Chapter 4: Elasticity

Chapter 4: Elasticity Preface: The price elasticity of demand measures how strongly demanders respond to a change in the price of a good. The price elasticity of demand can be used to make quantitative predictions of how changes affect the price and quantity demanded of a good. The income elasticity of demand measures how strongly demanders respond to a change in income, and the cross elasticity of demand measures how strongly demanders respond to the change in the price of another good. The price elasticity of supply measures how strongly suppliers respond to a change in the price of a good. e.g.: Demand for Pork (assume that $1 US. dollar = $30 NT. dollars) Case 1 P (measure in NT $) $90/kg $10/kg Q 5 kg kg Case P (measure in US $) $3/kg $4/kg Q 5kg kg Slope in Case 1. P 90 10 30 = = = 10 5 3 Case. P 3 4 1 = = 5 3 I. Price Elasticity of Demand A. In general, elasticity measures responsiveness. The price elasticity of demand measures how responsive demanders are to a change in the price of the good. This information is often useful for both businesses and governments. B. Calculating the Price Elasticity of Demand 1

1. The price elasticity of demand is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on a buyer s plans remain unchanged. The price elasticity of demand is equal to the absolute value of: Percentage change in quantity demanded. Percentage change in price (= / ) 1 units-free measure Q P P = P P Q K K $ K K = = K$ K K K ( ) ( ) (P 1,Q 1 (P,Q ) Q P P = P P Q Q Q1 P P 1 P1 + P Q1 + Q. The demand elasticity formula yields a negative value, because price and quantity move in opposite directions. However, it is the magnitude, or absolute value, of the

measure that reveals how responsive the quantity change has been to a price change. So we use the magnitude or the absolute value of the price elasticity of demand. C. The table below has two points on the demand curve for pizza from a particular pizza parlor. Price Quantity (dollars per demanded pizza) (pizzas per week) 14 500 16 400 1. The absolute value of the percent change in quantity demanded is [(500 400) 450] 100 =. percent.. The absolute value of the percentage change in price is [($14 $16) $15] 100 = 13.3 percent. 3. Between these two points on the demand curve, the price elasticity of demand is.% 13.3% = 1.67. D. Inelastic and Elastic Demand 1. If the price elasticity of demand is less than 1, the good is said to have an inelastic demand. In this case, the percentage change in the quantity demanded is less than the percentage change in price.. If the quantity demanded remains constant when the price changes, then the good is said to have perfectly inelastic demand. The price elasticity of demand is 0 and the good s demand curve is a vertical line. 3

3. If the price elasticity of demand is equal to 1, the good is said to have a unit elastic demand. In this case, the percentage change in the quantity demanded equals the percentage change in price. (If your demand function looks like P Q = c - c is a constant, then you will get a demand curve which is unit elastic demand.) 4. If the price elasticity of demand is greater than 1, the good is said to have an elastic demand. In this case, the percentage change in the quantity demanded exceeds the percentage change in price. 5. If the quantity demanded changes by an infinitely large percentage in response to a tiny price change, then the good is said to have perfectly elastic demand. The price elasticity of demand is infinite. 4

6. The table has some real-life elasticities from the book. Furniture 1.6 Motor vehicles 1.14 Clothing 0.64 Oil 0.05 E. Elasticity Along a Straight-Line Demand Curve 1. With the exception of a vertical demand curve and a horizontal demand curve (along which the elasticity is 0 and infinite, respectively) the price elasticity of demand changes when moving along a linear demand curve.. As the figure illustrates, at points on the demand curve above the midpoint, the price elasticity of demand is elastic while at points below the midpoint, the price elasticity of demand is inelastic. At the midpoint, the price elasticity of demand is unit elastic. F. Total Revenue and Elasticity 1. The total revenue (TR) from the sale of a good equals the price of the good multiplied by the quantity sold ( TR = P Q ). a).if demand is elastic, a 1 percent price cut increases the quantity sold by more than 1 percent and total revenue increases. b).if demand is unit elastic, a 1 percent price cut increases the quantity sold by 1 percent and total revenue does not change. c).if demand is inelastic, a 1 percent price cut increases the quantity sold by less than 1 percent and total revenue decreases.. The total revenue test is a method of estimating the price elasticity of demand by observing the change in total revenue that results from a change in price, when all other influences on the quantity sold remain the same. a).if a price cut increases total revenue, demand is elastic. And if a price hike decreases total revenue, demand is elastic. b).if a price cut does not change total revenue, demand is unit elastic. And if a price hike does not change total revenue, demand is unit elastic. 5

c).if a price cut decreases total revenue, demand is inelastic. And if a price hike increases total revenue, demand is inelastic. d) In part b (shown here), as the quantity increases from zero to 5, demand is elastic, and total revenue increases. At 5, demand is unit elastic, and total revenue is at its maximum. As the quantity increases from 5 to 50, demand is inelastic, and total revenue decreases. 6

3. Similarly, when a price changes, a consumer s change in expenditure depends on the consumer s elasticity of demand. a).if demand is elastic, then a price cut means that expenditure on the item increases. b).if demand is inelastic, then a price cut means that expenditure on the item decreases. c).if demand is unit elastic, then a price cut means that expenditure on the item does not change. If ε > 1 & P, then Q implies expenditure (P*Q) on that item If ε < 1 & P, then Q implies expenditure on that item If ε = 1 & P, then Q implies expenditure on that item does not change. G. The Factors that Influence the Elasticity of Demand The magnitude of the price elasticity of demand depends on: 1. The closeness of substitutes: The closer and more numerous the substitutes for a good or service, the more elastic the demand.. The proportion of income spent on the good: The greater the proportion of income spent on a good or service, the more elastic the demand. 3. The amount of time elapsed since the price change: The longer the time elapsed since the price change, the more elastic the demand. Price elasticity of needs vs. wants. Necessities, such as food or housing, generally have inelastic demand because there are few substitutes for food and shelter. Luxuries, such as exotic vacations, generally have elastic demand. Example: Most people s demand for salt is inelastic, largely because most people spend a miniscule amount of their income on salt. However large Northern cities demand for salt is significantly more elastic. These cities use salt to treat their roads after a snow storm. Salt is a significant fraction of their budgets. Because the proportion of their income they spend on salt is large, the price elasticity of demand for these cities is much larger than that of ordinary consumers. 7

How do gasoline purchases respond to changes in price over time? Consumer response to changes in the price of gasoline over time is a good example of the impact the amount of time elapsed has on the quantity demanded. When gas prices rise from $ to $4, consumers initially have few options available. At first, with a given car with a given gas mileage, higher gas prices do not reduce the quantity of gas consumers purchase by very much. As time passes and gasoline prices continue to remain high, some consumers eventually find ways to adjust their gas purchases by purchasing more fuel efficient cars, taking new jobs that are closer to their homes, or by taking fewer road trips. II. More Elasticities of Demand A. Cross Elasticity of Demand 1. The cross elasticity of demand is a measure of the responsiveness of the demand for a good to a change in the price of a substitute or compliment, other things remaining the same.. The cross elasticity of demand is equal to: Percentage change in quantity demanded. Percentage change in price of a substitute or complement The changes in the quantity demanded and the price are percentages of the average price and quantity demanded over the range of change. 3. The cross elasticity of demand is positive for substitutes and negative for complements. 4. Example: a). Cross Elasticity of demand for substitute goods (Pizza and Burger) P burger P pizza D (P burger =$.5) P =$.5 P 1 =$1.5 D (P burger =$1.5) Q burger Q 1 =9 Q =11 Q pizza 8

Q ε pizza = p burger P pizza = p pizza burger p + p 1 1 Q + Q = + + 1.5 + 1.5 9 + 11 = 10 = 0.4 Conclusion: Cross elasticity of demand is positive for substitute goods b). Cross Elasticity of demand for complement goods (Pizza and Soft drink) P soft drink P pizza D (P soft drink =$1.5) P soft drink =$.5 P soft drink =$1.5 D (P soft drink =$.5) Q soft drink Q =9 Q 1 =11 Q pizza pizza p + 1 p Q pizza 9 11 ε pizza = = = = 0. 4 p Q + soft drink P 1 Q.5 1.5 10 p soft drink P i Q i Conclusion: Cross elasticity of demand is negative for complement goods. B. Income Elasticity of Demand 1. The income elasticity of demand is a measure of the responsiveness of the demand for a good to a change in the income, other things remaining the same.. The income elasticity of demand is equal to: 9

Percentage change in quantity demanded. Percentage change in income The changes in the quantity demanded and income are percentages of the average income and quantity demanded over the range of change. 3. The income elasticity of demand is positive for normal goods and negative for inferior goods. a). If the income elasticity of demand is greater than 1, demand is income elastic and the good is a normal good. As income increases, the percentage of income spent on income elastic goods increases b). If the income elasticity of demand is positive but less than 1, demand is income inelastic and the good is a normal good. As income increases, the percentage of income spent on income inelastic goods decreases. c). If the income elasticity of demand is negative the good is an inferior good. 4. The table below has some real-life income elasticities from the book. Airline Travel 5.8 Restaurant Meals 1.61 Clothing 0.51 Food 0.14 5. Example: 10

P pizza D (Income=$105) D (Income=$975) Q 1 =9 Q =11 Q pizza I + I 1000 ε income = = = 100 = 4 I Q1 + Q 105 975 10 50 Conclusion: (1). Normal goods: a. ε income 1 income elastic b. 0 ε income 1 income inelastic (). Inferior goods: ε income 0 III. Elasticity of Supply A. The elasticity of supply measures how responsive suppliers are to a change in the price of the good.. B. The elasticity of supply measures the responsiveness of the quantity supplied to a change in the price of a good when all other influences on selling plans remain unchanged. The elasticity of supply is equal to: Percentage change in quantity supplied. Percentage change in price 11

C. Three Cases of Elasticity of Supply 1. Supply is perfectly inelastic if the elasticity of supply equals 0. In this case, the supply curve is vertical.. Supply is unit elastic if the elasticity of supply equals 1. In this case, the supply curve is linear and passes through the origin. If any supply curve is linear and passes through the origin, the supply is unit elastic; the slope of the supply curve is irrelevant. (but WHY?) 1

3. Supply is perfectly elastic if the elasticity of supply is infinite. In this case, the supply curve is horizontal. D. The table below has two points on the supply curve for pizza from a particular pizza parlor. Price (dollars per pizza) Quantity supplied (pizzas per week) 14 300 16 400 1. The percentage change in the quantity supplied is [(400 300) 350] 100 = 8.6 percent.. The percentage change in price is [($16 $14) $15] 100 = 13.3 percent. 3. Between these two points, the elasticity of supply is 8.6% 13.3% =.15. E. Supply is elastic if the elasticity of supply exceeds 1, unit elastic if the elasticity of supply equals 1, and inelastic if the elasticity of supply is less than 1. F. The Factors that Influence the Elasticity of Supply 1. Resource substitution possibilities: The more unique or rare are the productive resources used to produce the good, the smaller the elasticity of supply. The more common the productive resources used to produce the good, the larger the elasticity of supply.. The time frame for substitution possibilities: The longer the amount of time that producers have to adjust to a change in price, the more elastic will be the supply. 13

a).momentary supply refers to the period of time immediately following a price change. For some goods, the momentary supply can be perfectly inelastic fresh fish the day of a price hike. For other goods, the momentary supply can be quite elastic when the number of telephone calls increases on a holiday, the supply increases with no change in price. b).short-run supply shows how the quantity supplied responds to a price change when only some of the technologically adjustments have been made. c).long-run supply shows how the quantity supplied responds to a price change when all of the technologically adjustments have been made. 14