Both the demand and also supply curve show the relationship between price and the variety of units demanded or supplied. Price elasticity is the ratio between the percentage change in the quantity demanded (Qd) or gave (Qs) and the corresponding percent change in price. The price elasticity that demand is the percentage readjust in the quantity demanded of a an excellent or service divided through the percentage adjust in the price. The price elasticity that supply is the percentage adjust in amount supplied split by the percentage adjust in price.

You are watching: Generally, we calculate elasticity as the:

Elasticities deserve to be usefully divided into three large categories: elastic, inelastic, and also unitary. One elastic demand or elastic supply is one in which the elasticity is better than one, describe a high responsiveness to alters in price. Elasticities that are much less than one suggest low responsiveness to price changes and also correspond come inelastic demand or inelastic supply. Unitary elasticities suggest proportional responsiveness the either need or supply, together summarized in Table 1.

If . . .Then . . .And it Is dubbed . . .
\%\;change\;in\;quantity > \%\;change\;in\;price\frac\%\;change\;in\;quantity\%\;change\;in\;price) > 1Elastic
\%\;change\;in\;quantity = \%\;change\;in\;price\frac\%\;change\;in\;quantity\%\;change\;in\;price) = 1Unitary
\%\;change\;in\;quantity

Before we acquire into the nitty gritty the elasticity, gain this write-up on elasticity and ticket price at the at sight Bowl.

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To calculation elasticity, instead of using straightforward percentage changes in quantity and also price, economists use the typical percent readjust in both quantity and also price. This is dubbed the Midpoint method for Elasticity, and is stood for in the following equations:


= l}\%\;change\;in\;quantity & \frac Q _ 2 - Q _ 1 ( Q _ 2 + Q _ 1 )/2 \times 100 \\<1em> \%\;change\;in\;price & \frac ns _ 2 - ns _ 1 ( ns _ 2 + ns _ 1 )/2 \times 100 \endarray

The benefit of the is Midpoint Method is the one obtains the same elasticity in between two price clues whether there is a price boost or decrease. This is since the formula uses the same base for both cases.

Calculating Price Elasticity of Demand

Let’s calculate the elasticity between points A and also B and between points G and H presented in figure 1.

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Figure 1. Calculating the Price Elasticity of Demand. The price elasticity of demand is calculated together the percentage readjust in quantity split by the percentage adjust in price.

First, use the formula to calculate the elasticity as price decreases from $70 at point B to $60 at suggest A:


= l}\%\;change\;in\;quantity & \frac 3,000 - 2,800 ( 3,000 + 2,800 )/2 \times 100 \\<1em> & \frac 200 2,900 \times 100 \\<1em> & = 6.9 \\<1em> \%\;change\;in\;price & \frac 60 - 70 ( 60 + 70 )/2 \times 100 \\<1em> & \frac -10 65 \times 100 \\<1em> & -15.4 \\<1em> Price\;Elasticity\;of\;Demand & \frac 6.9\% -15.4\% \\<1em> & 0.45 \endarray

Therefore, the elasticity the demand in between these 2 points is \frac 6.9\% -15.4\%  which is 0.45, one amount smaller than one, reflecting that the need is inelastic in this interval. Price elasticities of need are always an unfavorable since price and quantity demanded constantly move in opposite directions (on the need curve). By convention, we always talk around elasticities as hopeful numbers. Therefore mathematically, we take the absolute value of the result. Us will ignore this detail from now on, while remembering to translate elasticities as hopeful numbers.

This way that, follow me the demand curve between point B and also A, if the price alters by 1%, the quantity demanded will change by 0.45%. A readjust in the price will result in a smaller sized percentage adjust in the quantity demanded. Because that example, a 10% increase in the price will result in only a 4.5% decrease in amount demanded. A 10% decrease in the price will an outcome in only a 4.5% increase in the quantity demanded. Price elasticities of need are an adverse numbers indicating the the need curve is bottom sloping, but are review as absolute values. The complying with Work that Out feature will go you v calculating the price elasticity the demand.


Finding the Price Elasticity the Demand

Calculate the price elasticity of need using the data in figure 1 for boost in price indigenous 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
= l}\%\;change\;in\;quantity & \frac Q _ 2 - Q _ 1 ( Q _ 2 + Q _ 1 )/2 \times 100 \\<1em> \%\;change\;in\;price & \frac p _ 2 - p _ 1 ( p _ 2 + ns _ 1 )/2 \times 100 \endarray
= l}\%\;change\;in\;quantity & \frac 1,600 - 1,800 ( 1,600 + 1,800 )/2 \times 100 \\<1em> & \frac -200 1,700 \times 100 \\<1em> & -11.76 \\<1em> \%\;change\;in\;price & \frac 130 - 120 ( 130 + 120 )/2 \times 100 \\<1em> & \frac 10 125 \times 100 \\<1em> & 8.0 \endarray
= l}Price\;Elasticity\;of\;Demand & \frac \%\;change\;in\;quantity \%\;change\;in\;price \\<1em> & \frac -11.76 8 \\<1em> & 1.47 \endarray

Therefore, the elasticity of need from G come H 1.47. The magnitude of the elasticity has increased (in absolute value) as we relocated up follow me the demand curve indigenous points A come B. Recall that the elasticity between these two points to be 0.45. Need was inelastic in between points A and B and also elastic in between points G and H. This reflects us that price elasticity of demand changes at various points along a straight-line demand curve.


Calculating the Price Elasticity of Supply

Assume the an apartment rents for $650 per month and also at the price 10,000 units space rented as presented in number 2. Once the price rises to $700 per month, 13,000 units room supplied right into the market. By what portion does apartment it is provided increase? What is the price sensitivity?

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Figure 2. Price Elasticity of Supply. The price elasticity of it is provided is calculated as the percentage adjust in quantity separated by the percentage adjust in price.

Using the Midpoint Method,


= l}\%\;change\;in\;quantity & \frac 13,000 - 10,000 ( 13,000 + 10,000 )/2 \times 100 \\<1em> & \frac 3,000 11,500 \times 100 \\<1em> & 26.1 \\<1em> \%\;change\;in\;price & \frac \$700 - \$650 ( \$700 + \$650 )/2 \times 100 \\<1em> & \frac 50 675 \times 100 \\<1em> & 7.4 \\<1em> Price\;Elasticity\;of\;Demand & \frac 26.1\% 7.4\% \\<1em> & 3.53 \endarray

Again, similar to the elasticity of demand, the elasticity of supply is not adhered to by any units. Elasticity is a ratio of one percentage change to an additional percentage change—nothing more—and is review as an pure value. In this case, a 1% increase in price causes rise in quantity provided of 3.5%. The higher than one elasticity of supply means that the percentage change in quantity gave will be better than a one percent price change. If you"re beginning to wonder if the principle of slope fits into this calculation, check out the complying with Clear It increase box.


Is the elasticity the slope?

It is a usual mistake to confuse the steep of one of two people the it is provided or need curve with its elasticity. The steep is the rate of adjust in units along the curve, or the rise/run (change in y over the readjust in x). For example, in figure 1, each point shown top top the demand curve, price fall by $10 and also the number of units demanded rises by 200. Therefore the steep is –10/200 along the entire demand curve and does not change. The price elasticity, however, alters along the curve. Elasticity between points A and also B was 0.45 and also increased to 1.47 in between points G and also H. Elasticity is the percentage change, i m sorry is a various calculation from the slope and has a different meaning.

When we are at the upper finish of a need curve, whereby price is high and the quantity demanded is low, a small change in the quantity demanded, also in, say, one unit, is pretty huge in portion terms. A adjust in price of, say, a dollar, is going to be much less essential in percent terms than it would have been at the bottom of the need curve. Likewise, at the bottom the the demand curve, the one unit readjust when the amount demanded is high will be little as a percentage.

So, at one finish of the demand curve, wherein we have a big percentage readjust in quantity demanded end a tiny percentage change in price, the elasticity worth would be high, or demand would be relatively elastic. Also with the same adjust in the price and also the same adjust in the amount demanded, in ~ the other finish of the need curve the quantity is much higher, and the price is much lower, therefore the percentage adjust in amount demanded is smaller and the percentage adjust in price is much higher. That method at the bottom that the curve we"d have a little numerator over a huge denominator, for this reason the elasticity measure would be lot lower, or inelastic.

As we relocate along the demand curve, the values for quantity and price go up or down, depending on which method we room moving, therefore the percentages for, say, a $1 difference in price or a one unit difference in quantity, will adjust as well, which method the ratios of those percentages will change.


Key Concepts and Summary

Price elasticity measures the responsiveness the the amount demanded or gave of a great to a change in the price. The is computed as the percentage adjust in quantity demanded (or supplied) separated by the percentage change in price. Elasticity deserve to be explained as elastic (or very responsive), unit elastic, or inelastic (not really responsive). Elastic need or supply curves suggest that quantity demanded or gave respond come price transforms in a higher than proportional manner. One inelastic need or it is provided curve is one where a provided percentage change in price will cause a smaller sized percentage adjust in quantity demanded or supplied. A unitary elasticity means that a provided percentage adjust in price leads to an equal percentage adjust in quantity demanded or supplied.


Review Questions

What is the formula for calculating elasticity?What is the price elasticity of demand? deserve to you describe it in your very own words?What is the price elasticity of supply? have the right to you describe it in your own words?

Critical thinking Questions

Transatlantic air travel in service class has actually an approximated elasticity of need of 0.40 much less than transatlantic air travel in economic climate class, through an approximated price elasticity the 0.62. Why do you think this is the case?What is the relationship between price elasticity and also position top top the demand curve? for example, as you move up the need curve to greater prices and lower quantities, what wake up to the measure elasticity? exactly how would you explain that?

Problems

The equation because that a demand curve is ns = 48 – 3Q. What is the elasticity in relocating from a quantity of 5 to a quantity of 6?The equation because that a need curve is p = 2/Q. What is the elasticity of demand as price drops from 5 come 4? What is the elasticity of demand as the price falls from 9 come 8? would certainly you suppose these answers to be the same?The equation for a it is provided curve is 4P = Q. What is the elasticity the supply together price rises native 3 come 4? What is the elasticity of supply as the price rises native 7 come 8? would you expect these answer to it is in the same?The equation for a supply curve is p = 3Q – 8. What is the elasticity in moving from a price of 4 come a price the 7?

Glossary

elastic demandwhen the elasticity of need is better than one, denote a high responsiveness of amount demanded or supplied to transforms in priceelastic supplywhen the elasticity of either supply is higher than one, denote a high responsiveness of quantity demanded or supplied to transforms in priceelasticityan economics principle that procedures responsiveness the one variable to changes in one more variableinelastic demandwhen the elasticity of demand is much less than one, indicating the a 1 percent rise in price payment by the consumer leads to much less than a 1 percent readjust in purchase (and evil versa); this shows a short responsiveness by consumer to price changesinelastic supplywhen the elasticity of supply is much less than one, indicating the a 1 percent boost in price paid to the for sure will an outcome in a much less than 1 percent increase in production by the firm; this indicates a low responsiveness the the firm come price rises (and vice versa if price drop)price elasticitythe relationship between the percent adjust in price leading to a corresponding percentage readjust in the quantity demanded or suppliedprice elasticity the demandpercentage change in the quantity demanded the a great or service divided the percentage adjust in priceprice elasticity that supplypercentage adjust in the amount supplied divided by the percentage readjust in priceunitary elasticitywhen the calculate elasticity is same to one indicating that a change in the price the the great or organization results in a proportional change in the amount demanded or supplied

Solutions

Answers come Self-Check Questions

From point B to point C, price rises from $70 come $80, and also Qd decreases native 2,800 to 2,600. So:
= l}\%\;change\;in\;quantity & \frac 2,600 - 2,800 ( 2,600 + 2,800 )/2 \times 100 \\<1em> & \frac -200 2,700 \times 100 \\<1em> & -7.41 \\<1em> \%\;change\;in\;price & \frac 80 - 70 ( 80 + 70 )/2 \times 100 \\<1em> & \frac 10 75 \times 100 \\<1em> & 13.33 \\<1em> Elasticity\;of\;Demand & \frac -7.41\% 13.33\% \\<1em> & 0.56 \endarray

The need curve is inelastic in this area; that is, that is elasticity worth is much less than one.

Answer from suggest D to point E:


= l}\%\;change\;in\;quantity & \frac 2,200 - 2,400 ( 2,200 + 2,400 )/2 \times 100 \\<1em> & \frac -200 2,300 \times 100 \\<1em> & -8.7 \\<1em> \%\;change\;in\;price & \frac 100 - 90 ( 100 + 90 )/2 \times 100 \\<1em> & \frac 10 95 \times 100 \\<1em> & 10.53 \\<1em> Elasticity\;of\;Demand & \frac -8.7\% 10.53\% \\<1em> & 0.83 \endarray

The need curve is inelastic in this area; that is, that is elasticity worth is less than one.

Answer from suggest G to allude H:


= l}\%\;change\;in\;quantity & \frac 1,600 - 1,800 ( 1,600 + 1,800 )/2 \times 100 \\<1em> & \frac -200 1,700 \times 100 \\<1em> & -11.76 \\<1em> \%\;change\;in\;price & \frac 130 - 120 ( 130 + 120 )/2 \times 100 \\<1em> & \frac 10 125 \times 100 \\<1em> & 7.81 \\<1em> Elasticity\;of\;Demand & \frac -11.76\% 7.81\% \\<1em> & -1.51 \endarray

The need curve is elastic in this interval.From suggest J to point K, price rises native $8 come $9, and quantity rises indigenous 50 to 70. So:
= l}\%\;change\;in\;quantity & \frac 70 - 50 ( 70 + 50 )/2 \times 100 \\<1em> & \frac 20 60 \times 100 \\<1em> & 33.33 \\<1em> \%\;change\;in\;price & \frac \$9 - \$8 ( \$9 + \$8 )/2 \times 100 \\<1em> & \frac 1 8.5 \times 100 \\<1em> & 11.76 \\<1em> Elasticity\;of\;Supply & \frac 33.33\% 11.76\% \\<1em> & 2.83 \endarray


The it is provided curve is elastic in this area; the is, the elasticity worth is greater than one.

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From suggest L to allude M, the price rises native $10 to $11, while the Qs rises from 80 to 88:


= l}\%\;change\;in\;quantity & \frac 88 - 80 ( 88 + 80 )/2 \times 100 \\<1em> & \frac 8 84 \times 100 \\<1em> & 9.52 \\<1em> \%\;change\;in\;price & \frac \$11 - \$10 ( \$11 + \$10 )/2 \times 100 \\<1em> & \frac 1 10.5 \times 100 \\<1em> & 9.52 \\<1em> Elasticity\;of\;Demand & \frac 9.52\% 9.52\% \\<1em> & 1.0 \endarray

The supply curve has unitary elasticity in this area.

From allude N to point P, the price rises indigenous $12 to $13, and Qs rises native 95 to 100:


= l}\%\;change\;in\;quantity & \frac 100 - 95 ( 100 + 95 )/2 \times 100 \\<1em> & \frac 5 97.5 \times 100 \\<1em> & 5.13 \\<1em> \%\;change\;in\;price & \frac \$13 - \$12 ( \$13 + \$12 )/2 \times 100 \\<1em> & \frac 1 12.5 \times 100 \\<1em> & 8.0 \\<1em> Elasticity\;of\;Supply & \frac 5.13\% 8.0\% \\<1em> & 0.64 \endarray