Price Elasticity of Demand Formula

Price Elasticity of Demand Formula Overview

Let's go through an overview of the price elasticity of demand formula!

The price elasticity of demand formula measures how much the demand for goods and services changes when there is a change in the price.

But how much will the demand for a good change when there is a change in the price of a good or service? Is the change in demand the same for all goods?

The demand for a good or service is more elastic when the quantity demanded changes by much more than the price change.

On the other hand, the demand is inelastic when the quantity demanded for a good or service changes less than the price change.

The willingness of consumers to purchase less of a product as its price increases is what is measured by the price elasticity of demand formula for any given product. The elasticity of demand formula is important to determine whether a good is price elastic or inelastic.

The price elasticity of demand formula is calculated as the percentage change in quantity demanded divided by the percentage change in price.

The price elasticity of demand formula is as follows:

\(\hbox{Price elasticity of demand}=\frac{\%\Delta\hbox{Quantity demanded}}{\%\Delta\hbox{Price}}\)

The formula shows the percentage change in quantity demanded in response to a percentage change in price of the good in question.

Price Elasticity of Demand Calculation

Price elasticity of demand calculation is easy once you know the percentage change in quantity and percentage change in price. Let's calculate the price elasticity of demand for the example below.

Using the formula for price elasticity of demand, we can calculate the following:

\(\hbox{Price elasticity of demand}=\frac{\hbox{-10%}}{\hbox{5%}}=-2\)

This means that when there is an increase in the price of clothes, the quantity demanded for clothes drops by twice as much.

Midpoint Method to Calculate the Price Elasticity of Demand

The midpoint method to calculate the price elasticity of demand is used when calculating the price elasticity of demand between any two points on the demand curve.

The price elasticity formula is limited when calculating the price elasticity of demand as it does not yield the same result when calculating the price elasticity of demand for two different points on the demand curve.

Fig. 1 - Calculating price elasticity of demand between two different points

Let's consider the demand curve in Figure 1. The demand curve has two points, point 1 and point 2, which are associated with different price levels and different quantities.

At point 1, when the price is $6, the quantity demanded is 50 units. However, when the price is $4, at point 2, the quantity demanded becomes 100 units.

The percentage change in quantity demanded going from point 1 to point 2 is as follows:

\( \%\Delta Q = \frac{Q_2 - Q_1}{Q_1}\times100\%= \frac{100 - 50}{50}\times100\%=100 \%\)

The percentage change in price going from point 1 to point 2 is:

\( \%\Delta P = \frac{P_2 - P_1}{P_1}\times100\% = \frac{4 - 6}{6}\times100\%= -33\%\)

The price elasticity of demand going from point 1 to point 2 is therefore:

\(\hbox{Price elasticity of demand}=\frac{\hbox{% $\Delta$ Quantity demanded}}{\hbox{% $\Delta$ Price}} = \frac{100\%}{-33\%} = -3.03\)

Now, let's calculate the price elasticity of demand going from point 2 to point 1.

The percentage change in quantity demanded going from point 2 to point 1 is:

\( \%\Delta Q = \frac{Q_2 - Q_1}{Q_1}\times100\% = \frac{50 - 100}{100}\times100\%= -50\%\)

The percentage change in price going from point 2 to point 1 is:

\( \%\Delta P = \frac{P_2 - P_1}{P_1}\times100\% = \frac{6 - 4}{4}\times100\%= 50\%\)

The price elasticity of demand in such a case is:

\(\hbox{Price elasticity of demand}=\frac{\hbox{% $\Delta$ Quantity demanded}}{\hbox{% $\Delta$ Price}} = \frac{-50\%}{50\%} = -1\)

So, the price elasticity of demand going from point 1 to point 2 is not equal to the price elasticity of demand moving from point 2 to point 1.

In such a case, to eliminate this problem, we use the midpoint method to calculate the price elasticity of demand.

The midpoint method for calculating the price elasticity of demand uses the average value between the two points when taking the percentage change in difference instead of the initial value.

The midpoint formula to calculate the price elasticity of demand between any two points is as follows.

\(\hbox{Midpoint price elasticity of demand}=\frac{\frac{Q_2 - Q_1}{Q_m}}{\frac{P_2 - P_1}{P_m}}\)

Where

\( Q_m = \frac{Q_1 + Q_2}{2} \)

\( P_m = \frac{P_1 + P_2}{2} \)

\( Q_m \) and \( P_m \) are the midpoint quantity demanded and midpoint price respectively.

Using the midpoint formula for elasticity of demand let's calculate the price elasticity of demand in Figure 1.

When we move from point 1 to point 2:

\( Q_m = \frac{Q_1 + Q_2}{2} = \frac{ 50+100 }{2} = 75 \)

\( \frac{Q_2 - Q_1}{Q_m} = \frac{ 100 - 50}{75} = \frac{50}{75} = 0.666 = 67\% \)

\( P_m = \frac{P_1 + P_2}{2} = \frac {6+4}{2} = 5\)

\( \frac{P_2 - P_1}{P_m} = \frac{4-6}{5} = \frac{-2}{5} = -0.4 = -40\% \)

Replacing these results into the midpoint formula, we get:

\(\hbox{Midpoint price elasticity of demand}=\frac{\frac{Q_2 - Q_1}{Q_m}}{\frac{P_2 - P_1}{P_m}} = \frac{67\%}{-40\%} = -1.675 \)

When we move from point 2 to point 1:

\( Q_m = \frac{Q_1 + Q_2}{2} = \frac{ 100+50 }{2} = 75 \)

\( \frac{Q_2 - Q_1}{Q_m} = \frac{ 50 - 100}{75} = \frac{-50}{75} = -0.666 = -67\% \)

\( P_m = \frac{P_1 + P_2}{2} = \frac {4+6}{2} = 5\)

\( \frac{P_2 - P_1}{P_m} = \frac{6-4}{5} = \frac{2}{5} = 0.4 = 40\% \)

\(\hbox{Midpoint price elasticity of demand}=\frac{\frac{Q_2 - Q_1}{Q_m}}{\frac{P_2 - P_1}{P_m}} = \frac{-67\%}{40\%} = -1.675 \)

We get the same result.

Therefore, we use the midpoint price elasticity of demand formula when we want to calculate the price elasticity of demand between two different points on the demand curve.

Calculate Price Elasticity of Demand at Equilibrium

To calculate the price elasticity of demand at equilibrium we need to have a demand function and a supply function.

Let's consider the market for chocolate bars. The demand function for chocolate bars is given as \( Q^D = 200 - 2p \) and the supply function for chocolate bars is given as \(Q^S = 80 + p \).

Fig. 2 - Market for chocolates

Figure 2 illustrates the equilibrium point in the market for chocolates. To calculate the price elasticity of demand at the equilibrium point, we need to find the equilibrium price and the equilibrium quantity.

The equilibrium point occurs when the quantity demanded equals the quantity supplied.

Therefore, at the equilibrium point \( Q^D = Q^S \)

Using the functions for demand and supply above, we get:

\( 200 - 2p = 80 + p \)

Rearranging the equation, we get the following:

\( 200 - 80 = 3p \)

\(120 = 3p \)

\(p = 40 \)

The equilibrium price is 40$. Replacing the price in the demand function (or supply function) we get the equilibrium quantity.

\( Q^D = 200 - 2p = 200 - 2\times40 = 200-80 = 120\)

The equilibrium quantity is 120.

The formula for calculating the price elasticity of demand at the equilibrium point is as follows.

\( \hbox{Price elasticity of demand}=\frac{P_e}{Q_e} \times Q_d' \)

Where \(Q_d' \) is the derivative of demand function with respect to price.

\( Q^D = 200 - 2p \)

\(Q_d' =-2 \)

After replacing all the values in the formula we get:

\( \hbox{Price elasticity of demand}=\frac{40}{120}\times(-2) = \frac{-2}{3} \)

This means that when the price of chocolate bars increases by \(1\%\) the quantity demanded for chocolate bars falls by \(\frac{2}{3}\%\).

Types of Elasticity of Demand

The meaning of the number we get from calculating the elasticity of demand depends on the types of elasticity of demand.

There are five main types of elasticity of demand, including perfectly elastic demand, elastic demand, unit elastic demand, inelastic demand, and perfectly inelastic demand.

1. Perfectly elastic demand. Demand is perfectly elastic when the elasticity of demand is equal to infinity.This means that if the price were to increase even by 1%, there wouldn't be any demand for the product.
2. Elastic demand. Demand is elastic when the price elasticity of demand is greater than 1 in absolute value.This means a percentage change in price leads to a greater percentage change in quantity demanded.
3. Unit elastic demand. Demand is unit elastic when the price elasticity of demand is equal to 1 in absolute value.This means that the change in quantity demanded is proportional to the change in price.
4. Inelastic demand. Demand is inelastic when the price elasticity of demand is lower than 1 in absolute value. This means that a percentage change in price leads to a smaller percentage change in quantity demanded.
5. Perfectly inelastic demand. Demand is perfectly inelastic when the price elasticity of demand is equal to 0. This means that the quantity demanded will not change regardless of the price change.

Table 1 - Summary of the types of price elasticity of demand

Factors Affecting the Elasticity of Demand

Factors influencing the elasticity of demand include the availability of close substitutes, necessities and luxuries, and the time horizon as seen in Figure 3. There are many other factors influencing the price elasticity of demand; however, these are the main ones.

Factors Affecting the Elasticity of Demand: Availability of Close Substitutes

Because it is simpler for customers to transfer from one product to another, goods with nearby alternatives often have more elastic demand than those without.

Factors Affecting the Elasticity of Demand: Necessities and Luxuries

Whether a good is a necessity or a luxury impacts the elasticity of demand. Goods and services that are necessary tend to have inelastic demands, whereas luxury goods have a much more elastic demand.

Factors Affecting the Elasticity of Demand: Time Horizon

The time horizon also influences price elasticity of demand. Over the long term, many goods tend to be more elastic.