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# Price elasticity of demand and price elasticity of supply

How do quantities supplied and demanded react to changes in price?

## Key points

• Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded—or supplied—divided by the percentage change in price.
• Elasticity can be described as elastic—or very responsive—unit elastic, or inelastic—not very responsive.
• Elastic demand or supply curves indicate that the quantity demanded or supplied responds to price changes in a greater than proportional manner.
• An inelastic demand or supply curve is one where a given percentage change in price will cause a smaller percentage change in quantity demanded or supplied.
• Unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied.

## What is price elasticity?

Both demand and supply curves show the relationship between price and the number of units demanded or supplied. Price elasticity is the ratio between the percentage change in the quantity demanded, start text, Q, end text, start subscript, d, end subscript, or supplied, start text, Q, end text, start subscript, s, end subscript, and the corresponding percent change in price.
The price elasticity of demand is the percentage change in the quantity demanded of a good or service divided by the percentage change in the price. The price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price.
Elasticities can be usefully divided into five broad categories: perfectly elastic, elastic, perfectly inelastic, inelastic, and unitary. An elastic demand or elastic supply is one in which the elasticity is greater than one, indicating a high responsiveness to changes in price. An inelastic demand or inelastic supply is one in which elasticity is less than one, indicating low responsiveness to price changes. Unitary elasticities indicate proportional responsiveness of either demand or supply.
Perfectly elastic and perfectly inelastic refer to the two extremes of elasticity. Perfectly elastic means the response to price is complete and infinite: a change in price results in the quantity falling to zero. Perfectly inelastic means that there is no change in quantity at all when price changes.
If . . .It Is Called . . .
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start fraction, percent, space, c, h, a, n, g, e, space, i, n, space, q, u, a, n, t, i, t, y, divided by, percent, space, c, h, a, n, g, e, space, i, n, space, p, r, i, c, e, end fraction, is greater than, 1Elastic
start fraction, percent, space, c, h, a, n, g, e, space, i, n, space, q, u, a, n, t, i, t, y, divided by, percent, space, c, h, a, n, g, e, space, i, n, space, p, r, i, c, e, end fraction, equals, 1Unitary
start fraction, percent, space, c, h, a, n, g, e, space, i, n, space, q, u, a, n, t, i, t, y, divided by, percent, space, c, h, a, n, g, e, space, i, n, space, p, r, i, c, e, end fraction, is less than, 1Inelastic
start fraction, percent, space, c, h, a, n, g, e, space, i, n, space, q, u, a, n, t, i, t, y, divided by, percent, space, c, h, a, n, g, e, space, i, n, space, p, r, i, c, e, end fraction, equals, 0Perfectly inelastic

### Using the midpoint method to calculate elasticity

To calculate elasticity, instead of using simple percentage changes in quantity and price, economists sometimes use the average percent change in both quantity and price. This is called the Midpoint Method for Elasticity:
start text, M, i, d, p, o, i, n, t, space, m, e, t, h, o, d, space, f, o, r, space, e, l, a, s, t, i, c, i, t, y, end text, equals, start fraction, start fraction, Q, start subscript, 2, end subscript, minus, Q, start subscript, 1, end subscript, divided by, left parenthesis, start fraction, Q, start subscript, 2, end subscript, plus, Q, start subscript, 1, end subscript, divided by, 2, end fraction, right parenthesis, end fraction, divided by, start fraction, P, start subscript, 2, end subscript, minus, P, start subscript, 1, end subscript, divided by, left parenthesis, start fraction, P, start subscript, 2, end subscript, plus, P, start subscript, 1, end subscript, divided by, 2, end fraction, right parenthesis, end fraction, end fraction
The advantage of the midpoint method is that we get the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base for both cases. The midpoint method is referred to as the arc elasticity in some textbooks.

### Using the point elasticity of demand to calculate elasticity

A drawback of the midpoint method is that as the two points get farther apart, the elasticity value loses its meaning. For this reason, some economists prefer to use the point elasticity method. In this method, you need to know what values represent the initial values and what values represent the new values.
start text, P, o, i, n, t, space, e, l, a, s, t, i, c, i, t, y, space, end text, equals, start fraction, start fraction, start text, n, e, w, space, end text, Q, minus, start text, i, n, i, t, i, a, l, space, end text, Q, divided by, start text, i, n, i, t, i, a, l, space, end text, Q, end fraction, divided by, start fraction, start text, i, n, i, t, i, a, l, space, end text, P, minus, start text, n, e, w, space, end text, P, divided by, start text, i, n, i, t, i, a, l, space, end text, P, end fraction, end fraction

## Calculating price elasticity of demand

Let’s apply these formulas to a practice scenario. We'll calculate the elasticity between points start text, A, end text and start text, B, end text in the graph below.
The graph shows a downward sloping line that represents the price elasticity of demand.
Image credit: Figure 1 in "Price Elasticity of Demand and Price Elasticity of Supply" by OpenStaxCollege, CC BY 4.0
First, apply the formula to calculate the elasticity as price decreases from $70 at point start text, B, end text to$60 at point start text, A, end text:
$\begin{array}{ccc} \mathrm{\% ~ change in quantity} & = & \frac{3,000–2,800}{\left (3,000+2,800\right )/2}~ \times ~ 100\\ & = & \frac{200}{2,900}~ \times ~ 100\\ & = & 6.9\\ \mathrm{\% change in price} & = & \frac{60–70}{\left (60+70\right )/2}~ \times ~ 100\\ & = & \frac{–10}{65}~ \times ~ 100\\ & = & –15.4\\ \text{Price elasticity of demand} & = & \frac{~ ~ ~ ~ 6.9\% }{–15.4\% }\\ & = & 0.45 \end{array}$
The elasticity of demand between point start text, A, end text and point start text, B, end text is start fraction, space, space, space, space, 6, point, 9, percent, divided by, –, 15, point, 4, percent, end fraction, or 0.45. Because this amount is smaller than one, we know that the demand is inelastic in this interval.
This means that, along the demand curve between point start text, B, end text and point start text, A, end text, if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 4.5% decrease in quantity demanded. A 10% decrease in the price will result in only a 4.5% increase in the quantity demanded.

## Calculating the price elasticity of supply

Now let's try calculating the price elasticity of supply. We use the same formula as we did for price elasticity of demand:
$\begin{array}{ccc} \text{Price elasticity of supply} & = & \frac{\mathrm{\% ~ change ~in ~quantity}}{\mathrm{\% ~ change~ in ~price}} \end{array}$
Assume that an apartment rents for $650 per month and, at that price, 10,000 units are rented—you can see these number represented graphically below. When the price increases to$700 per month, 13,000 units are supplied into the market.
By what percentage does apartment supply increase? What is the price sensitivity?
The graph shows an upward sloping line that represents the supply of apartment rentals.
Image credit: Figure 2 in "Price Elasticity of Demand and Price Elasticity of Supply" by OpenStaxCollege, CC BY 4.0
We'll start by using the Midpoint Method to calculate percentage change in price and quantity:
$\begin{array}{ccc} \mathrm{\% ~ change~ in~ quantity} & = & \frac{13,000–10,000}{\left (13,000+10,000\right )/2}~ \times ~ 100\\ & = & \frac{3,000}{11,500}~ \times ~ 100\\ & = & 26.1\\ \mathrm{\% ~ change~ in~ price} & = & \frac{\ 700–\ 650}{\left (\ 700+\ 650\right )/2}~ \times ~ 100\\ & = & \frac{50}{675}~ \times ~ 100\\ & = & 7.4\end{array}$
Next, we take the results of our calculations and plug them into the formula for price elasticity of supply:
$\begin{array}{ccc} \mathrm{Price~ elasticity~ of~ supply} & = & \frac{\mathrm{\% change~ in~ quantity}}{\mathrm{\% change~ in~ price}}\\ & = & \frac{26.1}{7.4}\\ & = & 3.53 \end{array}$
Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more. It is read as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change.

## Summary

• Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded—or supplied—divided by the percentage change in price.
• Elasticity can be described as elastic—or very responsive—unit elastic, or inelastic—not very responsive.
• Elastic demand or supply curves indicate that the quantity demanded or supplied responds to price changes in a greater than proportional manner.
• An inelastic demand or supply curve is one where a given percentage change in price will cause a smaller percentage change in quantity demanded or supplied.
• Unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied.

## Self-check questions

Using the data shown in the table below about demand for smart phones, calculate the price elasticity of demand from point start text, B, end text to point start text, C, end text, point start text, D, end text to point start text, E, end text, and point start text, G, end text to point start text, H, end text. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
PointsPQ
A603,000
B702,800
C802,600
D902,400
E1002,200
F1102,000
G1201,800
H1301,600
Using the data shown in in the table below about supply of alarm clocks, calculate the price elasticity of supply from: point start text, J, end text to point start text, K, end text, point start text, L, end text to point start text, M, end text, and point start text, N, end text to point start text, P, end text. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
PointPriceQuantity Supplied
J$850 K$970
L$1080 M$1188
N$1295 P$13100

## Review Questions

• What is the formula for calculating elasticity?
• What is the price elasticity of demand? Can you explain it in your own words?
• What is the price elasticity of supply? Can you explain it in your own words?

## Critical-thinking questions

• Transatlantic air travel in business class has an estimated elasticity of demand of 0.40 less than transatlantic air travel in economy class, which has an estimated price elasticity of 0.62. Why do you think this is the case?
• What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that?

## Problems

• The equation for a demand curve is P, equals, 48, –, 3, Q. What is the elasticity in moving from a quantity of 5 to a quantity of 6?
• The equation for a demand curve is P, equals, 2, slash, Q. What is the elasticity of demand as price falls from 5 to 4? What is the elasticity of demand as the price falls from 9 to 8? Would you expect these answers to be the same?
• The equation for a supply curve is 4, P, equals, Q. What is the elasticity of supply as price rises from 3 to 4? What is the elasticity of supply as the price rises from 7 to 8? Would you expect these answers to be the same?
• The equation for a supply curve is P, equals, 3, Q, –, 8. What is the elasticity in moving from a price of 4 to a price of 7?

## Want to join the conversation?

• Transatlantic air travel in business class has an estimated elasticity of demand of 0.40 less than transatlantic air travel in economy class, with an estimated price elasticity of 0.62. Why do you think this is the case? For me, I feel that it is because business flights has a higher degree of necessity as compared to economy flights meant for leisure. As such, a change in airfare prices for business flights wouldn't impact much of the quantity demanded due to its higher indispensability.
• I would say that it is simply because business class travelers care less about the price, given that they are already not buying the cheapest option.
• What is the answer to critical question No.1
• The change in price has a less impact on preferences of the people with higher incomes, who prefer the business class. The price is not the most important criterion for these people, that is why any given percentage change in price will cause a smaller percentage change in quantity demanded.
The influence of the change in price is bigger for the people with less incomes, who prefer the economy class. This statistic shows us that the price has a remarkable significance for these people, because their purchasing power is less than people in business class, that is why the price should be a more important criterion for them. Additionally, despite the wage gap between the consumers the demand curve is inelastic for both classes in Transatlantic Air Travel.
• Hey for the first set of elasticity, from going to G to H it says the % change in price is 7.81 but when I divide 10 by 125 I get 0.08 which is 8%, so am I doing it wrong or is the answer wrong?
• You're right. It's supposed to be 8%. The answer is wrong.
• to find the price elasticity of the entire demand curve, is it correct to find the elasticity for all points and find the average of those values?
• No, there is no such thing as a price elasticity of the entire curve. The price elasticity is different for every point.
• Here's my answers to the problems:
(1) E = |(1/5.5)/(-3/31.5)| = 1.91 Thus the demand curve is elastic here.
(2) E1 = |(0.1/0.45)/(-1/4.5)| = 1 E2 = | [(1/36)/(17/72)]/(-1/8.5) | = 1 The demand curve at the two points are both unit elastic. In fact, the elasticity of price at every point of the curve equals to 1. Since P always equals to 2/Q on this curve, ΔP = P(new) - P(old) = 2/Q(new) - 2/Q(old) = 2(Q(old) - Q(new))/Q(new)*Q(old) = 2ΔQ/[Q(new)*Q(old)]; similarly, P(average) = (Q(new) + Q(old)) / Q(new)*Q(old). Thus we get %ΔP = 2ΔQ/(Q(new) + Q(old)) and plug it into the formula E = %ΔQ/%ΔP, we get E = (ΔQ * (Q(new) + Q(old))) / (0.5 * (Q(new) + Q(old)) * 2ΔQ) = 1.
(3) The method is the same as above. E1 = E2 = 1.
(4) E = 0.41
Hope it helps! :)
• Should i use the absolute values for the change of quantity and price if i want to measure elasticity? Because if i don't most of the problems turn out to be inelastic since the Elasticity is smaller than 1. is that correct?
• You could use the absolute values for the change of quantity and price, as you said, or you could just do the absolute value of the result of your calculation.Both methods are correct.
• Another question is, what happen if both demand and supply increase, but there is a larger increase in demand than the supply? How would the graph looks like? Pls do help me
• In the example above (apartments), when calculating the price elasticity of supply, why do you also split the change in price by two?
According to the example the answer is 7.4 %, shouldn't it be 14.8 % ?
• Incorrect. He made a wrong input in the y value but did the math correct. It was supposed to be 700-650 not 600.
(1 vote)
• I'm confused on problem 2. Since the problem Already gave me the price I thought all I had to do was find the quantity demanded. So I rewrote the equation as 2P=Q. But with that I end up with an equation of a supply curve then a demand. Please help!
(1 vote)
• P = 2/Q cannot be re-written as 2P = Q. That's incorrect algebra.
• Are there answers to the problems?
(1 vote)
• The answers to the self-check questions are below the questions. The answers to the other questions aren't given.