The price elasticity of demand is unit-elastic (based on the midpoint formula)

Q: What is the midpoint formula for elasticity of demand?

Midpoint Price = (P1 + P2) / 2 = (10 + 8) / 2 = 9. % change in qty demanded = (60 – 40) / 50 = 0.4. % change in price = (8 – 10) / 9 = -0.22. Arc Ed = 0.4 / -0.22 = 1.82.

Q: Is demand unit elastic at the midpoint?

The unit elastic demand is at the midpoint of the demand curve. The bottom half of the curve shows an inelastic demand because if the price rises, at any quantity below the midpoint, the expenditure increases despite the fact that the quantity is falling. At the top half of the diagram, the curve is elastic.

Q: What is price elasticity at midpoint?

To calculate elasticity along a demand or supply curve economists use the average percent change in both quantity and price. This is called the Midpoint Method for Elasticity, and is represented in the following equations: %changeinquantity=Q2−Q1(Q2+Q1)2×100. %changeinprice=P2−P1(P2+P1)2×100.

Q: What is unit elastic formula?

To calculate elasticity, take the percentage change in either demand or supply and divide it by the percent change in price. The resulting number is the goods elasticity value. If the number is equal to 1, then the good is unit elastic.

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Learning Objectives

Inhaltsverzeichnis Show

Calculating Price Elasticity of Demand
Key Concepts and Summary
Calculating Price Elasticity of Demand
WORK IT OUT
Calculating the Price Elasticity of Supply
CLEAR IT UP
What is the midpoint formula for elasticity of demand?
Is demand unit elastic at the midpoint?
What is price elasticity at midpoint?
What is unit elastic formula?

Table $\PageIndex{1}$: Elastic, Inelastic, and Unitary - Three Cases of Elasticity

If . . .	Then . . .	And It Is Called . . .
	$\frac{\text{% change in quantity}}{\text{% change in price}} > 1$	Elastic
	$\frac{\text{% change in quantity}}{\text{% change in price}} = 1$	Unitary
	$\frac{\text{% change in quantity}}{\text{% change in price}} < 1$	Inelastic

Calculating Price Elasticity of Demand

Calculating the Price Elasticity of Demand

Figure $\PageIndex{1}$: The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

Example $\PageIndex{1}$: Finding the Price Elasticity of Demand

Figure $\PageIndex{2}$: The price elasticity of supply is calculated as the percentage change in quantity divided by the percentage change in price.

Is the elasticity the slope?

Key Concepts and Summary

Glossary

elastic demandwhen the elasticity of demand is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in priceelastic supplywhen the elasticity of either supply is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in priceelasticityan economics concept that measures responsiveness of one variable to changes in another variableinelastic demandwhen the elasticity of demand is less than one, indicating that a 1 percent increase in price paid by the consumer leads to less than a 1 percent change in purchases (and vice versa); this indicates a low responsiveness by consumers to price changesinelastic supplywhen the elasticity of supply is less than one, indicating that a 1 percent increase in price paid to the firm will result in a less than 1 percent increase in production by the firm; this indicates a low responsiveness of the firm to price increases (and vice versa if prices drop)price elasticitythe relationship between the percent change in price resulting in a corresponding percentage change in the quantity demanded or suppliedprice elasticity of demandpercentage change in the quantity demanded of a good or service divided the percentage change in priceprice elasticity of supplypercentage change in the quantity supplied divided by the percentage change in priceunitary elasticitywhen the calculated elasticity is equal to one indicating that a change in the price of the good or service results in a proportional change in the quantity demanded or supplied

By the end of this section, you will be able to:

Calculate the price elasticity of demand
Calculate the price elasticity of supply

Both the demand and supply curve show the relationship between price and the number of units demanded or supplied. Price elasticity is the ratio between the percentage change in the quantity demanded [latex]Q_d[/latex] or supplied ([latex]Q_s[/latex]) and the corresponding percent change in price. The price elasticity of demand is the percentage change in the quantity demanded of a good or service divided by the percentage change in the price. The price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price. We can usefully divide elasticities into three broad categories: elastic, inelastic, and unitary. An elastic demand or elastic supply is one in which the elasticity is greater than one, indicating a high responsiveness to changes in price. Elasticities that are less than one indicate low responsiveness to price changes and correspond to inelastic demand or inelastic supply. Unitary elasticities indicate proportional responsiveness of either demand or supply, as Table 5.1 summarizes.

Table 5.1 Elastic, Inelastic, and Unitary: Three Cases of Elasticity

If . . .	Then . . .	And It Is Called . . .
% change in quantity > % change in price	\[\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price}>1\]	Elastic
% change in quantity = % change in price	\[\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price}=1\]	Unitary
% change in quantity < % change in price	\[\frac{\%\;change\;in\;quantity}{\%\;change\;in\;price}<1\]	Inelastic

Table 5.1 Elastic, Inelastic, and Unitary: Three Cases of Elasticity (Source: https://openstax.org/books/principles-microeconomics-2e/pages/1-introduction)(CC BY 4.0)

To calculate elasticity along a demand or supply curve economists use the average percent change in both quantity and price. This is called the Midpoint Method for Elasticity, and is represented in the following equations:
\[\%\;change\;in\;quantity=\frac{Q_2-Q_1}{\frac{\left(Q_2+Q_1\right)}2}\times 100\]
\[\%\;change\;in\;price=\frac{P_2-P_1}{\frac{\left(P_2+P_1\right)}2}\times 100\]
The advantage of the Midpoint Method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base (average quantity and average price) for both cases.

Calculating Price Elasticity of Demand

Let’s calculate the elasticity between points A and B and between points G and H as Figure 5.1 shows.

Figure 5.1 Price Elasticity of Demand We calculate the price elasticity of demand as the percentage change in quantity divided by the percentage change in price. Calculating the Price Elasticity of Demand. By Openstax. Source: Openstax. CC BY 4.0

First, apply the formula to calculate the elasticity as price decreases from $70 at point B to $60 at point A:
\[\% \text { change in quantity }=\frac{3,000-2,800}{(3,000+2,800) / 2} \times 100\]
\[=\frac{200}{2,900} \times 100\]
\[=6.9\]
\[\% \text { change in price }=\frac{60-70}{(60+70) / 2} \times 100\]
\[\frac{-10}{65}\times 100\]
\[=-15.4\]
\[\text { Price Elasticity of Demand }=\frac{6.9 \%}{-15.4 \%}\]
\[=0.45\]
Therefore, the elasticity of demand between these two points is \[\frac{6.9%}{-15.4%}\] which is 0.45, an amount smaller than one, showing that the demand is inelastic in this interval. Price elasticities of demand are always negative since price and quantity demanded always move in opposite directions (on the demand curve). By convention, we always talk about elasticities as positive numbers. Mathematically, we take the absolute value of the result. We will ignore this detail from now on, while remembering to interpret elasticities as positive numbers.This means that, along the demand curve between point B and A, if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 4.5% decrease in quantity demanded. A 10% decrease in the price will result in only a 4.5% increase in the quantity demanded. Price elasticities of demand are negative numbers indicating that the demand curve is downward sloping, but we read them as absolute values. The following Work It Out feature will walk you through calculating the price elasticity of demand.

WORK IT OUT

Finding the Price Elasticity of Demand

Calculate the price elasticity of demand using the data in Figure 5.1 for an increase in price from G to H. Has the elasticity increased or decreased?

Step 1. We know that:

\[Price\;Elasticity\;of\;Demand=\frac{\%\;change\;in\;quantity}{\%change\;in\;price}\]
Step 2. From the Midpoint Formula we know that:

\[\%\;change\;in\;quantity=\frac{Q_2-Q_1}{\frac{\left (Q_2+Q_1\right )}{2}}\times 100\]
\[\%\;change\;in\;price=\frac{P_2-P_1}{\frac{\left (P_2+P_1\right )}{2}}\times 100\]

Step 3. So we can use the values provided in the figure in each equation:

\[\%\;change\;in\;quantity=\frac{1,600–1,800}{\frac{\left (1,600+1,800\right )}{2}} × 100\]
\[=\frac{200}{1,700}\times 100\]
\[=\;–11.76\]
\[\%\;change\;in\;price=\frac{130–120}{\frac{\left (130+120\right )}{2}}\times 100\]
\[=\frac{10}{125}\times 100\]
\[=8.0\]
Step 4. Then, we can use those values to determine the price elasticity of demand:

\[Price\;Elasticity\;of\;Demand=\frac{\%\;change\;in\;quantity}{\%change\;in\;price}\]
\[=\frac{–11.76}{8}\]
\[=1.47\]
Therefore, the elasticity of demand from G to is H 1.47. The magnitude of the elasticity has increased (in absolute value) as we moved up along the demand curve from points A to B. Recall that the elasticity between these two points was 0.45. Demand was inelastic between points A and B and elastic between points G and H. This shows us that price elasticity of demand changes at different points along a straight-line demand curve.

Calculating the Price Elasticity of Supply

Assume that an apartment rents for $650 per month and at that price the landlord rents 10,000 units are rented as Figure 5.2 shows. When the price increases to $700 per month, the landlord supplies 13,000 units into the market. By what percentage does apartment supply increase? What is the price sensitivity?

Figure 5.2 Price Elasticity of Supply We calculate the price elasticity of supply as the percentage change in quantity divided by the percentage change in price. Price Elasticity of Supply. By Openstax. Source: Openstax CC BY 4.0

Using the Midpoint Method,
\[\% \text { change in quantity }=\frac{13,000-10,000}{(13,000+10,000) / 2} \times 100\]
\[=\frac{3,000}{11,500} \times 100\]
\[=26.1\]
\[\% \text { change in price }=\frac{5700-5650}{(5700+5650) 2} \times 100\]
\[=\frac{50}{675} \times 100\]
\[=7.4\]
\[\text { Price Elasticity of Demand }=\frac{26.1 \%}{7.4 \%}\]
\[=3.53\]
Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and we read it as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change. If you’re starting to wonder if the concept of slope fits into this calculation, read the following Clear It Up box.

CLEAR IT UP

Is the elasticity the slope?

It is a common mistake to confuse the slope of either the supply or demand curve with its elasticity. The slope is the rate of change in units along the curve, or the rise/run (change in y over the change in x). For example, in Figure 5.2, at each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200 compared to the point to its left. The slope is –10/200 along the entire demand curve and does not change. The price elasticity, however, changes along the curve. Elasticity between points A and B was 0.45 and increased to 1.47 between points G and H. Elasticity is the percentage change, which is a different calculation from the slope and has a different meaning.

When we are at the upper end of a demand curve, where the price is high and the quantity demanded is low, a small change in the quantity demanded, even in, say, one unit, is pretty big in percentage terms. A change in the price of, say, a dollar, is going to be much less important in percentage terms than it would have been at the bottom of the demand curve. Likewise, at the bottom of the demand curve, that one unit change when the quantity demanded is high will be small as a percentage.

Thus, at one end of the demand curve, where we have a large percentage change in quantity demanded over a small percentage change in price, the elasticity value would be high, or demand would be relatively elastic. Even with the same change in the price and the same change in the quantity demanded, at the other end of the demand curve the quantity is much higher, and the price is much lower, so the percentage change in quantity demanded is smaller and the percentage change in price is much higher. That means at the bottom of the curve we’d have a small numerator over a large denominator, so the elasticity measure would be much lower, or inelastic.

As we move along the demand curve, the values for quantity and price go up or down, depending on which way we are moving, so the percentages for, say, a $1 difference in price or a one unit difference in quantity, will change as well, which means the ratios of those percentages and hence the elasticity will change.

What is the midpoint formula for elasticity of demand?

Midpoint Price = (P₁ + P₂) / 2 = (10 + 8) / 2 = 9. % change in qty demanded = (60 – 40) / 50 = 0.4. % change in price = (8 – 10) / 9 = -0.22. Arc E_d = 0.4 / -0.22 = 1.82.

Is demand unit elastic at the midpoint?

The unit elastic demand is at the midpoint of the demand curve. The bottom half of the curve shows an inelastic demand because if the price rises, at any quantity below the midpoint, the expenditure increases despite the fact that the quantity is falling. At the top half of the diagram, the curve is elastic.

What is price elasticity at midpoint?

What is unit elastic formula?

To calculate elasticity, take the percentage change in either demand or supply and divide it by the percent change in price. The resulting number is the goods elasticity value. If the number is equal to 1, then the good is unit elastic.