Price elasticity of demand and price elasticity of supply (article)

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, $Q_{d}$ ‍, or supplied, $Q_{s}$ ‍, 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 . . .
$\frac{% change in quantity}{% change in price} = \infty$ ‍	Perfectly elasti
$\frac{% change in quantity}{% change in price} > 1$ ‍	Elastic
$\frac{% change in quantity}{% change in price} = 1$ ‍	Unitary
$\frac{% change in quantity}{% change in price} < 1$ ‍	Inelastic
$\frac{% change in quantity}{% change in price} = 0$ ‍	Perfectly 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:

$Midpoint method for elasticity = \frac{\frac{Q_{2} - Q_{1}}{(\frac{Q_{2} + Q_{1}}{2})}}{\frac{P_{2} - P_{1}}{(\frac{P_{2} + P_{1}}{2})}}$ ‍

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.

$Point elasticity = \frac{\frac{new Q - initial Q}{initial Q}}{\frac{initial P - new P}{initial P}}$ ‍

Calculating price elasticity of demand

Let’s apply these formulas to a practice scenario. We'll calculate the elasticity between points $A$ ‍ and $B$ ‍ in the graph below.

The graph shows a downward sloping line that represents the price elasticity of demand.

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:

$\begin{array}{ccc} Price elasticity of supply & = & \frac{% change in quantity}{% change in price} \end{array}$ ‍

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.

We'll start by using the Midpoint Method to calculate percentage change in price and quantity:

$\begin{array}{ccc} % change in quantity & = & \frac{13, 000 - 10, 000}{(13, 000 + 10, 000) / 2} \times 100 \\ = & \frac{3, 000}{11, 500} \times 100 \\ = & 26.1 \\ % change in price & = & \frac{$ 700 - $ 650}{($ 700 + $ 650) / 2} \times 100 \\ = & \frac{50}{675} \times 100 \\ = & 7.4 \end{array}$ ‍

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 $B$ ‍ to point $C$ ‍, point $D$ ‍ to point $E$ ‍, and point $G$ ‍ to point $H$ ‍. Classify the elasticity at each point as elastic, inelastic, or unit elastic.

Points	P	Q
A	60	3,000
B	70	2,800
C	80	2,600
D	90	2,400
E	100	2,200
F	110	2,000
G	120	1,800
H	130	1,600

[Show solution.]

Using the data shown in in the table below about supply of alarm clocks, calculate the price elasticity of supply from: point $J$ ‍ to point $K$ ‍, point $L$ ‍ to point $M$ ‍, and point $N$ ‍ to point $P$ ‍. Classify the elasticity at each point as elastic, inelastic, or unit elastic.

Point	Price	Quantity Supplied
J	$8	50
K	$9	70
L	$10	80
M	$11	88
N	$12	95
P	$13	100

[Show solution.]

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 $P = 48 - 3 Q$ ‍. What is the elasticity in moving from a quantity of 5 to a quantity of 6?
The equation for a demand curve is $P = 2 / Q$ ‍. 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 $4 P = Q$ ‍. 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 $P = 3 Q - 8$ ‍. What is the elasticity in moving from a price of 4 to a price of 7?

[Attribution]

As an enthusiast with demonstrable expertise in the field of price elasticity, I'll provide a comprehensive understanding of the concepts covered in the article.

1. Price Elasticity Overview:

Definition: Price elasticity measures how the quantity demanded or supplied of a good responds to changes in its price.
Calculation: It is computed as the percentage change in quantity demanded (or supplied) divided by the percentage change in price.

2. Types of Elasticity:

Elasticity Categories:
- Perfectly Elastic
- Elastic
- Unitary
- Inelastic
- Perfectly Inelastic
Characteristics:
- Elastic: Elasticity greater than 1, indicating high responsiveness to price changes.
- Inelastic: Elasticity less than 1, indicating low responsiveness to price changes.
- Unitary: Elasticity equal to 1, indicating proportional responsiveness.

3. Calculating Elasticity:

Midpoint Method (Arc Elasticity):
- Formula: (Q2 - Q1) / ((Q2 + Q1) / 2) / (P2 - P1) / ((P2 + P1) / 2)
- Advantage: Provides consistent elasticity values regardless of price increase or decrease.
Point Elasticity:
- Formula: (New Q - Initial Q) / Initial Q / (Initial P - New P) / Initial P
- Drawback: Losing meaning as points get farther apart; some prefer the midpoint method.

4. Applying Formulas:

Example: Elasticity of Demand Calculation:
- Given a demand curve, if the price decreases from $70 to $60, and quantity changes from 2,800 to 3,000:
  - Result: Elasticity of demand is 0.45 (indicating inelastic demand).
Example: Elasticity of Supply Calculation:
- Given a supply curve, if price increases from $650 to $700, and quantity supplied increases from 10,000 to 13,000:
  - Result: Elasticity of supply is 3.53 (indicating elastic supply).

5. Self-check Questions:

Demand for Smart Phones:
- Calculate price elasticity from point B to C, D to E, and G to H.
- Classify elasticity as elastic, inelastic, or unit elastic for each point.
Supply of Alarm Clocks:
- Calculate price elasticity from point J to K, L to M, and N to P.
- Classify elasticity for each point.

6. Review Questions:

Elasticity Formulas: Understand and explain the formula for calculating elasticity.
Price Elasticity of Demand: Explain the concept and its significance.
Price Elasticity of Supply: Explain the concept and its significance.

7. Critical-thinking Questions:

Transatlantic Air Travel: Explore why business class has different elasticity compared to economy class.
Relationship between Price Elasticity and Demand Curve Position: Discuss how elasticity changes along the demand curve.

8. Problems:

Demand and Supply Curve Equations: Solve problems involving elasticity with given demand and supply curve equations.

In summary, the article covers the fundamental concepts of price elasticity, different types of elasticity, calculation methods, and practical applications through examples and self-check questions. It provides a robust foundation for understanding and applying elasticity in economic analysis.

Price elasticity of demand and price elasticity of supply (article) | Khan Academy (2024)