand curve will be vertical.
6. If Ped is between 0 and 1 (i.e. the % change in demand from A to B is smaller than the percentage
change in price), then demand is inelastic.
7. If Ped = 1 (i.e. the % change in demand is exactly the same as the % change in price), then demand
isunit elastic. A 15% rise in price would lead to a 15% contraction in demand leaving total spending
the same at each price level.
8. If Ped > 1, then demand responds more than proportionately to a change in price i.e. demand is
elastic. For example if a 10% increase in the price of a good leads to a 30% drop in demand. The price
elasticity of demand for this price change is –3
The table below gives an example of the relationships between prices; quantity demanded and total
revenue.
Change in the market
What happens to total revenue?
Ped is inelastic and a firm raises its price.
Total revenue increases
Ped is elastic and a firm lowers its price.
Total revenue increases
Ped is elastic and a firm raises price.
Total revenue decreases
Ped is -1.5 and the firm raises price by 4%
Total revenue decreases
Ped is -0.4 and the firm raises price by 30%
Total revenue increases
Ped is -0.2 and the firm lowers price by 20%
Total revenue decreases
Ped is -4.0 and the firm lowers price by 15%
Total revenue increases
PRICE ELASTICITY - PROBLEMS
Problem 1 : Yesterday, the price of envelopes was $3 a box, and Julie was willing to buy 10 boxes. Today, the
price has gone up to $3.75 a box, and Julie is now willing to buy 8 boxes. Is Julie's demand for envelopes elastic
or inelastic? What is Julie's elasticity of demand?
To find Julie's elasticity of demand, we need to divide the percent change in quantity by the percent change in
price.
Her elasticity of demand is the absolute value of _________. Julie's elasticity of demand is elastic/ inelastic,
since it is less/more than 1.
Problem 2: If Neil's elasticity of demand for hot dogs is constantly 0.9, and he buys 4 hot dogs when the price is
$1.50 per hot dog, how many will he buy when the price is $1.00 per hot dog?
This time, we are using elasticity to find quantity, instead of the other way around. We will use the same formula,
plug in what we know, and solve from there.
Problem 3: Which of the following goods are likely to have elastic demand, and which are likely to have inelastic
demand?
Water
Home heating oil
Pepsi
Heart medication
Oriental rugs
Chocolate
Problem 4: If supply is unit elastic and demand is inelastic, a shift in which curve would affect quantity more?
Price more?
Problem 5: Katherine advertises to sell cookies for $4 a dozen. She sells 50 dozen, and decides that she can
charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the elasticity of demand?
Assuming that the elasticity of demand is constant, how many would she sell if the price were $10 a box?
To find the elasticity of demand, we need to divide the percent change in quantity by the percent change in
price.
The elasticity of demand is ________ and is Elastic / Inelastic
To find the quantity when the price is $10 a box, we use the same formula:
The new demand at ____________ a dozen will be ___________ dozen cookies.
Multiple Choice
1. The quantity of a good demanded rises from 1000 to 1500 units when the price falls from
$1.50 to $1.00 per unit. The price elasticity of demand for this product is approximately:
A. 1.0
B. .16
C. 2.5
D. 4.0
2. If the elasticity of demand for a commodity is estimated to be 1.5, then a decrease in price
from $2.10 to $1.90 would be expected to increase daily sales by:
A. 50%
B. 1.5%
C. 5%
D. 15%
3. Demand is said to be inelastic when:
A. the percentage change in quantity demanded is greater than the percentage change
in price of a good
B. in a linear demand curve, quantity demanded is close to zero (given the price) so that
the percentage change in quantity demanded will be very high
C. the percentage change in price exceeds the percentage change in quantity demanded
of a good
D. a relatively small change in price results in a relatively big change in quantity
demanded
4. Suppose that the Board of Directors of the local symphony proposes that the admission
price to hear the orchestra be raised as a means of raising additional funds to support music
programs. Its members are implicitly assuming that the price elasticity of demand for a ticket
is:
A. less than unity
B. greater than unity
C. unity
D. it really says nothing about price elasticity
5. The determinants of the price elasticity of demand of a particular commodity include all of
the following except:
A. the availability of substitutes for the commodity
B. the time period involved
C. the ease with which resources can be shifted to and from the production of this
commodity to other uses
D. the degree of specificity with which the commodity is defined
6. The fact that the expenditure on food as a percentage of income has declined as income has
increased indicates that food:
A. is an inferior good
B. is a luxury good
C. has an income elasticity of demand less than unity
D. is a normal good with an elastic demand
E. there is not enough information to be able to determine what type of good food is
7. A tax will be borne completely by suppliers if:
A. the demand curve is perfectly inelastic while the supply curve is upward sloping
B. the demand curve is downward sloping while the supply curve is perfectly inelastic
C. the supply curve is perfectly elastic and the demand curve is negatively slope
D. price elasticities of both supply and demand equal one
E. both the demand and supply curves are perfectly inelastic
8. The quantity of a good demanded rises from 90 units to 110 units when the price falls from
$1.20 to $.80 per unit. The price elasticity of demand for this product approximates:
A. .5
B. 1.0
C. 2.0
D. 4.0
9. A downhill ski area is experiencing a decline in the number of lift tickets sold, falling
revenues, and inadequate profits. The average price of a lift ticket is $20 and there are 2,500
tickets sold daily on average. The estimated price elasticity of demand is 1.5 and the lifts are
currently operating at an average of 75 percent of capacity. Which of the following methods is
most likely to increase the ski area's revenues and profits.
A. a 10 percent increase in the average price of a lift ticket.
B. an aggresive advertising campaign.
C. a 10 percent increase in the average price of a lift ticket combined with an aggresive
advertising campaign.
D. a 10 percent decrease in the average price of a lift ticket.
10. Consumers will bear more of the burden of a tax the:
A. more elastic supply is.
B. more elastic demand is.
C. the more inelastic supply is.
D. consumers always bear the burden of the tax since they pay the final price.
E. none of the above.
11. An income elasticity of demand equal to 2 for a particular product means that:
A. demand curves for the product slope upward.
B. the product is an inferior good.
C. a 10 percent increase in income will yield a 20 percent increase in the quantity sold.
D. a 20 percent increase in income will result in a 10 percent increase in the quantity
sold.
E. (% change in Q) / (% change in P) = 2.
12. From which of the following data might you estimate a price elasticity of supply?
A. a price hike from $7 to $13 causes sales to fall from 16,000 shirts to 8,000 shirts
monthly.
B. farmers increase soybean plantings 15 percent when the price increases 5 percent.
C. Ford's production increases when Chevy sales fall because GM raises prices.
D. the output of tennis balls slumps 8 percent when the prices of racquets go up 12
percent.
E. steel production and sales rise 18 percent when national income grows 13 percent.
Use the graph below to answer question number 13
13. Total revenue:
A. varies inversely with price in range b.
B. is always maximized at the midpoint of any demand curve.
C. remains unchanged as price changes in range b.
D. varies directly with price in range a.
E. none of the above.
14. In the last 20 years real medical expenditures have more than doubled. Physicians supply
medical services at a lower cost than do hospitals. Thus, it has been suggested that total
medical expenditures could be decreased by increasing the supply of physicians. Which of the
following findings would support this position?
A. it is found that the cross elasticity of demand between physicians and hospitals is
positive and relatively large.
B. it is found that the cross elasticity of demand between physicians and hospitals is
negative and relatively large in absolute value.
C. it is found that the cross elasticity of demand between physicians and hospitals is
relatively large in absolute value.
D. it is found that the demand for physicians is relatively inelastic.
E. there is not enough information given above to determine the effect that an increase
in the supply of physicians will have on medical expenditures.
15. You are a supplier of peanuts. Your research department estimates that the price elasticity
of demand for peanuts is 2.5. By what percentage will quantity demanded rise if you lower
price from $4 to $2?
A. 16.67 percent.
B. 167 percent.
C. 67 percent.
D. 50 percent.
E. none of the above.
16. A long-run demand curve, as compared to a short-run demand curve for the same
commodity, is generally:
A. more elastic
B. less elastic
C. of the same elasticity
D. steeper if the curves are plotted against the same horizontal scale.
E. none of the above.
ADDITIONAL - Practice Problems on Elasticity
1. Anna owns the Sweet Alps Chocolate store. She charges $10 per pound for her hand made
chocolate. You, the economist, have calculated the elasticity of demand for chocolate in her town
to be 2.5. If she wants to increase her total revenue, what advice will you give her and why? Be
able to explain your answer.
2. If the cross elasticity of demand between peanut butter and milk is -1.11, then are peanut butter
and milk substitutes or complements? Be able to explain your answer.
3. A 10 percent increase in income brings about a 15 percent decrease in the demand for a good.
What is the income elasticity of demand and is the good a normal good or an inferior good? Be
able to explain your answer.
4. If the price of a good increases by 8% and the quantity demanded decreases by 12%, what is
the price elasticity of demand? Is it elastic, inelastic or unitary elastic?
5. Discount stores sell relatively elastic goods. Ceteris paribus, explain why selling at a relatively
low price is profitable for them?