Explain the relationship between price elasticity of demand and total expenditure

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From the lesson

Week 2 - Supply and Demand

Using the Supply-Demand Framework to Predict and Explain Market Outcomes as well as to Show the Impacts of Government Intervention. Some Key Elasticities of Demand and Supply.

Taught By

Mark Zupan
Professor of Economics and Public Policy

Have you ever wanted to buy more of something just because its price dropped? Let's say you've been buying an apple a day for $2 for the past month. News came in that the price of an apple has been reduced to $1. Suddenly, you start buying $3 worth of apples a day. What happened? Well, it means your demand for apples is price elastic. The total expenditures test is concerned with checking just how price elastic your demand for apples is. Read on for a total expenditure Test definition, the formula, and more!

Elasticity of Demand Total Expenditure Test

The total expenditures test is used to determine the elasticity of demand for a particular product. In other words, it checks the price elasticity of demand of a given product.

The total expenditures test is used to determine how elastic the demand for a particular product is.

Wait, let's not move too fast here. What is the price elasticity of demand in the first place? When there is a change in price of a product, consumers often react by changing their quantity demanded of that product. In other words, when the price of a product changes, consumers respond by changing how much of that product they're willing and able to buy at any point.

However, it is important to note that consumers will react differently to the price changes of different products. For instance, they may buy more apples when the price of apples goes down, but they may not change the number of painkillers they buy even if the price of painkillers goes down. Price elasticity of demand, therefore, refers to how much quantity demanded changes as a result of a change in price.

Price elasticity of demand refers to how much quantity demanded changes as a result of a change in price.

Just remember price change and quantity demanded change.

Demand can be elastic, inelastic, or unit elastic. Let's look at what these three mean.

Demand can be elastic, inelastic, or unit elastic.

Elastic demand and the total expenditures test

Elastic demand describes a situation where a change in price results in a relatively larger change in quantity demanded.

Demand is elastic when a change in price causes a relatively larger change in quantity demanded.

Figure 1. Elastic Demand, StudySmarter Originals

Figure 1 above shows elastic demand. Looking at Figure 1, you can see that the distance from P1 to P2 (change in price) is smaller when compared to the distance between Q1 and Q2 (change in quantity demanded). This shows the concept of elastic demand. The small change from P1 to P2 resulted in a larger change from Q1 to Q2.

Inelastic demand and the total expenditures test

For inelastic demand, a change in price results in a relatively smaller change in quantity demanded.

Demand is inelastic when a change in price causes a relatively smaller change in quantity demanded.

Figure 2. Inelastic Demand, StudySmarter Originals

Figure 2 above shows inelastic demand. Looking at Figure 2, you can see that the change in price shown by the distance from P1 to P2 is larger when compared to the change in quantity demanded or distance between Q1 and Q2. From this, we can conclude that a change in price caused a smaller change in quantity demanded, therefore, this is inelastic demand.

Unit elastic demand and the total expenditures test

In some cases, a change in price results in an equally proportional change in quantity demanded, and this is referred to as unit elastic demand.

Demand is unit elastic when a change in price causes a proportional change in quantity demanded.

Figure 3. Unit Elastic Demand, StudySmarter Originals

Look at Figure 3 for an illustration of unit elastic demand. Figure 3 shows that the change in price or the distance from P1 to P2 is proportional to the change in quantity demanded or the distance between Q1 and Q2. This shows unit elastic demand.

Note that the comparison is not about the number, but the proportional size of the change. So, if price changes from 1 to 2 (change of 100%) and quantity demanded changes from 2 to 4 (change of 100%), these two changes are the same proportional size.

Total Expenditures Test Definition

What is the definition of the total expenditures test? The total expenditures test determines the demand elasticity of a given product. Economists look at how much the total expenditure has changed when price changes, and this informs us about the demand elasticity of the product we are looking at.

The total expenditures test is a test to determine the demand elasticity of a given product.

Total Expenditure Test: Total expenditure formula

Total expenditure is calculated by multiplying the price by the quantity demanded. Economists use the following formula:

$\hbox{Total Expenditure}=\hbox{Price (P)}\times\hbox{Quantity Demanded (Q)}$

Total expenditure can also be referred to as what consumers spend on a product at a given price. Let's look at a simple example.

An apple sells for $2 a piece, and Kent buys 3 apples. What is Kent's total expenditure?

The price is $2 and the quantity demanded is 3:

P=2 and Q=3

Using the formula:

$\hbox{Total Expenditure}=\hbox{Price (P)}\times\hbox{Quantity Demanded (Q)}$

We have:

$\hbox{Total Expenditure}=2\$\times3=6\$$

Therefore, Kent's total expenditure is $6

Explain the Purpose of the Total Expenditures Test

The purpose of the total expenditures test helps economists determine the price elasticity of demand for a product. We do this by looking at the effect of a price change on the total expenditure. In other words, how did the total expenditure change when the price changed?

The total expenditures test helps economists determine the price elasticity of demand for a product.

So, how exactly can one use the total expenditures test to determine the demand elasticity of a product? Follow three simple rules!

The first rule is that if the total expenditure reduces when the price increases, the demand for a good is price elastic.
In contrast, if the total expenditure increases when the price decreases, the demand for a good is price elastic. In other words, if they go opposite ways, the demand for a good is price elastic.
The second rule is that if the total expenditure reduces when the price decreases, the demand for a good is price inelastic.
In contrast, if the total expenditure increases when the price increases, the demand for a good is price inelastic. In other words, if they go the same way, the demand for a good is price inelastic.
The third rule is that if the total expenditure does not change when the price changes, the demand for a good is unit elastic.

Let's try our hand on an example now.

When an apple sells for $2 a piece, Kent buys 3 apples. But when the price of apples reduces from $2 to $1, Kent buys 9 apples. What is Kent's demand elasticity for apples?

First, note that we're dealing with a reduction in price. Keep this in mind, we'll come back to it soon.

Second, calculate the total expenditure when the price of an apple was $2:

$\hbox{Total Expenditure 1}=2\$\times3=6\$$

Third, calculate the total expenditure after the price of an apple reduced to $1:

$\hbox{Total Expenditure 2}=1\$\times9=9\$$

Fourth, observe the change in total expenditure from Total Expenditure 1 to Total Expenditure 2.

In this case, the total expenditure increased from $6 to $9.

Now, compare the changes in total expenditure and price. Since we noted that there was a reduction in price, and we have found that total expenditure has increased, we can conclude that Kent's demand elasticity for apples is price elastic, based on the first rule.

Total Expenditure Example

Now, let's try another example where we find the total expenditure and the elasticity of demand.

When tap water sells for $5 a liter, and Kent buys 5 liters. When the price of tap water reduces from $5 to $3, Kent buys 6 liters. What is Kent's demand elasticity for tap water?

First, we note that we're dealing with areduction in price.

Second, we calculate the total expenditure when the price of tap water was $5.

$\hbox{Total Expenditure 1}=5\$\times5=25\$$

Third, we calculate the total expenditure after the price of tap water reduced to $3.

$\hbox{Total Expenditure 2}=3\$\times6=18\$$

Fourth, we observe the change in total expenditure from Total Expenditure 1 to Total Expenditure 2. In this case, the total expenditure reducedfrom $25 to $18.

Now, when we compare the changes in total expenditure and price, we can see that they both decreased. This means that Kent's demand elasticity for tap water is price inelastic, based on the second rule.

Great! You finished this topic. You should read our article on the Elasticity of Demand, it goes deeper into how demand elasticity works!

Total Expenditures Test - Key takeaways

The total expenditures test is used to determine how elastic the demand for a particular product is.
Price elasticity of demand refers to how much quantity demanded changes as a result of a change in price of a good.
If the total expenditure reduces when the price increases, the demand for a good is price elastic. In contrast, if the total expenditure increases when the price decreases, the demand for a good is price elastic. In other words, if they go opposite ways, the demand for a good is price elastic.
If the total expenditure reduces when the price decreases, the demand for a good is price inelastic. In contrast, if the total expenditure increases when the price increases, the demand for a good is price inelastic. In other words, if they go the same way, the demand for a good is price inelastic.
If the total expenditure does not change when the price changes, the demand for a good is unit elastic.

What is the relationship between price elasticity of demand and total expenditure?

When demand is elastic, a fall in the price of a commodity results in increase in total expenditure on it. On the other hand, when price increases, total expenditure decreases. It means, in case of highly elastic demand, price and total expenditure move in the opposite directions.

What is the relationship between price elasticity of demand and total revenue?

Price and total revenue have a negative relationship when demand is elastic (price elasticity > 1), which means that increases in price will lead to decreases in total revenue. Price changes will not affect total revenue when the demand is unit elastic (price elasticity = 1).

What is price elasticity of demand explain the total expenditure method to measure it?

Total expenditure = Commodity Price x Commodity demandOnly three degrees of the elasticity of demand can be calculated by this method. I. Equal to unit Elasticity – When total expenditure remains constant due to increase or decrease in price elasticity of demand is equal to unity.

What will elasticity of demand if total expenditure increase due to increase in price?

If the total expenditure reduces when the price increases, the good is price elastic. If the total expenditure reduces when price decreases, the good is price inelastic. If the total expenditure does not change when price changes, the good is unit elastic.