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. Elasticities can be usefully divided into three broad categories: elastic, inelastic, and unitary. An
To calculate elasticity, instead of using simple percentage changes in quantity and price, 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=Q2–Q1Q2+ Q1/2 × 100% change in price=P2– P1P2+ P1/2 × 100 The advantage of the is ## Calculating Price Elasticity of DemandLet’s calculate the elasticity between points A and B and between points G and H shown in [link]. First, apply the formula to calculate the elasticity as price decreases from $70 at point B to $60 at point A: % change in quantity=3,000–2,800(3,000+2,800)/2 × 100=2002,900 × 100=6.9% change in price=60–70(60+70)/2 × 100=–1065 × 100=–15.4Price Elasticity of Demand= 6.9%–15.4%=0.45 Therefore, the elasticity of demand between these two points is 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. So 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 are read as absolute values. The following Work It Out feature will walk you through calculating the price elasticity of demand.
Finding the Price Elasticity of Demand Calculate the price elasticity of demand using the data in [link] for an increase in price from G to H. Has the elasticity increased or decreased? Step 1. We know that: Price Elasticity of Demand=% change in quantity% change in price Step 2. From the % change in quantity=Q2–Q1(Q2+Q1)/2 × 100% change in price=P2–P1(P2+P1)/2 × 100 Step 3. So we can use the values provided in the figure in each equation: % change in quantity=1,600–1,800(1,600+1,800)/2 × 100=–2001,700 × 100=–11.76% change in price=130–120(130+120)/2 × 100=10125 × 100=8.0 Step 4. Then, those values can be used to determine the price elasticity of demand: Price Elasticity of Demand=% change in quantity% change in price=–11.768=1.47 Therefore, the elasticity of demand from G to H 1.47. The magnitude of the elasticity has increased (in absolute value) as we moved up along the ## Calculating the Price Elasticity of SupplyAssume that an apartment rents for $650 per month and at that price 10,000 units are rented as shown in [link]. When the price increases to $700 per month, 13,000 units are supplied into the market. By what percentage does apartment supply increase? What is the price sensitivity? Using the % change in quantity=13,000–10,000(13,000+10,000)/2 × 100=3,00011,500 × 100=26.1% change in price=$700–$600($700+$650)/2 × 100=50675 × 100=7.4Price Elasticity of Supply=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 is read 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.
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 [link], each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200. So 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 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 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. So, 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 will change. Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded (or supplied) divided by the percentage change in price. Elasticity can be described as elastic (or very responsive), unit elastic, or inelastic (not very responsive). Elastic demand or supply curves indicate that quantity demanded or supplied respond to price changes in a greater than proportional manner. An inelastic demand or supply curve is one where a given percentage change in price will cause a smaller percentage change in quantity demanded or supplied. A unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied. ## Self-Check Questions
From the data shown in [link] about demand for smart phones, calculate the price elasticity of demand from: point B to point C, point D to point E, and point G to point H. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
From point B to point C, price rises from $70 to $80, and Qd decreases from 2,800 to 2,600. So: % change in quantity=2600–28002600+2800÷2 × 100=–2002700 × 100=–7.41% change in price=80–7080+70÷2 × 100=1075 × 100=13.33Elasticity of Demand=–7.41%13.33%=0.56 The demand curve is inelastic in this area; that is, its elasticity value is less than one. Answer from Point D to point E: % change in quantity=2200–24002200+2400÷2 × 100=–2002300 × 100=–8.7% change in price=100–90100+90÷2 × 100=1095 × 100=10.53Elasticity of Demand=–8.7% 10.53%=0.83 The demand curve is inelastic in this area; that is, its elasticity value is less than one. Answer from Point G to point H: % change in quantity=1600–1800 1700 × 100 =–2001700 × 100 =–11.76% change in price=130–120 125 × 100 =10125 × 100 =7.81Elasticity of Demand=–11.76% 7.81% =–1.51 The demand curve is elastic in this interval.
From the data shown in [link] about supply of alarm clocks, calculate the price elasticity of supply from: point J to point K, point L to point M, and point N to point P. Classify the elasticity at each point as elastic, inelastic, or unit elastic.
From point J to point K, price rises from $8 to $9, and quantity rises from 50 to 70. So: % change in quantity=70–5070+50÷2 × 100=2060 × 100=33.33% change in price=$9–$8$9+$8÷2 × 100=18.5 × 100=11.76Elasticity of Supply=33.33%11.76%=2.83 The supply curve is elastic in this area; that is, its elasticity value is greater than one. From point L to point M, the price rises from $10 to $11, while the Qs rises from 80 to 88: % change in quantity=88–8088+80÷2 × 100=884 × 100=9.52%change in price=$11–$10$11+$10÷2 × 100=110.5 × 100=9.52Elasticity of Demand=9.52%9.52%=1.0 The supply curve has unitary elasticity in this area. From point N to point P, the price rises from $12 to $13, and Qs rises from 95 to 100: % change in quantity=100–95100+95÷2×100=597.5×100=5.13% change in price=$13–$12$13+$12÷2 × 100=112.5 × 100=8.0Elasticity of Supply=5.13%8.0% =0.64 The supply curve is inelastic in this region of the supply curve. ## Review Questions
What is the formula for calculating elasticity?
What is the price elasticity of demand? Can you explain it in your own words?
What is the price elasticity of supply? Can you explain it in your own words? ## Critical Thinking Questions
Transatlantic air travel in business class has an estimated elasticity of demand of 0.40 less than transatlantic air travel in economy class, with an estimated price elasticity of 0.62. Why do you think this is the case?
What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? ## Problems
The equation for a demand curve is P = 48 – 3Q. What is the elasticity in moving from a quantity of 5 to a quantity of 6?
The equation for a demand curve is P = 2/Q. What is the elasticity of demand as price falls from 5 to 4? What is the elasticity of demand as the price falls from 9 to 8? Would you expect these answers to be the same?
The equation for a supply curve is 4P = Q. What is the elasticity of supply as price rises from 3 to 4? What is the elasticity of supply as the price rises from 7 to 8? Would you expect these answers to be the same?
The equation for a supply curve is P = 3Q – 8. What is the elasticity in moving from a price of 4 to a price of 7? elastic demand when the elasticity of demand is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in price elastic supply when the elasticity of either supply is greater than one, indicating a high responsiveness of quantity demanded or supplied to changes in price elasticity an economics concept that measures responsiveness of one variable to changes in another variable inelastic demand when 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 changes inelastic supply when 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 elasticity the relationship between the percent change in price resulting in a corresponding percentage change in the quantity demanded or supplied price elasticity of demand percentage change in the quantity demanded of a good or service divided the percentage change in price price elasticity of supply percentage change in the quantity supplied divided by the percentage change in price unitary elasticity when 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 This work is licensed under a Creative Commons Attribution 4.0 International License. You can also download for free at http://cnx.org/contents/ Attribution: |