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## Midpoint Method Economics

The midpoint method in economics is used to find the price elasticity of supply and demand. **Elasticity** is used to gauge how responsive the quantity supplied or quantity demanded is when one of the determinants of supply and demand changes.

To calculate the elasticity, there are two methods: the point elasticity method and the **midpoint method**. The midpoint method, also referred to as arc elasticity, is a method to calculate the elasticity of supply and demand using the *average* percent change in price or quantity.

**Elasticity **measures how responsive or sensitive the quantity demanded or supplied is to price changes.

The **midpoint method** uses the average or the midpoint between two data points to calculate the percent change in the price of a good and its percent change in quantity supplied or demanded. Those two values are then used to calculate the elasticity of supply and demand.

The midpoint method avoids any confusion or mix-ups that result from using other methods of calculating elasticity. The midpoint method does this by giving us the same percent change in value regardless of if we calculate the elasticity from point A to point B or from point B to point A.

As a reference, if point A is 100 and point B is 125, the answer changes depending on which point is the numerator and which one is the denominator.

\[ \frac {100}{125}=0.8 \ \ \ \hbox{versus} \ \ \ \frac{125}{100}=1.25\]

Using the midpoint method eliminates the scenario above by using the *midpoint* between the two values: 112.5.

If a demand or supply is **elastic**, then there is a large change in the quantity demanded or supplied when the price changes. If it is **inelastic**, the quantity does not change very much, even if there is a significant price change. To learn more about elasticity, have a look at our other explanation - Elasticity of Supply and Demand.

## Midpoint Method vs Point Elasticity

Let's have a look at the midpoint method vs the point elasticity method. Both are perfectly acceptable ways of calculating the elasticity of supply and demand, and they both require mostly the same information to perform. The difference in the information required comes from needing to know which value is the initial value for the point elasticity method since this will tell us if the price rose or fell.

### Midpoint Method vs Point Elasticity: Point Elasticity Formula

The point elasticity formula is used to calculate the elasticity of a demand or supply curve from one point to another by dividing the change in value by the starting value. This gives us the percent change in value. Then, to calculate the elasticity, the percent change in quantity is divided by the percent change in price. The formula looks like this:

\[\hbox{Point Elasticity of Demand}=\frac{\frac{Q_2-Q_1}{Q_1}}{\frac{P_2-P_1}{P_1}}\]

Let's set this into practice by looking at an example.

When the price of a loaf of bread decreased from $8 to $6, the quantity people demanded increased from 200 to 275. To calculate the elasticity of demand using the point elasticity method, we will plug these values into the formula above.

\(\hbox{Point Elasticity of Demand}=\frac{\frac{275-200}{200}}{\frac{$6-$8}{$8}}\)

\(\hbox{Point Elasticity of Demand}=\frac{0.37}{-$0.25}\)

\(\hbox{Point Elasticity of Demand}=-1.48\)

Economists traditionally denote elasticity as an absolute value, so they disregard the negative when calculating. For this example, it means that the elasticity of demand is 1.48. Since 1.48 is greater than 1, we can conclude that the demand for bread is *elastic*.

If we graph the points from the example on a chart, it will look something like Figure 1 below.

To briefly illustrate the problem with the point elasticity method, we will use Figure 1 again, only this time calculating an *increase* in the price of bread.

The price of a loaf of bread increased from $6 to $8, and the quantity demanded decreased from 275 to 200.

\(\hbox{Point Elasticity of Demand}=\frac{\frac{200-275}{275}}{\frac{$8-$6}{$6}}\)

\(\hbox{Point Elasticity of Demand}=\frac{-0.27}{$0.33}\)

\(\hbox{Point Elasticity of Demand}=-0.82\)

Now the elasticity of demand is *less* than 1, which would indicate that demand for bread is *inelastic*.

See how using the point elasticity method can give us two different impressions of the market even though it is the same curve? Let's look at how the midpoint method can avoid this situation.

### Midpoint Method vs Point Elasticity: Midpoint Method Formula

The midpoint method formula has the same purpose of calculating the elasticity of supply and demand, but it uses the average percent change in value to do so. The formula for calculating elasticity using the midpoint method is:

\[\hbox{Elasticity of Demand}=\frac{\frac{(Q_2-Q_1)}{(Q_2+Q_1)/2}}{\frac{(P_2-P_1)}{(P_2+P_1)/2}}\]

If we examine this formula closely, we see that rather than dividing the change in value by the initial value, it is divided by the average of the two values.

This average is calculated in the \((Q_2+Q_1)/2\) and the \((P_2+P_1)/2\) portions of the elasticity formula. This is where the midpoint method gets its name. The average is the *midpoint* between the old value and the new value.

Rather than using two points to calculate the elasticity, we will use the midpoint because the midpoint between two points is the same no matter the direction of the calculation. We will use the values in Figure 2 below to prove this.

For this example, we will first calculate the elasticity of demand for bales of hay when there is a decrease in price. Then we will see if the elasticity changes if the price were to increase instead, using the midpoint method.

The price of a bale of hay drops from $25 to $10, making the quantity demanded increase from 1,000 bales to 1,500 bales. Let's plug those values in.

\(\hbox{Elasticity of Demand}=\frac{\frac{(1,500-1,000)}{(1,500+1,000)/2}}{\frac{($10-$25)}{($10+$25)/2}}\)

\(\hbox{Elasticity of Demand}=\frac{\frac{500}{1,250}}{\frac{-$15}{$17.50}}\)

\(\hbox{Elasticity of Demand}=\frac{0.4}{-0.86}\)

\(\hbox{Elasticity of Demand}=-0.47\)

Remembering to use the absolute value, the elasticity of demand for bales of hay is between 0 and 1, making it inelastic.

Now, out of curiosity, let's calculate the elasticity if the price were to increase from $10 to $25.

\(\hbox{Elasticity of Demand}=\frac{\frac{(1,000-1,500)}{(1,000+1,500)/2}}{\frac{($25-$10)}{($25+$10)/2}}\)

\(\hbox{Elasticity of Demand}=\frac{\frac{-500}{1,250}}{\frac{$15}{$17.50}}\)

\(\hbox{Elasticity of Demand}=\frac{-0.4}{0.86}\)

\(\hbox{Elasticity of Demand}=-0.47\)

Look familiar? When we use the midpoint method, the elasticity will be the same no matter what the starting and ending point is on the curve.

As demonstrated in the example above, when the midpoint method is used, the percentage change in price and quantity is the same in either direction.

**To be Elastic... or Inelastic?**

How do we know if the elasticity value makes people inelastic or elastic? To make sense of the elasticity values and know the elasticity of demand or supply, we just have to remember that if the absolute elasticity value is between 0 and 1, consumers are inelastic to changes in price. If the elasticity is between 1 and infinity, then the consumers are elastic to price changes. If the elasticity happens to be 1, it is unit elastic, meaning that people adjust their quantity demanded proportionally.

## Purpose of the Midpoint Method

The main purpose of the midpoint method is that it gives us the same elasticity value from one price point to another, and it does not matter if the price decreases or increases. But how? It gives us the same value because the two equations use the same denominator when dividing the change in value to calculate the percent change.

The change in value is always the same, regardless of an increase or decrease, since it is simply the difference between the two values. However, if the denominators change depending on if the price increases or decreases when we are calculating the percent change in value, we will not get the same value. The midpoint method is more useful when the values or data points provided are further apart, such as if there is a significant price change.

The disadvantage of the midpoint method is that it is not as precise as the point elasticity method. This is because as the two points get farther apart, the elasticity value becomes more general for the whole curve than just a portion of the curve. Think of it this way. High-income people are going to be insensitive or inelastic to a price increase because they have the disposable income to be more flexible. Low-income people are going to be highly elastic to increases in price because they are on a set budget. Mid-income people are going to be more elastic than high-income people and less elastic than low-income people. If we lump them all together, we get the elasticity of demand for the entire population, but this is not always useful. Sometimes it is important to understand the elasticity of individual groups. This is when using the point elasticity method is superior.

## Midpoint Method Example

To finish off, we will look at a midpoint method example. If we pretend that the price of pick-up trucks jumped from $37,000 to $45,000 because the world ran out of steel, the number of trucks demanded would fall from 15,000 to just 8,000. Figure 3 shows us what it would look like on a graph.

Figure 3 shows us how consumers would react if the price suddenly increased from $37,000 to $45,000. Using the midpoint method, we will calculate the elasticity of demand for pick-up trucks.

\(\hbox{Elasticity of Demand}=\frac{\frac{(8,000-15,000)}{(8,000+15,000)/2}}{\frac{($45,000-$37,000)}{($45,000+$37,000)/2}}\)

\(\hbox{Elasticity of Demand}=\frac{\frac{-7,000}{11,500}}{\frac{$8,000}{$41,000}}\)

\(\hbox{Elasticity of Demand}=\frac{-0.61}{0.2}\)

\(\hbox{Elasticity of Demand}=-3.05\)

The elasticity of demand for pick-up trucks is 3.05. That tells us that people are very elastic to the price of trucks. Since we used the midpoint method, we know that the elasticity would be the same even if the price of trucks decreased from $45,000 to $37,000.

## Midpoint Method - Key takeaways

- The midpoint method uses the midpoint between two data points to calculate the percent change in the price and its quantity supplied or demanded. This percent change is then used to calculate the elasticity of supply and demand.
- The two methods for calculating elasticity are the point elasticity method and the midpoint method.
- The midpoint method formula is: \(\hbox{Elasticity of Demand}=\frac{\frac{(Q_2-Q_1)}{(Q_2+Q_1)/2}}{\frac{(P_2-P_1)}{(P_2+P_1)/2}}\)
- The advantage of using the midpoint method is that the elasticity does not change regardless of the initial value and new value.
- The disadvantage of the midpoint method is that it is not as precise as the point elasticity method as the points move farther apart.

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##### Frequently Asked Questions about Midpoint Method

What is the midpoint method in economics?

The midpoint method is a formula in economics that uses the midpoint between two values or their average to calculate elasticity.

What is the midpoint method used for?

The midpoint method is used to find the elasticity of supply or demand in economics without having to consider if the price is increasing or decreasing.

What is the midpoint method for price elasticity?

The midpoint method calculates elasticity by using the average percent change in the price of a good and its quantity supplied or demanded to calculate the elasticity of supply and demand.

Why is the midpoint formula used to calculate elasticity?

The midpoint formula is used to calculate elasticity because it gives us the same elasticity value regardless of if the price increases or decreases, whereas when using the point elasticity we have to know which value is the initial value.

What is the advantage of the midpoint method?

The main advantage of the midpoint method is that it gives us the same elasticity value from one price point to another and it does not matter if the price decreases or increases.

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