Business
Arc Elasticity
Arc elasticity is a measure of the responsiveness of one variable to a change in another variable along a specific arc of the demand curve. It is calculated by taking the average of the initial and final values of the variables and using this average as the base for percentage change calculations. This method is used to account for changes in both price and quantity demanded.
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9 Key excerpts on "Arc Elasticity"
eBook - PDF- David Stager(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
The general concept of elasticity is defined as the percentage change in one variable resulting from a given percentage change in another variable. Price Elasticity of Demarid The measure of the relationship of price and quantity demanded is termed price elasticity of demand. Applying the general definition given above to this specific context yields the following definition of the price elasticity of demand: percentage change in (¿^ percentage change in where £ ^ is the coefficient or measure of elasticity, is the quantity demanded of product X , and is the price of X. Note that there is a minus sign in the above formula. There is nor-mally an inverse relationship between a change in price and the quan-tity demanded: a decrease in price will result in an increase in quantity, and vice versa. The elasticity coefficient would therefore be negative, but including the additional minus sign ensures that the measure will be positive —a simple convenience now generally adopted. Alterna-tively, some economics textbooks simply drop the minus sign in the calculation. Point versus Arc Elasticity Elasticity, or the degree of responsiveness of consumers to price changes, is usually different for each price level. Elasticity is therefore ideally measured at a particular price, or at a par-ticular point on the demand curve. This is called point elasticity. But Demand, Supply, and Market Prices 41 changes in price and quantity of such small dimensions that they can be referred to as points are not measurable except with calculus.^ An alternative measure, Arc Elasticity, can be used to approximate the value of the point elasticity. This measures the responsiveness of consumers over a short segment of a demand curve, rather than at a particular point. The example in Box 3.1 shows how this calculation is made. The formula for Arc Elasticity is: + (¿2 where is (Qg - Qi) and AP is (Pg - ^i).
eBook - PDF- William Boyes, Michael Melvin(Authors)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
The Arc Elasticity is calculated in the following way: Q 2 Q 1 ( Q 1 þ Q 2 ) = 2 P 2 P 1 ( P 1 þ P 2 ) = 2 Notice that [ Q 2 þ Q 1 ]/2 is the average quantity and [ P 2 þ P 1 ]/2 is the average price over the price range from P 1 to P 2 . So the Arc Elasticity formula is simply the change in quantity divided by the change in price multiplied by the ratio of the average price to the average quantity: [ D Q = D P ] [average P = average Q ] Chapter 20 Elasticity: Demand and Supply 441 Copyright 2016 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. As an example, suppose that at a price of $6 per ticket, the average moviegoer demands 2 tickets per month, and at a price of $4 per ticket, the average moviegoer purchases 6 tickets per month. Calculate the price elasticity of demand using the arc and the point elasticity. First, the Arc Elasticity. The change in quantity demanded is ( Q 2 Q 1 ) ¼ 6 2 ¼ 4. The percentage change is the change divided by the base. The base is the average of the two quantities: ( Q 1 þ Q 2 )/2. With 4 as the base, the change in quantity demanded divided by the base is 4/4 ¼ 1. The change in price is $4 $6 and the average price is [$6 þ $4]/2 ¼ $5. So the price elasticity is 1 = ( 2 = 5) ¼ 5 = 2 According to these calculations, demand is elastic over the price range $4 to $6. Using the same information, the point elasticity is the change in quantity demanded ( Q 2 Q 1 ) ¼ 4.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
The elasticity of demand for good with respect to price p k is However, the point-price elasticity can be computed only if the formula for the demand function, Q d = f ( P ), is known so its derivative with respect to price, dQ d / dP , can be determined. Arc Elasticity A second solution to the asymmetry problem of having a PED dependent on which of the two given points on a demand curve is chosen as the original point and which as the new one is to compute the percentage change in P and Q relative to the average of the two prices and the average of the two quantities, rather than just the change relative to one point or the other. Loosely speaking, this gives an average elasticity for the section of the actual demand curve—i.e., the arc of the curve—between the two points. As a result, this measure is known as the Arc Elasticity , in this case with respect to the price of the good. The Arc Elasticity is defined mathematically as: This method for computing the price elasticity is also known as the midpoints formula, because the average price and average quantity are the coordinates of the midpoint of the straight line between the two given points. However, because this formula implicitly assumes the section of the demand curve between those points is linear, the greater the curvature of the actual demand curve is over that range, the worse this approximation of its elasticity will be. ____________________ WORLD TECHNOLOGIES ____________________ History The illustration that accompanied Marshall's original definition of PED, the ratio of PT to Pt Together with the concept of an economic elasticity coefficient, Alfred Marshall is credited with defining PED (elasticity of demand) in his book Principles of Economics , published in 1890.
eBook - PDFMicroeconomics
Theory and Applications
- Edgar K. Browning, Mark A. Zupan(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
The basic problem in this case is that the elasticity of demand tends to vary from one point (one P, Q d combination) to another on the demand curve, and for a large change in price and quantity we need an average value over the entire range. Consequently, when we deal with large changes in price and quantity, we should use the following Arc Elasticity formula: Q Q Q P P P d d d . 1 2 1 2 1 2 1 2 ( ) ( ) Note that this formula differs from the point elasticity formula only in using the average of the two quantities, ( / )( ), 1 2 1 2 Q Q d d and the average of the two prices, (1 / 2)(P 1 + P 2 ). Applying this formula to the preceding figures yields the true value of the elasticity over the entire range of prices considered: Q Q Q P P P d d d 1 2 1 2 1 2 1 2 1 2 1 000 1 ( ) ( ) , ( , 000 2 000 1 50 1 50 3 00 1 0 1 2 , ) . ( . . ) . $ $ $ . Arc Elasticity formula Q Q Q P P P d d d 1 2 1 2 1 2 1 2 ( ) ( ) 34 Chapter Two • Supply and Demand • Thus, we have two formulas. The first works well when small changes in P and Q d are involved because, in that case, which P and Q d are used makes little difference. The sec- ond formula avoids the problem of having to pick one specific point by using the average values of price and quantity demanded and should be used with large changes in price and quantity demanded. Demand Elasticities Vary among Goods We can never know why people respond exactly as they do. Nonetheless, two general factors seem to have a pronounced effect on the elasticity of demand for a particular product. The first, and most important, factor is the availability and closeness of substitutes. The more substitutes there are for some product, and the better the substitutes, the more elastic will be the demand for the product. When there are good substitutes, a change in the price of the product will lead to considerable substitution among products by consumers.
eBook - PDF- Neva Goodwin, Jonathan M. Harris, Julie A. Nelson, Brian Roach, Mariano Torras, Jonathan Harris, Julie Nelson(Authors)
- 2019(Publication Date)
- Routledge(Publisher)
1.7 P RICE E LASTICITY OF D EMAND IN THE R EAL W ORLD Economists have estimated the elasticity of demand for many goods and services. In order to esti-mate an elasticity, one needs information on the quantity demanded at different prices. In some cases, variations in prices commonly occur over time. Gasoline is a good example of a product whose price fluctuates. In other cases, price variations may occur across geographic regions. For example, different electric utilities charge different electricity rates. However, estimating elasticity is not as simple as tracking how the quantity sold responds to price variations. Remember that elasticity measures movement along a demand curve as price changes, ceteris paribus. Thus an accurate measurement of elasticity requires that none of the nonprice deter-minants of demand have caused the demand curve to shift. Although economists cannot prevent these changes from occurring, they can use statistical techniques to attempt to isolate the effects of price changes on the quantity demanded. We normally cannot speak of “the” elasticity of demand for a particular good. Different economists may obtain different elasticity values for the same product because of variations in the statistical tech-niques that they use or the region studied. For example, the elasticity of demand for cigarettes has been found to vary between developed and developing countries. As we discuss further later in the chapter, elasticity can change depending on the time allowed for consumers to adjust their behavior. For these reasons, many economic analyses consider a range of elasticity values for a particular good. Thus the effect of a price change on revenues will commonly be difficult to predict accurately, C HAPTER 5 – E LASTICITY 118 but we hope that the actual result will fall within our forecasted range. This is another illustration of the tradeoff between precision and accuracy, as discussed in Chapter 4.
eBook - PDF- Steven A. Greenlaw, Timothy Taylor(Authors)
- 2015(Publication Date)
- Openstax(Publisher)
Chapter 5 | Elasticity 103 How would customers of the 18-year-old firm react? Would they abandon Netflix? Would the ease of access to other venues make a difference in how consumers responded to the Netflix price change? The answers to those questions will be explored in this chapter: the change in quantity with respect to a change in price, a concept economists call elasticity. Introduction to Elasticity In this chapter, you will learn about: • Price Elasticity of Demand and Price Elasticity of Supply • Polar Cases of Elasticity and Constant Elasticity • Elasticity and Pricing • Elasticity in Areas Other Than Price Anyone who has studied economics knows the law of demand: a higher price will lead to a lower quantity demanded. What you may not know is how much lower the quantity demanded will be. Similarly, the law of supply shows that a higher price will lead to a higher quantity supplied. The question is: How much higher? This chapter will explain how to answer these questions and why they are critically important in the real world. To find answers to these questions, we need to understand the concept of elasticity. Elasticity is an economics concept that measures responsiveness of one variable to changes in another variable. Suppose you drop two items from a second-floor balcony. The first item is a tennis ball. The second item is a brick. Which will bounce higher? Obviously, the tennis ball. We would say that the tennis ball has greater elasticity. Consider an economic example. Cigarette taxes are an example of a “sin tax,” a tax on something that is bad for you, like alcohol. Cigarettes are taxed at the state and national levels. State taxes range from a low of 17 cents per pack in Missouri to $4.35 per pack in New York. The average state cigarette tax is $1.51 per pack. The 2014 federal tax rate on cigarettes was $1.01 per pack, but in 2015 the Obama Administration proposed raising the federal tax nearly a dollar to $1.95 per pack.
eBook - PDFMicroeconomics
A Global Text
- Judy Whitehead(Author)
- 2020(Publication Date)
- Routledge(Publisher)
The value of the price elasticity of demand depends on: • The availability of substitutes . Demand for a commodity is more price elastic where there are close substitutes. • The extent to which the commodities may be characterized as luxuries or necessities . Luxury goods are more price elastic whereas necessities are more inelastic. • Time period . Demand is more price elastic in the long-run than in the short-run. • Alternative uses . The more alternative uses a commodity has, the greater the price elasticity of demand. C H A P T E R 3 61 MARKET DEMAND AND ELASTICITY C H A P T E R 3 • The proportion of total income spent on the product . The greater the proportion the higher the elasticity. Arc Elasticity of demand The above measures of price elasticity of demand refer to what may be called the point elasticity of demand. This is appropriate for small changes in price. For larger changes in price, the formula for arc price elasticity of demand is used. This may be expressed (with the subscript x omitted) as: Q ( P 1 + P 2 ) / 2 η P = · P ( Q 1 + Q 2 ) / 2 3.2.2 The PCC and the price elasticity of demand Price elasticity of demand may be determined from the shape of the price consumption curve ( PCC ). As explained in Chapter 2, the price consumption curve is the line joining successive equilibrium points as the price of good x falls. The price elasticity of demand can be derived from the price consumption curve using money and one good ( x ). The relationship is as follows: • Where η P = 1 in absolute terms (unitary elastic demand), the PCC is a horizontal line. • Where η P < 1 in absolute terms (inelastic demand), the PCC is an upward sloping line. • Where η P > 1 in absolute terms (elastic demand), the PCC is a downward sloping line. Unitary elastic demand Figure 3.2 describes a consumer’s budget line AB and an equilibrium point R on indifference curve IC 1 . Focusing on good x , define good y as the money the consumer can spend on all other goods (except x ).
eBook - PDF- Steven A. Greenlaw, Timothy Taylor, David Shapiro(Authors)
- 2017(Publication Date)
- Openstax(Publisher)
Chapter 5 | Elasticity 107 How would customers of the 18-year-old firm react? Would they abandon Netflix? Would the ease of access to other venues make a difference in how consumers responded to the Netflix price change? We will explore the answers to those questions in this chapter, which focuses on the change in quantity with respect to a change in price, a concept economists call elasticity. Introduction to Elasticity In this chapter, you will learn about: • Price Elasticity of Demand and Price Elasticity of Supply • Polar Cases of Elasticity and Constant Elasticity • Elasticity and Pricing • Elasticity in Areas Other Than Price Anyone who has studied economics knows the law of demand: a higher price will lead to a lower quantity demanded. What you may not know is how much lower the quantity demanded will be. Similarly, the law of supply states that a higher price will lead to a higher quantity supplied. The question is: How much higher? This chapter will explain how to answer these questions and why they are critically important in the real world. To find answers to these questions, we need to understand the concept of elasticity. Elasticity is an economics concept that measures responsiveness of one variable to changes in another variable. Suppose you drop two items from a second-floor balcony. The first item is a tennis ball. The second item is a brick. Which will bounce higher? Obviously, the tennis ball. We would say that the tennis ball has greater elasticity. Consider an economic example. Cigarette taxes are an example of a “sin tax,” a tax on something that is bad for you, like alcohol. Governments tax cigarettes at the state and national levels. State taxes range from a low of 17 cents per pack in Missouri to $4.35 per pack in New York. The average state cigarette tax is $1.69 per pack. The 2014 federal tax rate on cigarettes was $1.01 per pack, but in 2015 the Obama Administration proposed raising the federal tax nearly a dollar to $1.95 per pack.
eBook - PDF- Steven A. Greenlaw, Timothy Taylor, David Shapiro(Authors)
- 2017(Publication Date)
- Openstax(Publisher)
A unitary elasticity means that a given percentage change in price leads to an equal percentage change in quantity demanded or supplied. 5.2 Polar Cases of Elasticity and Constant Elasticity Infinite or perfect elasticity refers to the extreme case where either the quantity demanded or supplied changes by an infinite amount in response to any change in price at all. Zero elasticity refers to the extreme case in which a percentage change in price, no matter how large, results in zero change in quantity. Constant unitary elasticity in either a supply or demand curve refers to a situation where a price change of one percent results in a quantity change of one percent. 5.3 Elasticity and Pricing In the market for goods and services, quantity supplied and quantity demanded are often relatively slow to react to changes in price in the short run, but react more substantially in the long run. As a result, demand and supply often (but not always) tend to be relatively inelastic in the short run and relatively elastic in the long run. A tax incidence depends on the relative price elasticity of supply and demand. When supply is more elastic than demand, buyers bear most of the tax burden, and when demand is more elastic than supply, producers bear most of the cost of the tax. Tax revenue is larger the more inelastic the demand and supply are. 5.4 Elasticity in Areas Other Than Price Elasticity is a general term, that reflects responsiveness. It refers to the change of one variable divided by the percentage change of a related variable that we can apply to many economic connections. For instance, the income elasticity of demand is the percentage change in quantity demanded divided by the percentage change in income. The cross-price elasticity of demand is the percentage change in the quantity demanded of a good divided by the percentage change in the price of another good.
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