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Price Elasticity of Demand = 43.85% / 98%. Barnett [reference pages] Cost: C = fixed cost + variable cost (C= 270 + .15x . C.4 Calculating Elasticity Using Calculus. \end{align*} \]. Then \( \frac{dq}{dp}=-50 \). Well, that is the situation Netflix customers found themselves in 2011 â a 60% price hike to retain the same service. Did they abandon Netflix? When we use the mid-point method, we are just taking an average of the two points. Calculus I:DerivativesElasticityPrice Elasticity of Demand. Elasticity of demand is a measure of how demand reacts to price changes. By the end of this section, you will be able to: Imagine going to your favorite coffee shop and having the waiter inform you the pricing has changed. The formula for the point elasticity of demand is . This is because the denominator is an average rather than the old value. The book itself, in the remainder, is restricted to linear problems only. The third part of the book deals with the mathematical theory of linear elasticity in full extent. Calculate the elasticity of supply. Retrieved from https://www.thoughtco.com/using-calculus-to-calculate-elasticities-1146248. Thus we can calculate any elasticity through the formula: Found inside – Page iThis open access book shows how to use sensitivity analysis in demography. This shows the responsiveness of quantity supplied to a change in price. Own-price elasticity of demand is equal to: 3. Finding the price elasticity of demand requires that we first compute percentage changes in price and in quantity demanded. At a price of $5, a 1% increase in price would decrease demand by only 0.133%. ThoughtCo. instructions how to enable JavaScript in your web browser, §11: Implicit Differentiation and Related Rates, §2: The Fundamental Theorem and Antidifferentiation, §2: Calculus of Functions of Two Variables. Cross price elasticity of demand (XED) = (∆QX/QX) ÷ (∆PY/PY) Where, QX = Quantity of product X. PY = Price of the product. What does (the absolute value of) own price elasticity of demand equal? = 1 unit elasticity (demand change equal to price change) [259] E(p) > 1 elastic (large demand change with price) Arc elasticity is a measure of how the relationship between the demand and price of a good or service changes over time with a change in either of those metrics. Or will revenue increase because demand didn't drop very much? This is not a coincidence. The formula: % Change in the Demand for X % Change in the Price of X . Found inside – Page 363Applications to the equations of hydrodynamics and elasticity: See [212]. 1.9.4 Calculus with the nabla operator The nabla operator: Many formulas of vector ... Cross-Price Elasticity Formula. Suppose that a 2% increase in price results in a 6% decrease in quantity demanded. Whereas elasticity of demand measures responsiveness of quantity demanded to a price change, own-price elasticity of supply measures the responsiveness of quantity supplied. Now, let us take the example of influence price on the sale of a certain soft drink in order to illustrate the concept of price elasticity of demand. We would say that the tennis ball has greater elasticity. Sound absurd? Price elasticity: Signifies how responsive supply or demand is after a price change. A company sells \( q \) ribbon winders per year at $\( p \) per ribbon winder. Found inside – Page 66Appendix 3B: The calculus behind supply and demand We demonstrate the use of calculus ... The formula for cross- price elasticity is (3B.2) where good, ... This is called the tangent modulus. This lesson will discuss the law of demand and the demand curve. It’s normalized – that means the particular prices and quantities don't matter, and everything is treated as a percent change. Elasticity from Point B to Point A. The answers to those questions will be explored in this chapter with a concept economists call elasticity. b) -2. g(18)\approx & 5 + (1.4)(18 - 20) = 2.2 Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. Stress α Strain. Read on to learn how to calculate the price elasticity of demand with the midpoint method! The ΔQ/ ΔP corresponds to the inverse slope of the curve. Now, let us understand how to calculate their values. But how is this degree of responsiveness seen in our models? Both the demand and supply curve show the relationship between price and quantity, and elasticity can improve our understanding of this relationship. We will examine this even further when we introduce consumer theory, but for now we can develop our understanding by applying what we know about elasticities. Enter positive values for elasticities (absolute values). To maximize the revenue, we could solve for when \( E = 1 \): \end{align*} \]. In addition to MyMathLab®, a complete online course solution, a comprehensive series of video lectures is available for this text. In Topic 3 we discussed how goods can be inferior/normal or substitutes/complements. How to calculate the income elasticity of demand. How do we use it to calculate the elasticity at Point A? At a price of $15, a 1% increase in price would decrease demand by 2.571%. Suppose the initial price is $0 . In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at point a is defined as = ′ ()= → () = → () = → () % % or equivalently = .It is thus the ratio of the relative (percentage) change in the function's output () with respect to the relative change in its input , for infinitesimal . The modulus of elasticity formula is simply stress divided by strain. a) -1. Both mid-point and point-slope formulas are important for calculating elasticity in different situations. The ΔQ/ ΔP corresponds to the inverse slope of the curve. Income Elasticity of Demand Formula. If you want to pay your usual $3 for a cup of coffee, you must choose between creamer and sweetener. The most complete single-volume treatment of classical elasticity, this text features extensive editorial apparatus, including a historical introduction. As with cross-price elasticity, whether our elasticity is positive or negative provides valuable information about how the consumer views the good: A normal good will have a positive income elasticity, since if the % change in income is positive, the % change in quantity will be positive and vice-versa. This reinforces the conclusion that mid-point represents an average. The modulus of elasticity, also known as Young's modulus, is a material property and a measure of its stiffness under compression or tension. Found insideA formula for measuring the change in one variable produced by a change in a ... of producing the 100th unit:: The formula for elasticity involves calculus, ... This tells us that it would take a relatively large price change in order to cause a relatively small change in quantity demanded. The next thing to input is the final price which is also a monetary . Calculating Price Elasticity of Demand. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Remember that when a fraction is divided by a fraction, you can rearrange it to a fraction multiplied by the inverse of the denominator fraction. The PED calculator employs the midpoint formula to determine the price elasticity of demand. How did customers of the 18-year-old firm react? This distinctive, text-specific manual uses Excel instructions and formulas to reinforce vital concepts. Where Ep is the arc elasticity; Q is the quantity of good sold ; P is the price of the good at the same time; Arc Elasticity Definition. You can calculate it by dividing by the percentage change in supply or demand quantity by the percentage change in price. To avoid this, we will instead rely on averages. Whereas before we could ignore positives and negatives with elasticities, with cross-price, this matters. If the price increases by 1%, the demand will decrease by E%. https://www.thoughtco.com/using-calculus-to-calculate-elasticities-1146248 (accessed October 6, 2021). (2020, August 27). Elasticity is the property of solid materials to return to their original shape and size after the forces deforming them have been removed. The initial price and demand are denoted by P i and Q i respectively. Managerial Economics 101 — get an easy-to-understand intro to fundamental aspects of managerial economics and the theory of price determination Whose side are you on? — make sense out of the relationship between price and quantity to ... §10: Elasticity of Demand §11: Implicit Differentiation and Related Rates; Chapter 3: The Integral §1: The Definite Integral §2: The Fundamental Theorem and Antidifferentiation §3: Antiderivatives of Formulas §4: Substitution §5: Additional Integration Techniques §6: Area, Volume, and Average Value §7: Applications to Business IMPORTANT! Our formula for elasticity, [latex]\frac{\%\Delta Quantity}{\%\Delta Price}[/latex], can be used for most elasticity problems, we just use different prices and quantities for different situations. This shows the responsiveness of the quantity demanded to a change in price. Elasticity of demand for D1 (points a to b in the left diagram above) =. Moffatt, Mike. c) Neither a) nor b). Recall slope is calculated as rise/run. %ÎQuantity: The following equation is used to calculate Cross Price Elasticity of Demand XED: Cross Price Elasticity Formula . The Percentage Change in Quantity Demanded is the New Quantity Demanded minus the Old Quantity Demanded divided by the Old Quantity Demanded. In Figure 4.1a we were given two points and looked at elasticity as movements along a curve. The standard levels of elasticity typically include elastic, inelastic and unitary. Solve the expression above for \(f(x)\), and you’ll get the tangent line approximation: To approximate the value of \(f(x)\) using TLA, find some \(a\) where, Another way to look at the same formula: \[\Delta y\approx f'(a)\Delta x\]. We would feel very unsure using this information to approximate \(g(55)\). To show this, take natural logs and differentiate, treating and as constants. Calculate Price Elasticity With Percentage Change Formula: Input: First of all, you have to add the percentage change in quantity into the designated filed; Then, you have to enter percentage change in price into the designated field; Output: Price Elasticity of Demand (according to Percentage Change Formula) Type of Elasticity; Elasticity Summary Found inside – Page vii... functions , integral calculus , infinite series , numerical equations ... to special problems in navigation , surveying , elasticity , architecture ... From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students. d) All of the above could be the value of cross price elasticity of demand. The demand for products that people have to buy, such as onions, tends to be inelastic. Stress is applied to force per unit area, and strain is proportional change in length. Right away, this should raise a red flag about calculating the elasticity between at two points, if percentage change is dependant on the direction (A to B or B to A) then how can we ensure a consistent elasticity value? When the price increases will revenue go down because the demand dropped so much? ThoughtCo, Aug. 27, 2020, thoughtco.com/using-calculus-to-calculate-elasticities-1146248. 500 units are produced at the start and 600 at the end. The price elasticity of demand equation can be further elaborated into the following, PED = { (D1 - D0) ÷ (D1 + D0)} ÷ { (P1 - P0) ÷ (P1 + P0)} Where, D0 = Initial Quantity of Demand. About this unit. To calculate elasticity, instead of using simple percentage changes in quantity and price, economists use the average percent change. [latex]\frac{\frac{\Delta Q}{(Q1+Q2)/2}}{\frac{\Delta P}{(P1+P2)/2}}[/latex] = [latex]\frac{\frac{\Delta Q}{Q1+Q2}}{\frac{\Delta P}{P1+P2}}[/latex]. Calculating the derivative, \( \frac{dq}{dp}=-2p \). The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. Price elasticity typically refers to price elasticity of demand that measures the response of demand of a particular item to the change in its price. We can write the expression for Modulus of Elasticity using the above equation as, E = (F*L) / (A * δL) So we can define modulus of Elasticity as the ratio of normal stress to longitudinal strain. In July 2011, the company announced a packaging change. To generate the values you need, follow these simple steps: First, input the initial price which is a monetary value. 6. b) 0.8. Price has fallen by 33%. Our equation is as follows: [latex]\frac{\%\Delta Q\;Good A}{\%\Delta P\;Good B}[/latex]. This user friendly, mathematically sound focuses on using the graphing calculator to explore new ideas which are validated by calculus methods, to create concepts using calculus and then support them with numerical or graphical techniques ... The price elasticity of demand (which is often shortened to demand elasticity) is defined to be the percentage change in quantity demanded, q, divided by the percentage change in price, p. The formula for the demand elasticity (ǫ) is: ǫ = p q dq dp. "Using Calculus to Calculate Elasticities." Calculating the income elasticity of demand is simple. 4. A substitute will have a positive cross-price elasticity, since if the % change in price is positive, the % change in quantity will be positive and vice-versa. The quantity of coffee sold falls from 6 to 4, meaning the percentage change is [latex]\frac{\left(4-6\right)}{6}[/latex] = -33%. This is because the formula uses the same base for both cases. This is called the Midpoint Method for Elasticity, and is represented in the following equations: % change in quantity = Q2−Q1 (Q2+Q1)/2 ×100 % change in price = P2−P1 (P2+P1)/2 ×100 % change in quantity = Q 2 − Q . The own price elasticity of demand is the percentage change in the quantity demanded of a good or service divided by the percentage change in the price. We would like to adapt elasticity to that case. The elasticity of demand for D1 between points a and b is 1.80 between points a and b b. For discrete changes in price and quantity demanded, the average price and quantity demanded can be used as the base in calculating percentage changes. Note that we don't know if these approximations are close – but they're the best we can do with the limited information we have to start with. In 2014, Netflix also raised its streaming video subscription price from $7.99 to $8.99 per month for new U.S. customers. We need to find \( q \) when \( p = 70 \): \[ q = 11500. Khan Academy is a 501(c)(3) nonprofit organization. Interactive classrooms and well-crafted problems promote student learning. Since it’s inception, the hallmark of Applied Calculus is its innovative and engaging problems. Topic 1: Introductory Concepts and Models. Demand is Qx = 110 - 4Px. Price Elasticity of Demand Formula. Customers wishing to retain both streaming video and DVD rental would be charged $15.98 per month â a price increase of about 60%. 5.1 THE PRICE ELASTICITY OF DEMAND <Computing the Price Elasticity of Demand We can use this formula to calculate the price elasticity of demand for a Starbucks latte: Price elasticity of demand Percentage change in quantity demanded This analysis gives us elasticity as a single point. Moffatt, Mike. This responsiveness can also be measured with elasticity by the income elasticity of demand. Our equation is as follows: [latex]\frac{\%\Delta Q}{\%\Delta Income}[/latex]. \[ \begin{align*} Modulus of Elasticity for Normal Weight Concrete formula is defined as the stiffness or resistance to deformation of a material. Notice that this gives us the same number as calculating elasticity from Point A to B. Mike Moffatt, Ph.D., is an economist and professor. Note also that 18 and 23 are sort of close to 20, so we can hope these approximations are pretty good. &= \left|\frac{p\cdot D'(p)}{D(p)}\right| We saw how to calculate various elasticities when we're given numerical examples. By using the formula, the price elasticity of demand equals 100% divided by 50%. The P/Q portion of our equation corresponds to the values at the point, which are $4.5 and 4. Use this information to approximate \(g(23)\) and \(g(18)\). Using the tangent line approximation: Using Calculus to Calculate Elasticities. The formula of Price elasticity Formula Of Price Elasticity Price elasticity is calculated by dividing the percentage change in quantity by percentage change in price. ID is the initial demand. σ = E ε. b) 1. In the same period, cost to produce goes from $20 . Thorough, clearly delineated spreadsheet and TI Graphing Calculator instruction appears throughout the text, and an acclaimed author website at www.wanermath.com provides interactive tutorials, powerful utilities, conceptualization tools, ... If pizza is a normal good, then which of the following could be the value of income elasticity of demand? In this case, raising prices increases revenue. A inferior good will have a negative income elasticity, since if the % change in income is positive, the % change in quantity will be negative and vice-versa. Divide the percentage change in quantity by the percentage change in price. a) 1/3. Our analysis of elasticity has been centred around demand, but the same principles apply to the supply curve. First, we need to solve the demand equation so it gives \( q \) in terms of \( p \), so that we can find \( \frac{dq}{dp} \): \( p=300-0.02q \), so \( q=15000-50p \). This is often a two-semester course. (The word "Applied" in this title distinguishes this volume from the shorter edition.)The book introduces calculus in real-world contexts; the primary goal is to provide a sound, intuitive understanding ... This adds another dimension to our discussion of complements/substitutes. Price Elasticity of Demand = 0.45 Explanation of the Price Elasticity formula. Solving for gives . Example: Let us use an example to demonstrate the price elasticity of demand calculation using a formula. Find the elasticity of demand when the price is $5 and when the price is $15. Using the same numbers, consider what happens when quantity demanded decreases from 6 coffees to 4 coffees, ([latex]\frac{\left(4-6\right)}{6}[/latex]) this change results in a 33% decrease in quantity demanded. This elasticity calculator is simple and easy to use making it a convenient tool for companies and businesses. The demand for products that people can do without, or put off buying, such as cars, tends to be elastic. Use the mid-point formula in your calculation. Found inside – Page 90Formula : Elasticities for Log - Linear Demand . ... Using the calculus formula for an elasticity yields ali ( P PE E.P. = B.CPB - PBMPMHBH ap , cPB. Thus, to calculate it the percentage change in the quantity of the first good is divided by the percentage change in price in the second good. This is called the mid-point method for elasticity, and is represented in the following equations: The advantage of the mid-point method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. (The other critical component is marginal cost.) How do we use it to calculate the elasticity at Point A? Mid-point gives an average of elasticities between two points, whereas point-slope gives the elasticity at a certain point. For example, a cross-price elasticity of -4 suggests an individual strongly prefers to consume two goods together, compared to a cross-price elasticity of -0.5. This topic will explain how to answer these questions and why they are critically important in the real world. \end{align*} \]. Solution: Here, P = 4500 ΔP = 1000 (a fall in price; 5500- 4500 = 1000) S = 450 units. To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video. Revenue could be raised by decreasing prices. Using Calculus To Calculate Income Elasticity of Demand, Calculate Cross-Price Elasticity of Demand (Calculus), Using Calculus to Calculate Price Elasticity of Supply, A Beginner's Guide to Elasticity: Price Elasticity of Demand, The Effects of a Black Market on Supply and Demand, A Primer on the Price Elasticity of Demand, Using Calculus To Calculate Price Elasticity of Demand, Using Calculus To Calculate Cross-Price Elasticity of Demand, Using Calculus To Calculate Price Elasticity of Supply, Ph.D., Business Administration, Richard Ivey School of Business, B.A., Economics and Political Science, University of Western Ontario, Elasticity = (percentage change in Z) / (percentage change in Y), (percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z), Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z). I don't quite understand what this equation means. The technique is like calculating the cross-price elasticity or the own-price elasticity. a) A 1% increase in price will result in a 50% increase in quantity supplied. The cross elasticity of demand is an economic concept that measures the responsiveness in the quantity demanded of one good when the price for another good changes. In this case, raising prices decreases revenue. Here is the mathematical formula: Own-price elasticity of demand (OED) = % Changes in quantity demanded of goods X /% Changes at the price of goods X. Found inside – Page 158Let me illustrate with the example: When D(p) = 10,000(50 − p), D0(p) = −10,000, and so The calculus-based formula for elasticity of demand is D0(p 0 )p0 ... 1.1 What Is Economics, and Why Is It Important? Consequently, the supply of the product is increased to 600 units. Even though mid-point and Point-Slope appear to be fairly different formulas, mid-point can be rewritten to show how similar the two really are. Notice that compared to point-slope: [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{P}{Q}[/latex], the only difference is that point-slope is the inverse of the slope multiplied by a single point, whereas mid-point is the inverse of the slope multiplied by multiple points. This solidifies the fact that there is a different elasticity at every point on our line, a concept that will be important when we discuss revenue. If the difference between P0 and P1 or Q0 and Q1 is high . Please consider a donation to this channel: https://www.paypal.com/cgi-bin/webscr?cmd=_donations&business=T2MPM6MSQ3UT8¤cy_code=USD&source=urlSee my ot. 1. How much will this price change affect the demand for Netflix’s products? From the midpoint formula we know that. p=& \sqrt{\frac{400}{3}}\approx 11.55. Even if the price goes up, people still have to buy about the same amount of onions, and revenue will not go down. The Compressive strain in terms of modulus of elasticity and compressive stress formula is defined as the ratio of compressive stress to the modulus of elasticity is calculated using compressive_strain = (Compressive Stress / Modulus of Elasticity).To calculate Compressive strain in terms of modulus of elasticity and compressive stress, you need Compressive Stress (σ c) and Modulus of . If the price of a complement rises our demand will fall, if the price of a substitute rises our demand will rise. For cross-price elasticity this means: A complement will have a negative cross-price elasticity, since if the % change in price is positive, the % change in quantity will be negative and vice-versa. We know that Price Elasticity of Demand = percent change in quantity percent change in price Price Elasticity of Demand = percent change in quantity percent change in price. If you're looking for how to calculate the price elasticity of demand, simply follow this formula. Found inside... 164 Differential, 283 Differential equation approximate solution, ... 352–363 elastic demand, 355 inelastic demand, 355 point elasticity, 355 relative ... \[ E = \left| \frac{-2(15)^2}{400-(15)^2} \right| \approx 2.571 \] So the demand is elastic when the price is $15. This gives us our point-slope formula. But what about revenue = price \( \times \) quantity? a) 0. Suppose there is an increase in quantity demanded from 4 coffees to 6 coffees. We can write the expression for Modulus of Elasticity using the above equation as, E = (F*L) / (A * δL) So we can define modulus of Elasticity as the ratio of normal stress to longitudinal strain. Note that the law of demand implies that dq/dp < 0, and so ǫ will be a negative number. Formula to Calculate Price Elasticity of Demand. New specs require students to include the minus or plus signs along with the coefficient. II is the initial income. \[ \begin{align*} Moffatt, Mike. \[ \begin{align*} D1 = Final Quantity of Demand. It depends on the shape of the graph of \(f\). However, in reality, price elasticity rarely functions as a direct causal relationship because products typically fall into different categories according to their importance and value to the consumer. If XED > 0, then the products are substitutes of each other. No other info was given. c) A 1% increase in price will result in a 2% increase in quantity supplied. 8. This means we can also write \(E\) as \(-\dfrac{p}{q}\cdot \dfrac{dq}{dp}\) or \(-\dfrac{p\cdot D'(p)}{D(p)}\). [latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { Q }_{ 2 }-{ Q }_{ 1 } }{ ({ Q }_{ 2 }+{ Q }_{ 1 })/2 } \times 100 \\[1em] \%\;change\;in\;price & \frac { { P }_{ 2 }-{ P }_{ 1 } }{ ({ P }_{ 2 }+{ P }_{ 1 })/2 } \times 100 \end{array}[/latex], Creative Commons Attribution 4.0 International License, [latex]\frac{\%\Delta Quantity}{\%\Delta Price}[/latex], [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{\left(P1+P2\right)}{\left(Q1+Q2\right)}[/latex],  [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{P}{Q}[/latex], Calculate the income elasticity of demand and the cross-price elasticity of demand, Apply concepts of price elasticity to real-world situations. σ is the Stress, and ε denotes strain. The accepted modulus of elasticity of steel is 29,000,000 . We would feel more confident using this information to approximate \(g(20.003)\). Note that since demand is [normally] a decreasing function of \(p\), the derivative is [normally] negative. a) 0.2. Donate or volunteer today! d) None of the above. Anyone who has studied economics knows the law of demand: a higher price will lead to a lower quantity demanded. %ÎQuantity: The quantity of coffee sold increases from 4 to 6, meaning the percentage change is [latex]\frac{\left(6-4\right)}{4}[/latex] = 50%. Price elasticity of demand. Thus we can calculate any elasticity through the formula: We'll look at how to apply this to four different situations: Next: Using Calculus To Calculate Price Elasticity of Demand. (ITM) 2) You can choose tangent at a specified stress level. The more elastic a firm, the more it can increase production when prices are rising, and decrease its production when prices are falling. Our equation is as follows: [latex]\frac{\%\Delta Q\;Supplied}{\%\Delta P}[/latex]. This innovative text for undergraduates provides a thorough and self-contained treatment of all the mathematics commonly taught in honours degree economics courses. It is suitable for use with students with and without A level mathematics. In general, the closer the better. An inverse demand function of the form has a constant price elasticity of demand . Cross Price Elasticity Formula. d) All of the above. Increasing the price would lead to an increase in revenue, so it seems that the company should increase its price. How sensitive are things to change in price? Price elasticities of . Here is Marshall's (1890) one percent change in price scenario that he opens his formal discussion of elasticity with: "…we may say that the elasticity of demand is one, if a fall of one 7. Instead of $3 for a cup of coffee with cream and sweetener, you will now be charged $2 for a black coffee, $1 for creamer, and $1 for your choice of sweetener. For arc elasticity we have two quantity-price points \((quantity_1,price_1)\) and \((quantity_2,price_2)\text{. Using the mid-point method to calculate the elasticity between Point A and Point B: [latex]\begin{array}{r @{{}={}} l}\%\;change\;in\;quantity & \frac { { 6 }-{ 4 } }{ ({ 6 }+{ 4 })/2 } \times 100 \\[1em] & \frac { 2 }{ 5 } \times 100 \\[1em] & 40\% \\[1em] \%\;change\;in\;price & \frac { { 3.00 }-{ 4.50 } }{ ({ 3.00 }+{ 4.50 })/2 } \times 100 \\[1em] & \frac { -1.50 }{ 3.75 } \times 100 \\[1em] & -40\% \\[1em] Price\;Elasticity\;of\;Demand & \frac { 40\% }{ 40\% } \\[1em] & 1 \end{array}[/latex]. 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