Economics
Income Elasticity of Demand Formula
The income elasticity of demand formula measures the responsiveness of the quantity demanded for a good to a change in consumer income. It is calculated by dividing the percentage change in quantity demanded by the percentage change in income. A positive income elasticity indicates a normal good, while a negative elasticity indicates an inferior good.
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eBook - PDF- W. Keith Bryant, Cathleen D. Zick(Authors)
- 2005(Publication Date)
- Cambridge University Press(Publisher)
Since the income elasticity is measured in percentage terms, the response in demand for one good to changes in income can be compared with the responses in the demand for others. Definition : The income elasticity of demand for a good is the percentage change in the quantity demanded due to a 1 percent change in income, with preferences and relative prices constant. In general, the formula is N x = ( q x / q x ) 100 / ( Y / Y ) 100 = ( q x / Y )( Y / q x ) (3.3) where q x is the change in the quantity demanded of good X due to the change in income, Y is the change in income, and q x and Y are the pre-change values of the quantity of X demanded and income, respectively. There are two computing formulas for the income elasticity: the point and the arc income elasticity. The former formula is used to compute the income elasticity at a specific point on an Engel curve, and the latter is used when the change in income is large. The differences between point and arc elasticities can be more easily understood when discussed in terms of a diagram. Figure 3.4 illustrates the Engel curve 0E for good X . Consider the income elasticity at point A , where the household demands q a x amount of good X when its income is Y a . The slope of the Engel curve at point A represents the change in income, Y , divided by the change in q x , q x ; that is, Y / q x . It can be found by taking the slope of the tangent to the Engel curve at A . Straight line d a AA is the tangent to 0E at point A . Suppose the equation for the tangent is Y = d a + n a q x ; (3.4) d a is the vertical intercept of d a AA and n a is the slope, Y / q x , at A . Now, draw a straight line from point A to the origin; that is 0A .
eBook - PDF- Tucker, Irvin Tucker(Authors)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
CONCLUSION: In general, the price elasticity coefficient of demand is higher the longer a price change persists. 5-4 OTHER ELASTICITY MEASURES The elasticity concept has other applications beyond calculating the price elasticity of demand. Broadly defined, it is a technique for measuring the response of one variable to changes in some other variable. 5-4a INCOME ELASTICITY OF DEMAND Recall from Chapter 3 that an increase in income can increase demand (shift the demand curve rightward) for a normal good or service and decrease demand (shift the demand curve leftward) for an inferior good or service. To measure exactly how consumption responds to changes in income, economists calculate the income elasticity of demand . Income elasticity of demand is the ratio of the percentage change in the quantity demanded of a good or service to a given percentage change in income. We use a midpoints formula similar to the one we used for calculating price elasticity of demand: E I ¼ percentage change in quantity demanded percentage change in income E I ¼ % Δ Q % Δ I ¼ Q 2 Q 1 Q 1 þ Q 2 I 2 I 1 I 1 þ I 2 Where E I is the income elasticity of demand coefficient, Q 1 and Q 2 represent quantities demanded before and after the income change, and I 1 and I 2 represent income before and after the income change. For a normal good or service, the income elasticity of demand is positive , E I > 0. Recall that for this type of good, demand and income move in the same direction. Thus, the variables in the numerator and denominator change in the same direction. For an inferior good or service, the reverse is true, and the income elasticity of demand is negative , E I < 0. Income elasticity of demand The ratio of the percentage change in the quantity demanded of a good or service to a given percent-age change in income. CHAPTER 5 | Price Elasticity of Demand and Supply 141 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
eBook - PDF- Irvin Tucker(Author)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
ChAPTEr 5 • Price Elasticity of Demand 103 5–1 PRICE ELASTICITY OF DEMAND In Chapter 3, when you studied the demand curve, the focus was on the law of demand. This law states there is an inverse relationship between the price and the quantity demanded of a good or service. In this chapter, the emphasis is on measuring the relative size of changes in the price and the quantity demanded. Now we ask: By what percentage does the quantity demanded rise when the price falls by, say, 10 percent? 5–1a The Price Elasticity of Demand Midpoints Formula 1 Economists use a price elasticity of demand formula to measure the degree of consumer responsiveness, or sensitivity, to a change in price. Price elasticity of demand is the ratio of the percentage change in the quantity demanded of a product to a percentage change in its price. Price elasticity of demand explains how strongly consumers react to a change in price. Think of quantity demanded as a rubber band. Price elasticity of demand measures how “stretchy” the rubber band is when the price changes. Suppose a university’s enroll-ment drops by 20 percent because tuition rises by 10 percent. Therefore, the price elas-ticity of demand is 2 (−20 percent/+10 percent). The number 2 means that the quantity demanded (enrollment) changes 2 percent for each 1 percent change in price (tuition). Note there should be a minus sign in front of the 2 because, under the law of demand, price and quantity move in opposite directions. However, economists drop the minus sign because we know from the law of demand that quantity demanded and price are inversely related. The number 2 is an elasticity coefficient , which economists use to measure the degree of elasticity. The elasticity formula is E d uni003D.bold percentage change in quantity demanded percentage change in price where E d is the elasticity of demand coefficient. Here you must take care. There is a prob-lem using this formula .
eBook - ePubMicroeconomics
A Global Text
- Judy Whitehead(Author)
- 2014(Publication Date)
- Routledge(Publisher)
Countries aiming to benefit from a currency devaluation must pay special attention to price elasticities of demand for both their imports and for their exports. This is the foundation of the Marshall–Lerner condition, which states that in order for a fall in a country’s exchange rate (devaluation) to reduce the country’s Balance of Payments deficit (i.e. increase the country’s foreign reserves), the sum of the price elasticity of demand coefficients for exports and imports must be greater than one.3.3 The Income Elasticity of Demand
In addition to the price elasticity of demand, the income elasticity of demand provides a useful tool for the analysis of consumer behaviour and for planning by the firm or the state.3.3.1 Definition of income elasticity of demand
The income elasticity (This may be written as: or:ηY) for commodity x may be defined as:where the Y used for income in the above equations is really the Ȳ used to symbolize real (as opposed to nominal) income.As explained in Chapter 2 , the income-consumption curve (ICC ) is used to derive the Engel curve. The Engel curve is then used for illustration of the income elasticity of demand. The Engel curve shows the relationship between real income (Ȳ ) and the quantity of commodity x demanded (Qx).Using Figure 3.11 , the income elasticity of demand ηY for good x may be computed using the formula for income elasticity. The income elasticity at the point R (ηY (R )) on the Engel curve is found diagrammatically as follows:- Drop a perpendicular from the point R to the X -axis at S .
- Take a perpendicular from the point R across to the Y -axis at A .
- Identify from the diagram, the components of the income elasticity formula:
Figure 3.11 The Engel curve and income elasticity of demandIn the income elasticity formula given above, it is the inverse of the slope of the Engel curve that is represented by the expression:In Figure 3.11 , the slope of the Engel curve at the point R may be expressed as:- Hence, inverting the slope at the point R gives:
- Also from the elasticity formula, the following may be identified at the point R : Y = OA and Qx = OS . Hence:
- Walter Nicholson, Christopher Snyder(Authors)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. CHAPTER 4 ● Demand Curves 119 4-14 Income Elasticity of Demand Another type of elasticity is the income elasticity of demand ( e Q , I ). This concept records the relationship between changes in income and changes in quantity demanded (holding other determinants of demand constant): Income elasticity of demand 5 e Q , I 5 Percentage change in Q Percentage change in I . (4.15) For a normal good, e Q,I is positive because increases in income lead to increases in purchases of the good. Among normal goods, whether e Q,I is greater than or less than 1 is a matter of some interest. Goods for which e Q,I . 1 might be called “luxury goods,” in that purchases of these goods increase more rapidly than income. For example, if the income elasticity of demand for automobiles is 2, then a 10 percent increase in income will lead to a 20 percent increase in automobile purchases. Auto sales would therefore be very responsive to business cycles that produce changes in people’s incomes. On the other hand, Engel’s Law suggests that food has an income elasticity of much less than 1. If the income elastic-ity of demand for food were 0.5, for example, then a 10 percent rise in income would result in only a 5 percent increase in food purchases. Considerable research has been done to determine the actual val-ues of income elasticities for various items, and we discuss the results of some of these studies in the final section of this chapter. 4-15 Cross-Price Elasticity of Demand Earlier, we showed that a change in the price of one good will affect the quantity demanded of many other goods.
eBook - PDF- David Besanko, Ronald Braeutigam(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
53 2.3 OTHER ELASTICITIES We can use elasticity to characterize the responsiveness of demand to any of the determinants of demand. Two of the more common elasticities in addition to the price elasticity of demand are the income elasticity of demand and the cross-price elasticity of demand. INCOME ELASTICITY OF DEMAND The income elasticity of demand is the ratio of the percentage change of quantity demanded to the percentage change of income, holding price and all other determi- nants of demand constant: , 100% 100% Q Q Q I I I or, after rearranging terms, , Q I Q I I Q (2.5) Table 2.5 shows estimated income elasticities of demand for two different types of U.S. households: those whose incomes place them below the poverty line and those whose incomes place them above it. For both types of households, the estimated income elasticities of demand are positive, indicating that the quantity demanded of the good increases as income increases. However, it is also possible that income elasticity of demand can be negative. Some studies suggest that in economically advanced countries in Asia, such as Japan and Taiwan, the income elasticity of demand for rice is negative. 19 OTHER ELASTICITIES 2.3 income elasticity of demand The ratio of the percentage change of quantity demanded to the percentage change of income, holding price and all other determinants of demand constant. Price Elasticity of Demand in a Local Gasoline Market Extending the methodology utilized in the study by Berry, Levinsohn, and Pakes described in Applica- tion 2.4, Jean-François Houde estimated demand func- tions for local gasoline stations in Quebec City, Canada using data from 1991 to 2001. 18 One of the novelties of Houde’s study is that it explicitly incorporated the spatial structure of demand—that is, the fact that for local retail ser- vices such as gasoline stations, a key determinant of demand is the location of sellers compared to the loca- tions and commuting patterns of consumers.
eBook - PDF- William Boyes, Michael Melvin(Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
A change in any one of these “determinants of demand” will cause the demand curve to shift, and a measure of elasticity exists for each. 20-2a The Cross-Price Elasticity of Demand The cross-price elasticity of demand measures the degree to which goods are substitutes or complements (for a discussion of substitutes and complements, see the chapter “Scarcity and Opportunity Costs”). The cross-price elasticity of demand is defined as the percentage change in the quantity demanded of one good divided by the percentage change in the price of a related good, everything else held constant. When the cross-price elasticity of demand is positive, the goods are substitutes; when the cross-price elasticity of demand is negative, the goods are complements. If a 1 percent increase in the price of a movie ticket leads to a 5 percent increase in the quan-tity of movies that are downloaded off the Internet, movies at the theater and down-loaded movies are substitutes. If a 1 percent rise in the price of a movie ticket leads to a 5 percent drop in the quantity of popcorn consumed, movies and popcorn are comple-ments. Complements are items used together while substitutes are items used in place of each other. 20-2b The Income Elasticity of Demand The income elasticity of demand measures the magnitude of consumer responsiveness to income changes. The income elasticity of demand is defined as the percentage change in the quantity demanded for a product divided by the percentage change in income, everything else held constant (Figure 3). Goods whose income elasticity of demand is greater than zero are normal goods . Products that are often called necessities have lower income elasticities than products known as luxuries. Gas, electricity, health-oriented drugs, and physicians’ services might be consid-ered necessities. Their income elasticities are about 0.4 or 0.5. On the other hand, people tend to view dental services, automobiles, and private education as luxury goods.
eBook - PDFMicroeconomics
A Global Text
- Judy Whitehead(Author)
- 2020(Publication Date)
- Routledge(Publisher)
76 THE INCOME ELASTICITY OF DEMAND 3.3 Countries aiming to benefit from a currency devaluation must pay special attention to price elasticities of demand for both their imports and for their exports. This is the foundation of the Marshall–Lerner condition, which states that in order for a fall in a country’s exchange rate (devaluation) to reduce the country’s Balance of Payments deficit (i.e. increase the country’s foreign reserves), the sum of the price elasticity of demand coefficients for exports and imports must be greater than one. 3.3 THE INCOME ELASTICITY OF DEMAND In addition to the price elasticity of demand, the income elasticity of demand provides a useful tool for the analysis of consumer behaviour and for planning by the firm or the state. 3.3.1 Definition of income elasticity of demand The income elasticity ( η Y ) for commodity x may be defined as: proportionate change in quantity of good x ( Q x ) η Y = proportionate change in income ( Y ) This may be written as: d Q x / Q x η Y = d Y / Y or: d Q x Y η Y = · d Y Q x ¯ where the Y used for income in the above equations is really the Y used to symbolize real (as opposed to nominal) income. As explained in Chapter 2, the income-consumption curve ( ICC ) is used to derive the Engel curve. The Engel curve is then used for illustration of the income elasticity of demand. The Engel curve shows the relationship between real income ( Y ¯ ) and the quantity of commodity x demanded ( Q x ). Using Figure 3.11 , the income elasticity of demand η Y for good x may be computed using the formula for income elasticity. The income elasticity at the point R ( η Y ( R )) on the Engel curve is found diagrammatically as follows: • Drop a perpendicular from the point R to the X -axis at S . • Take a perpendicular from the point R across to the Y -axis at A . • Identify from the diagram, the components of the income elasticity formula: C H A P T E R 3 d Q x Y η Y = · d Y Q x 77
eBook - PDFEconomics
A Contemporary Introduction
- William A. McEachern(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 94 Part 2 Introduction to the Market System be represented as Δp and the change in quantity as Δq. The formula for calculating the price elasticity of demand E D between the two points is the percentage change in quan- tity demanded divided by the percentage change in price, or E D 5 Δq 4 Δp (q1q9)/2 (p1p9)/2 Again, the same elasticity results whether going from the higher price to the lower price or the other way around. This is sometimes called the midpoint formula, because the bases for computing percentages are midway between the two points on the curve. Elasticity expresses a relationship between two amounts: the percentage change in quantity demanded and the percentage change in price. Because the focus is on the per- centage change, we don’t need to be concerned with how output or price is measured. For example, suppose the good in question is apples. It makes no difference in the elasticity formula whether we measure apples in pounds, bushels, or even tons. All that matters is the percentage change in quantity demanded. Nor does it matter whether we measure price in U.S. dollars, Mexican pesos, Zambian kwacha, or Vietnamese dong. All that matters is the percentage change in price. Finally, the law of demand states that price and quantity demanded are inversely related, so the change in price and the change in quantity demanded move in opposite directions. In the elasticity formula, the numerator and the denominator have opposite signs, leaving the price elasticity of demand with a negative sign.
eBook - PDFMicroeconomics
A Contemporary Introduction
- William A. McEachern(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 94 Part 2 Introduction to the Market System be represented as Δ p and the change in quantity as Δ q . The formula for calculating the price elasticity of demand E D between the two points is the percentage change in quan-tity demanded divided by the percentage change in price, or E D 5 Δ q 4 Δ p ( q 1 q 9 )/2 ( p 1 p 9 )/2 Again, the same elasticity results whether going from the higher price to the lower price or the other way around. This is sometimes called the midpoint formula , because the bases for computing percentages are midway between the two points on the curve. Elasticity expresses a relationship between two amounts: the percentage change in quantity demanded and the percentage change in price. Because the focus is on the per-centage change , we don’t need to be concerned with how output or price is measured. For example, suppose the good in question is apples. It makes no difference in the elasticity formula whether we measure apples in pounds, bushels, or even tons. All that matters is the percentage change in quantity demanded. Nor does it matter whether we measure price in U.S. dollars, Mexican pesos, Zambian kwacha, or Vietnamese dong. All that matters is the percentage change in price. Finally, the law of demand states that price and quantity demanded are inversely related, so the change in price and the change in quantity demanded move in opposite directions.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Various research methods are used to determine price elasticity, including test markets, analysis of historical sales data and conjoint analysis. Definition PED is a measure of responsiveness of the quantity of a good or service demanded to changes in its price. The formula for the coefficient of price elasticity of demand for a good is: The above formula usually yields a negative value, due to the inverse nature of the relationship between price and quantity demanded, as described by the law of demand. For example, if the price increases by 5% and quantity demanded decreases by 5%, then the elasticity at the initial price and quantity = −5%/5% = −1. The only classes of goods which have a PED of greater than 0 are Veblen and Giffen goods. Because the PED is negative for the vast majority of goods and services, however, economists often refer to price elasticity of demand as a positive value (i.e., in absolute value terms). This measure of elasticity is sometimes referred to as the own-price elasticity of demand for a good, i.e., the elasticity of demand with respect to the good's own price, in order to distinguish it from the elasticity of demand for that good with respect to the change in the price of some other good, i.e., a complementary or substitute good. The latter type of elasticity measure is called a cross -price elasticity of demand. As the difference between the two prices or quantities increases, the accuracy of the PED given by the formula above decreases for a combination of two reasons. First, the PED for a good is not necessarily constant; as explained below, PED can vary at different points along the demand curve, due to its percentage nature. Elasticity is not the same thing as the slope of the demand curve, which is dependent on the units used for both price and quantity.
eBook - PDFIntroduction to Economics
Social Issues and Economic Thinking
- Wendy A. Stock(Author)
- 2013(Publication Date)
- Wiley(Publisher)
SUMMARY In this chapter, we learned about the elasticity of demand, which measures how respon- sive consumers are to changes in the prices of goods and services. When changes in quantity demanded are relatively large in response to price changes, demand is elas- tic. When changes in quantity demanded are relatively small in response to price changes, demand is inelastic. Goods with few substitutes and goods that are neces- sities have relatively inelastic demand. Demand tends to be more elastic for goods when consumers have more time to adjust to price changes and when consumers spend larger fractions of their incomes on the goods. How total revenue responds to price changes is influenced by the elasticity of demand. When the demand for a good is inelastic, sellers can increase total revenue by increasing the price of the good. When demand is elastic, sellers can increase total revenue by decreasing the price of the good. KEY CONCEPTS • Elasticity • Price elasticity of demand • Elastic demand • Inelastic demand • Perfectly inelastic demand • Perfectly elastic demand • Unit elastic demand • Elasticity coefficient • Total revenue K e y C o n c e p t s 9 1 9 2 C H A P T E R 5 E l a s t i c i t y DISCUSSION QUESTIONS AND PROBLEMS 1. Suppose that the adoption fee at the animal shelter is initially $15.00 and the average number of animals adopted per week at that price is 100. In the face of ris- ing costs, there is an increase in the pet adoption fees at the animal shelter from $15.00 to $22.50 (a 50 percent price increase). Proponents of the increase argue that it is necessary to raise revenues for the shelter. Critics of the plan worry that the fee increase might decrease adoptions enough to actually lower shelter revenues. a. What is the revenue earned by the shelter for ani- mal adoptions before the fee increase? b. Suppose animal adoptions fall by 10 percent in response to the 50 percent fee increase (to 90 animals per week).
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