Price elasticity of demand

Elasticity of Demand

Definitions

Price elasticity of demand

Measures how responsive quantity demanded is when the price of that product changes. “Elastic” means stretchable.

$$\text{Price elasticity of demand}=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in the selling price}}$$

This matters for managers because changing price doesn’t just change revenue per unit — it can also change the number of units sold.

Sidenote

Assumptions

Certain assumptions must be made to calculate the elasticity of demand:

• The only factor that causes a volume change is the price.
• Demand for a product can be calculated.

There are two methods of calculating price elasticity:

• The average arc method
• The non-average arc method

Interpreting the result

Before calculating elasticity, it helps to know how to interpret the result.

Definitions

Unit elastic ($=-1$)

Quantity demanded changes by the same percentage as price, but in the opposite direction.
For example, a $20\%$ decrease in price leads to a $20\%$ increase in demand.

Inelastic (between $0$ and $-1$)

Quantity demanded changes by a smaller percentage than price. This is common for necessities and addictive goods.
For example, consumers continue to buy bread or cigarettes even when prices increase.

Relatively elastic ($-1$ to $-\infty$)

Quantity demanded changes by a larger percentage than price. This is common for luxury goods.
For example, a small decrease in airfare can lead to a large increase in ticket sales.

Calculating elasticity

Let’s do an example of calculating elasticity, To calculate elasticity, you need to compare how much price changes with how much quantity demanded changes. This is usually done using percentage changes.

In this example, we are given both the original values and the new values, so we can calculate elasticity directly.

Average and non-average arc method

Use both the average arc method and the non-average arc method to calculate the elasticity of demand of the course content.

Example:

KTA sells educational courses online on its sites and its social media platforms. The research team has gathered some information on the demand pattern of the product, and the current demand is $10,000$ copies sold for $\$100$. Based on the market research, it’s estimated that the demand for the courses will rise to $15,000$ when the price is dropped to $\$80$.

Use both the average arc method and the non-average arc method to calculate the elasticity of demand of the course content.

Average arc method:
The average arc method uses the midpoint of the starting and ending values as the denominator for both quantity and price.

$$\begin{array}{rl}\text{Average quantity}& =\frac{10,000+15,000}{2}\\ & =12,500\\ \text{Average price}& =\frac{100+80}{2}\\ & =90\\ \text{\% change in quantity}& =\frac{15,000-10,000}{12,500}\\ & =0.4\\ \text{\% change in price}& =\frac{80-100}{90}\\ & =-0.22\\ \text{Price elasticity of demand}& =\frac{0.4}{-0.22}\\ & =-1.8\end{array}$$

This means the product is relatively elastic.

Steps taken:

• Identify the original and new quantity ($10,000$ to $15,000$)
• Identify the original and new price ($100$ to $80$)
• Calculate the average quantity and average price
• Find the percentage change in quantity using the average quantity
• Find the percentage change in price using the average price
• Substitute both values into the elasticity formula
• Divide to calculate elasticity

Now let’s use the non-average arc method to calculate elasticity.

Non-average arc method:
The non-average arc method uses the starting values (before the change) as the denominator.

$$\begin{array}{rl}\text{\% change in quantity}& =\frac{15,000-10,000}{10,000}\\ & =0.5\\ \text{\% change in price}& =\frac{80-100}{100}\\ & =-0.2\end{array}$$

$$\begin{array}{rl}\text{Price elasticity of demand}& =\frac{0.5}{-0.2}\end{array}$$

$$\begin{array}{rl}\text{Price elasticity of demand}& =\frac{0.5}{-0.2}\\ & =-2.5\end{array}$$

Steps taken:

• Identify the original and new quantity ($10,000$ to $15,000$)
• Identify the original and new price ($100$ to $80$)
• Find the percentage change in quantity using the starting quantity
• Find the percentage change in price using the starting price
• Substitute both values into the elasticity formula
• Divide to calculate elasticity

Sidenote

When to use non-average arc method

If a question doesn’t state which method to use, use the non-average arc method.

A CIMA BA1 question can also ask you to do the reverse calculation, for example asking you to calculate the new quantity demanded.

Example:

KTA’s price elasticity of demand was $-2.5$, and its current demand is $10,000$ units. The current price is $\$100$. If the price was to be dropped to $\$80$, how much would be the quantity demanded?

$$\begin{array}{rl}\text{\% change in price}& =\frac{80-100}{100}\\ & =-0.2\\ & \\ \frac{x}{-0.2}& =-2.5\\ x& =-2.5\times -0.2\\ & =0.5\end{array}$$

The percentage change in quantity demanded is $0.5$ (or $50\%$). Now find the new quantity:

$$\begin{array}{rl}\frac{x-10,000}{10,000}& =0.5\\ x-10,000& =0.5\cdot 10,000\\ x& =(0.5\times 10,000)+10,000\\ & =15,000\text{ copies}\end{array}$$

Steps taken:

• Calculate the percentage change in price
• Use elasticity to find percentage change in quantity
• Apply the change to the original quantity

What causes price elasticity of demand?

Necessities
Necessities tend to have more inelastic demand. That doesn’t mean demand never changes when price changes — it means the percentage change in quantity demanded is relatively small compared with the percentage change in price.

Example:

The price of sugar could fall by $20\%$ while quantity demanded rises by $2\%$. That’s still price inelastic.

Availability of substitutes

• If a product has close substitutes, a price rise can lead to a large drop in quantity demanded because customers switch to alternatives.

In some industries there may be no substitutes. For example, in power industries (e.g., electricity in developing countries), a parastatal company may produce electricity for the whole country. If it raises or lowers price, demand may not change much because there is no competition.

Income spent on a product

• The larger the share of income spent on a product, the more sensitive demand tends to be to price changes. Plane tickets or cruises are expensive, so a $10\%$ price drop can noticeably increase demand. A pen is cheap, so a price rise may not change demand much.

Why managers need to understand price elasticity

Managers need to know when to increase and decrease prices in order to increase the profitability of the organization.

Sidenote

Key rules:

• If a good is price elastic, a decrease in the selling price will increase revenue, but an increase in the selling price will decrease revenue.
• If a product is price inelastic, an increase in the selling price will increase revenue, but a decrease in the selling price will decrease revenue.

Using the earlier example:

• At $\$100$ and $10,000$ copies: sales revenue $=\$1,000,000$
• At $\$80$ and $15,000$ copies: sales revenue $=\$1,200,000$

The elasticity of demand was $-2.5$, which indicates relatively elastic demand, so the price decrease increased total revenue.

Price elasticity summary

Overall, price elasticity helps managers predict how customers will respond to price changes. By understanding whether demand is elastic or inelastic, managers can make more informed pricing decisions that maximize revenue and avoid unintended losses. Instead of guessing, they can use elasticity to choose pricing strategies that align with how customers actually behave.