Economics
Midpoint Method
The Midpoint Method is a technique used to calculate the price elasticity of demand. It involves measuring the percentage change in quantity demanded and the percentage change in price between two points on a demand curve. The midpoint formula is considered more accurate than the traditional percentage change formula because it avoids the bias that can result from choosing a base point.
Written by Perlego with AI-assistance
Related key terms
1 of 5
8 Key excerpts on "Midpoint Method"
eBook - PDF- Steven A. Greenlaw, Timothy Taylor, David Shapiro(Authors)
- 2017(Publication Date)
- Openstax(Publisher)
To calculate elasticity along a demand or supply curve 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 = Q 2 – Q 1 ⎛ ⎝ Q 2 + Q 1 ⎞ ⎠ /2 × 100 % change in price = P 2 – P 1 ⎛ ⎝ P 2 + P 1 ⎞ ⎠ /2 × 100 The advantage of the Midpoint Method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base (average quantity and average price) for both cases. Calculating Price Elasticity of Demand Let’s calculate the elasticity between points A and B and between points G and H as Figure 5.2 shows. Chapter 5 | Elasticity 109 Figure 5.2 Calculating the Price Elasticity of Demand We calculate the price elasticity of demand as the percentage change in quantity divided by the percentage change in price. 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 = 200 2,900 × 100 = 6.9 % change in price = 60 – 70 (60 + 70)/2 × 100 = –10 65 × 100 = –15.4 Price 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. 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%.
eBook - PDF- Irvin Tucker(Author)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Copyright 2019 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. 104 PArT 2 • The Microeconomy select the initial point as the base and then compute a percentage change. But price elas-ticity of demand involves changes between two possible initial base points ( P 1 , Q 1 or P 2 , Q 2 ). Economists solve this problem of different base points by using the midpoints as the base points of changes in prices and quantities demanded. The midpoints formula for price elasticity of demand is E d uni003D.bold change in quantity sum of quantities/2 uni00F7.bold change in price sum of prices/2 which can be expressed as E d uni003D.bold uni2206 Q uni2206 P uni003D.bold Q 2 2 Q 1 Q 1 uni002B.bold Q 2 P 2 2 P 1 P 1 uni002B.bold P 2 where Q 1 represents the first quantity demanded, Q 2 represents the second quantity demanded, and P 1 and P 2 are the first and second prices. Expressed this way, we divide the change in quantity demanded by the average quantity demanded. Then this value is divided by the change in the price divided by the average price. It does not matter if Q 1 or P 1 is the first or second number in each term because we are finding averages. Also note that you can drop the 2 as a divisor of both the ( Q 1 1 Q 2 ) and ( P 1 1 P 2 ) terms because the 2s in the numerator and the denominator cancel out. Now we can use the midpoints formula to calculate the price elasticity of demand to be equal to 3.7 regardless of whether Steel Porcupines raises the ticket price from $25 to $30 or lowers it from $30 to $25.
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.
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 - PDF- Neva Goodwin, Jonathan M. Harris, Julie A. Nelson, Brian Roach, Mariano Torras, Jonathan Harris, Julie Nelson(Authors)
- 2019(Publication Date)
- Routledge(Publisher)
The denomina-tor used to calculate the percentage change is the “base” value. But by changing the direction of the change, the base value can be the higher or the lower number. So the key to obtaining the same elasticity value regardless of the direction of the price change is to obtain the same denominators when calculating the percentage changes. We can do this by using the “midpoint formula.” Consider our example of price changing from $5 to $10 (or vice versa). The percentage change is either 50 percent or 100 percent depending on the direction of the change. To use the midpoint formula, instead of using the base value as the denominator when calculating the percentage change, we use the midpoint, or aver-age, of the two values: Midpoint = (new number + base number)/2 So for the price change between $5 and $10, in either direc-tion, the base value for the denominator when calculating the percentage change in price is now 7.5. For the quantity change, the midpoint between 800 and 1,000 is 900. Thus the elasticity value for a price increase from $5 to $10 using the midpoint for-mula would be: Elasticity = -( ) × -( ) × -= 800 1000 900 100 10 5 7 5 100 0 222 / / . . 2 100 0 6667 100 0 3333 × × -= . . You can test yourself by proving that you get the same elasticity value if the price decreases from $10 to $5. Note that the elas-ticity value here, –0.3333, is between our two previous elasticity estimates (–0.2 and –0.5) based on prices of $5 and $10. Note, however, that the elasticity obtained using the midpoint formula is not the exact midpoint of the two elasticity values using the conven-tional approach. C HAPTER 5 – E LASTICITY 116 1.6 E LASTICITY AND R EVENUES A common application of elasticity estimates is predicting how a company’s revenues will change in response to a price change. A business, such as Braeburn Publishing, can use an elasticity estimate to determine what price it should charge to maximize its revenues.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(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 - PDF- Steven A. Greenlaw, David Shapiro, Daniel MacDonald(Authors)
- 2022(Publication Date)
- Openstax(Publisher)
Using the Midpoint Method, you can calculate that between points A and B on the demand curve, the price changes by 66.7% and quantity demanded also changes by 66.7%. Hence, the elasticity equals 1. Between points B and C, price again changes by 66.7% as does quantity, while between points C and D the corresponding percentage changes are again 66.7% for both price and quantity. In each case, then, the percentage change in price equals the percentage change in quantity, and consequently elasticity equals 1. Notice that in absolute value, the declines in price, as you step down the demand curve, are not identical. Instead, the price falls by $8.00 from A to B, by a smaller amount of $4.00 from B to C, and by a still smaller amount of $2.00 from C to D. As a result, a demand curve with constant unitary elasticity moves from a steeper slope on the left and a flatter slope on the right—and a curved shape overall. 118 5 • Elasticity Access for free at openstax.org FIGURE 5.6 A Constant Unitary Elasticity Demand Curve A demand curve with constant unitary elasticity will be a curved line. Notice how price and quantity demanded change by an identical percentage amount between each pair of points on the demand curve. Unlike the demand curve with unitary elasticity, the supply curve with unitary elasticity is represented by a straight line, and that line goes through the origin. In each pair of points on the supply curve there is an equal difference in quantity of 30. However, in percentage value, using the Midpoint Method, the steps are decreasing as one moves from left to right, from 28.6% to 22.2% to 18.2%, because the quantity points in each percentage calculation are getting increasingly larger, which expands the denominator in the elasticity calculation of the percentage change in quantity. Consider the price changes moving up the supply curve in Figure 5.7. From points D to E to F and to G on the supply curve, each step of $1.50 is the same in absolute value.
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).
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
