When price of a good increases by 50% quantity demanded decreases by 25% What is the price elasticity of demand?

Elasticity of demand is an important variation on the concept of demand. Demand can be classified as elastic, inelastic or unitary.

An elastic demand is one in which the change in quantity demanded due to a change in price is large. An inelastic demand is one in which the change in quantity demanded due to a change in price is small.
The formula for computing elasticity of demand is:

(Q1 – Q2) / (Q1 + Q2)     
(P1 – P2) / (P1 + P2)

If the formula creates an absolute value greater than 1, the demand is elastic. In other words, quantity changes faster than price. If the value is less than 1, demand is inelastic. In other words, quantity changes slower than price. If the number is equal to 1, elasticity of demand is unitary. In other words, quantity changes at the same rate as price.

Elastic Demand

Elasticity of demand is illustrated in Figure 1. Note that a change in price results in a large change in quantity demanded. An example of products with an elastic demand is consumer durables. These are items that are purchased infrequently, like a washing machine or an automobile, and can be postponed if price rises. For example, automobile rebates have been very successful in increasing automobile sales by reducing price.

Close substitutes for a product affect the elasticity of demand. If another product can easily be substituted for your product, consumers will quickly switch to the other product if the price of your product rises or the price of the other product declines. For example, beef, pork and poultry are all meat products. The declining price of poultry in recent years has caused the consumption of poultry to increase, at the expense of beef and pork. So products with close substitutes tend to have elastic demand.

An example of computing elasticity of demand using the formula is shown in Example 1. When the price decreases from $10 per unit to $8 per unit, the quantity sold increases from 30 units to 50 units. The elasticity coefficient is 2.25.

Inelastic Demand

Inelastic demand is shown in Figure 2. Note that a change in price results in only a small change in quantity demanded. In other words, the quantity demanded is not very responsive to changes in price. Examples of this are necessities like food and fuel. Consumers will not reduce their food purchases if food prices rise, although there may be shifts in the types of food they purchase. Also, consumers will not greatly change their driving behavior if gasoline prices rise.

An example of computing inelasticity of demand using the formula above is shown in Example 2. When the price decreases from $12 to $6 (50%), the quantity of demand increases from 40 to only 50 (25%). The elasticity coefficient is .33.

This does not mean that the demand for an individual producer is inelastic. For example, a rise in the price of gasoline at all stations may not reduce gasoline sales significantly. However, a rise of an individual station’s price will significantly affect that station’s sales.

Unitary Elasticity

If the elasticity coefficient is equal to one, demand is unitarily elastic as shown in Figure 3. For example, a 10% quantity change divided by a 10% price change is one. This means that a 1% change in quantity occurs for every 1% change in price.

Don Hofstrand, retired extension value added agriculture specialist,

Imagine you are in a store and an item that you normally buy is currently on a 50% off sale. It would not be surprising if you decided to ‘stock up’ on this item and buy more of it to reap the benefits as you will use this item anyway. But what about if an item you don’t normally use is on an 80% off sale? Would you still buy more than two items? To answer this question, we need to use the concept of the price elasticity of demand. Let’s learn about it.

Price elasticity of demand is a measure of the responsiveness of the quantity demanded to a change in the own price of a good.

The ‘law’ of demand states that as the price of a good falls, the quantity demanded increases as consumers are willing to buy more units of a good at a lower price. The reverse is also true. As the price of a good rises, the quantity demanded decreases as consumers are willing to buy fewer units of a good at a higher price.

Figure 1 below shows a movement along the demand curve for a price rise and a price fall.

Figure 1. Movement along the demand curve, StudySmarter Originals

Consider a price increase from P1 to P2, which leads to a decrease in the quantity demanded from Q1 to Q2. A price decrease from P1 to P3 leads to an increase in the quantity demanded from Q1 to Q3. The proportion in which the quantity demanded will respond to price changes will be different not only for different levels of price changes but also will vary along the curve. This responsiveness is measured by the 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:

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

Let’s imagine the price of refrigerators rises from £20 to £21 (a rise of 5%), whilst the quantity demanded falls from 100 to 95 (a fall of 5%). Price elasticity of demand is then equal to: 5% over 5% = 1 in absolute value. We often use an absolute value for the price elasticity of demand for convenience, but its true value will always be negative. This is because of the law of demand: the quantity demanded of a good always falls when its price rises. Thus, the correct calculation would be -5% over 5%, which would give us a value of -1.

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

Think of price elasticity of demand as the steepness of the demand curve (its slope).

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.

Larry enjoys having a full English breakfast and consumes bacon every morning. Due to supply issues, the price of bacon has gone up by 100% and Larry decides to not consume bacon anymore. He reduces his bacon consumption by 100% (the same percentage as the price increase) as his demand has unitary price elasticity. Calculation: 100% / 100% = 1.

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.

John is a fan of Apple products. Whenever a new iPhone comes out he is the first one to pre-order it. If the price of Apple iPhones increases by 20%, John will still buy the same amount of iPhones. His demand would decrease, according to the law of demand, but by only 2% compared to the price change. This is because his demand for iPhones is price inelastic. Calculation: 2%/100% = 0.02.

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.

Kayla likes wearing jewellery. Due to an oversupply in the market, the price of jewellery decreases by 20%. Kayla rushes to buy more jewellery, increasing her demand by 60%. Her quantity demand increases by more compared to the price change. This is because her demand for jewellery is price elastic. Calculation: 60%/20% = 3.

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.

Figure 2. Three types of demand elasticity, StudySmarter

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.

Figure 3. Elasticities along a linear demand curve, StudySmarter

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

Demand is perfectly inelastic when its elasticity is equal to zero.

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.

In the market for inhalers for people suffering from asthma, demand would be perfectly price inelastic. No matter how much the price of inhalers rises, demand will stay the same as people suffering from asthma depend on them.

Figure 4. Perfectly price inelastic demand curve, StudySmarter

Demand is perfectly elastic when its elasticity is equal to infinity.

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

In a perfectly competitive market where there is a lot of suppliers with homogeneous products, demand is perfectly price elastic. If one supplier raises the price of their potatoes, they will simply lose all their customers. Consumers will switch to other suppliers due to all potatoes being the same.

Figure 5. Perfectly price elastic demand curve, StudySmarter

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.

Figure 6. Price elasticity of demand effects on total revenue, StudySmarter

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.

Figure 7. PED and total revenue, StudySmarter

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.

Check your understanding. Could a supplier have lowered their price whilst increasing revenue? Can you find a price where revenue would be greater than it was initially?

The answer is yes. Any price below the current price of 30, but not below 25, in fact, will result in higher revenue for the supplier. The revenue will be maximised at a price of 25. Any deviation below or above 25 would lead to a reduction in revenue for the supplier. This is generally true for all linear demand curves.

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.

Price elasticity of demand - Key takeaways

• Price elasticity of demand is a measure of the responsiveness of the quantity demanded to a change in the own price of a good.
• 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.
• There are three types of demand based on how much the quantity demanded of a good changes when its price changes: unitary price elastic demand, price inelastic demand, price elastic demand.
• Demand is unitary elastic if a change in the own price of a good leads to a proportionate change in the quantity demanded.
• Demand is price inelastic if a change in the own price of a good leads to a less than proportionate change in the quantity demanded.
• Demand is price elastic if a change in the own price of a good leads to a more than proportionate change in the quantity demanded.
• Price elasticity of demand varies along a linear demand curve.
• There are two special cases of the price elasticity of demand: perfectly inelastic demand and perfectly elastic demand.
• Price elasticity of demand is taken into account by producers in their pricing decisions.

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