Price Elasticity of Demand

The formula for calculating the price elasticity of demand

Price elasticity of demand is calculated as a percentage change in the quantity demanded divided by a percentage change in the price of a good.

The formula for the price elasticity of demand (PED) is:

$PED=\frac{\%\Delta Quantitydemanded}{\%\Delta Price}$

You can find a percentage change in a variable by using the following formula:

$\%\Delta =\frac{Newvalue-Oldvalue}{Oldvalue}*100\%$

Types of price elasticity of demand

There are three types of demand based on how much the quantity demanded of a good changes when its price changes.

These are:

• Unitary price elastic demand

• Price inelastic demand

• Price elastic demand

Unitary price elastic demand

Demand is unitary elastic (absolute value of elasticity equal to 1) if a change in the own price of a good leads to a proportionate change in the quantity demanded.

This type of demand is drawn as a line at a 45-degree angle to the horizontal axis as shown in the first diagram of Figure 2 below.

Price inelastic demand

Demand is price inelastic (elasticity is less than 1 in absolute value) if a change in the own price of a good leads to a less than proportionate change in the quantity demanded.

Consider an increase in the price from P1 to P2 as shown in Figure 2 across the three figures. In the case of price inelastic demand, shown in the second diagram, the price increase would reduce quantity demanded by less compared to demand with unitary elasticity.

Price elastic demand

Demand is price elastic (elasticity is greater than 1 in absolute value) if a change in the own price of a good leads to a more than proportionate change in the quantity demanded.

Consider an increase in the price from P1 to P2 as shown in Figure 2 across the three diagrams. In the case of price elastic demand, shown in the third diagram, the price increase would reduce quantity demanded by more compared to demand with unitary elasticity.

Fig. 2 - Three types of demand elasticity

How does the price elasticity vary along a linear demand curve?

Price elasticity of demand varies not only between different goods but also along the demand curve for an individual good as Figure 3 shows. At point 1 demand is unitary elastic. Anywhere along the demand curve between point 1 and point 2 demand is elastic. Demand is infinitely elastic at point 2. Anywhere along the curve between point 1 and point 3 demand is inelastic. Demand has zero elasticity at point 3.

Fig. 3 - Elasticities along a linear demand curve

What are the special cases of the price elasticity of demand?

There are two special cases of the price elasticity of demand:

• Perfectly inelastic demand

• Perfectly elastic demand

This happens when no matter how much the price of a good increases or decreases, the quantity demanded will stay the same. Perfectly price inelastic demand is shown in Figure 4.

Fig. 4 - Perfectly price inelastic demand curve

This happens when the consumers will demand any quantity at a single price. Perfectly elastic demand is shown in Figure 5.

Fig. 5 - Perfectly price elastic demand curve

How does the price elasticity of demand affect the total revenue of a supplier?

Price elasticity of demand is taken into account by producers in their pricing decisions. They consider whether increasing or decreasing the price of their product will lead to an increase or a decrease in their total revenue. In other words, the supplier will try to maximise the total revenue they receive from selling their good or service.

As you can see in Figure 6 below, a supplier’s total revenue varies with the total output produced. This happens because price elasticity varies along a linear demand curve, which is also a firm’s average revenue (AR) curve. The prices vary along the demand curve together with the price elasticity of demand.

At point A the demand is perfectly elastic and total revenue (TR) is equal to zero. Between point A and B the demand is elastic and TR is increasing reaching its maximum at point B. Point B is also the point where marginal revenue (MR) is equal to zero. Between point B and point C demand is inelastic and TR starts declining and eventually reaches zero at point C. Point C is also the point where average revenue (AR) is equal to zero. Demand at point C becomes perfectly inelastic. Therefore, the firm will try to produce its output at point B where total revenue is maximised and where MR=0.

Fig. 6 - Price elasticity of demand effects on total revenue

Example: the effect of price elasticity of demand on supplier’s revenue

Consider the following demand equation: Q = 100 – 2*P

We will now calculate the effect of a pricing decision on a supplier’s revenue. The initial price of a product is 30 at which 40 units of a product are demanded (Q=100-2*30=40). This is represented by point A on the demand curve in Figure 7 below.

Fig. 7 - PED and total revenue

The current total revenue the supplier is making is P*Q = 30*40 = 1200.

The supplier is thinking of introducing a 50% sale promotion (reducing the price to 15) in hope of increasing the quantity demanded, thereby increasing revenue. At the new price of 15 consumers will be willing to buy 70 units of the product. This is represented by point B on the demand curve in Figure 7. The new revenue would then be equal to 15*70 = 1050.

Despite a large potential increase in the quantity demanded, the supplier’s revenue would decrease if they implement the 50% sale. Why? This is because reducing the price to 15 takes us to the inelastic part of the demand curve, which is beyond the point of unitary elasticity. The point of unitary elasticity for this demand curve is at Q=50 and P=25 at point C in Figure 7. It is located at the midpoint of the demand curve.

Effect of price elasticity of demand on consumer expenditure

Total supplier revenue is equal to total consumer expenditure on a good or service. The following rule will help you easily identify if demand is price elastic, price inelastic, or has a unitary price elasticity:

• If the total amount spent by consumers on a particular good or service falls when the price increases, demand is price elastic.
• If the total amount spent by consumers on a particular good or service rises when the price increases, demand is price inelastic.
• If the total amount spent by consumers on a particular good or service remains constant when the price increases, demand has unitary price elasticity.