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Basic Introduction to Elasticity

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## Basic Introduction to Elasticity

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**Basic Introduction to Elasticity**Ted Mitchell**These slides identify**• The 3 basic uses of price elasticity • The basic definition of elasticity • The 3 basic types of price elasticity • Original Point Elasticity • Average point Elasticity • Arc Elasticity • The Flaw in Basic Approximation of Elasticity**Elasticity comes in many flavors**• Advertising Elasticity • Coupon Elasticity • Sales Force Call Elasticity, etc., etc. • The Best Known Flavor is Price Elasticity, Eqpaka Demand Elasticity**Price Elasticity = -1**-0.5 -0.75 -1 -1.25 -1.5 -1.75 Quantity Sold Maximum Revenue a/2 Price per Unit a/2b TJM**Revenue looks like R = aP - bP2**Revenue Price Elasticity -0.5 -0.75 -1 - 1.25 -1.5 -1.75 0 Price Optimal price, Pr = a/2b TJM**Sample Price Elasticities**• Restaurant meals -2.3 • Foreign travel, long-run - 4.0 • Airline travel, long-run -2.4 • Fresh green peas -2.8 • Automobiles, short-run -1.2 to - 1.5 • Chevrolet automobiles -4.0 • Fresh tomatoes -4.6**Three Classic Uses of the Elasticity Index**• 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity sold) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized**1) Comparing Sensitivities**• Most economists use the term elasticity to discuss the sensitivity of a change in one variable (price) to a change in another variable (quantity sold). • The price elasticity of the apple market in the USA is Eqp = -1.6 and the price elasticity of the orange market in Spain is Eqp -2.5 • The orange market is more sensitive to price changes than the apple market.**2) Calculating consequences of a price change**• The price elasticity of the apple market in the USA is Eqp = -1.6 and the price elasticity of the orange market in Spain is Eqp = -2.5 • Elasticity of -1.6 means that a 1% change in price will cause a 1.6% change in the quantity of apples that are sold • Elasticity of -2.5 means that a 1% change in price will cause a 2.5% change in the quantity of oranges that are sold • The two can be compared because elasticity is an index and an index is unit neutral.**3) Elasticity indicates the direction for improved revenues**• for a change in price to increase revenue • If the elasticity is between 0 and -0.99 then a increase in price increases revenues • If the elasticity is more negative than -1.0 then reduce the price to maximize utility • If elasticity is -0.1 then you have the price that maximizes revenue**If my elasticity is calculated as -0.5 then I should raise**my price to get more revenue Revenue Price Elasticity -0.5 -0.75 -1 - 1.25 -1.5 -1.75 0 Price Increase price if elasticity is - 0.50 TJM**Point Elasticity of Price is defined as**• The ratio of the percentage change in quantity sold to the percentage change in price from one period to another • Point Elasticity of Price = %∆Q/%∆P • Percentage change in price = (P2-P1)/P1 • Percentage change in quantity = (Q2-Q1)/Q1 • Point Eqp = (∆Q/Q)/(∆P/P)**You often see Point Elasticity**• Point Eqp = (∆Q/Q)/(∆P/P) • Written as • Point EQP = P(∆Q)/Q(∆P) • To avoid writing multiple ratios • Note the approximation to impact analysis • Impact of quantity change = I∆Q = P(∆Q) • Impact of price change = I∆P = Q(∆P)**Elasticity is easy**• If you know the details of the demand curve • Q = a-bP • Then using calculus to find the point elasticity, Eqp, is straight forward • Eqp = -bP/(a-bP) • and very accurate**BUT!!!**• You don’t know the details of demand curve! • You have only observations of last period and the current period • You are making an approximation to the point elasticity**Quantity**Sold Q2 = 3,000 X Q1 = 2,500 X P2 =$4 P1=$5 Price per Unit TJM**Quantity**Sold Demand Curve= Q = a-bP Q2 = 3,000 X Q1 = 2,500 X P2 = $4 Price per Unit P1 = $5 TJM**Quantity**Sold Area = Revenue = P x Q Q2 = 3,000 X Q1 = 2,500 X P2 = $4 Price per Unit P1 = $5 TJM**There are many different ways**• to calculate elasticity. They all depend on what value is used as the denominator in the percentage changes • 1) Original Point Elasticity is the classic • 2) Average Elasticity is to avoid the flaw in point calculation • 3) Arc Elasticity is a better way to avoid the the flaw in point**Point Elasticity**• 1) Point Elasticity = percentage change from the original quantity divided by the percentage change from the original price, Point Eqp = (%∆Qoriginal)/(%∆Priceoriginal) • Perfect: if you use calculus to find the slope at a point • Flawed in its Approximation: You get two different numbers depending on which is considered the original point**Elasticity at the original point on the demand curve**Quantity Sold -0.5 -0.75 -1 -1.25 -1.5 -1.75 Elasticity at the original point = -0.667 3,000 X 2,500 X $4 Price per Unit $5 TJM**The Flaw in Point Elasticity**• A calculation of Elasticity at the original point is Eqp = -0.667 • implies an increase in price would increase revenue • BUT my price is now at the optimal $5 price and any increase would decrease my revenue**Quantity**Sold -0.5 -0.75 -1 -1.25 -1.5 -1.75 Elasticity at the point = -0.667 3,000 X Elasticity at the point = -1.0 2,500 X $4 Price per Unit $5 TJM**Average Elasticity**• To avoid the flaw in point elasticity • 2) Average Elasticity = average percentage change from the average quantity divided by the average percentage change from the average price, Average Eqp = (%∆Qaverage)/(%∆Priceaverage)**For the Exam: know Arc Elasticity**• A better way of avoiding the flaw • Arc elasticity for marketing managers is calculated by using the Minimum of the two choices for the denominator in the % changes • 3) Arc Elasticity = percentage change from the minimum quantity divided by the percentage change from the minimum price, Arc Eqp = (%∆Qmin)/(%∆Pricemin)**Elasticity at the point = -0.667**Quantity Sold Elasticity at the point = -1.0 Arc Elasticity = -0.8 3,000 X 2,500 X $4 Price per Unit $5 TJM**With the Arc Elasticity the starting point is irrelevant**• There is no such thing as an ideal measure of arc elasticity • Many Economists like to use the averages of the two points to have an average denominator • Marketing managers like using the minimum values for denominators because it is consistent with Impact Analysis**What are the Three Classic Uses of Elasticity?**• 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized**Exam Question #1**• If the car market has a price elasticity of -2.5 and the housing market has a price elasticity of -1.7, then which one is more sensitive to a price change? • A) the car market • B) the housing market • C) not enough information to know?**Exam Question #1**• If the car market has a price elasticity of -2.5 and the housing market has a price elasticity of -1.7, then which one is more sensitive to a price change? • A) By definition the car market is correct • B) the housing market • C) not enough information to know?**Three Classic Uses of the Elasticity Index**• 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized**Exam Question #2**• If the price elasticity in your market is -2.5 and you decrease your price by 2%, then you can expect your sales volume to increase by 5%. True or False? • True • False**Exam Question #2**• If the price elasticity in your market is -2.5 and you decrease your price by 2%, then you can expect your sales volume to increase by 5%. True or False? • True is correct • %∆Q = (Elasticity of Price) x (%∆P) • %∆Q = (-2.5) x (-2%) = 5%increase in quantity**Three Classic Uses of the Elasticity Index**• 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized**Exam Question #3**• If the price elasticity of your market is -2.75, then an increase in your selling price will decrease your revenue. True or false? • A) True • B) False**Exam Question #3**• If the price elasticity of your market is -2.75, then an increase in your selling price will decrease your revenue. True or false? • A) True is the correct answer • B) False**Price Elasticity = -1**-0.5 -0.75 -1 -1.25 -1.5 -1.75 Quantity Sold Maximum Revenue a/2 Price per Unit a/2b TJM**Price Elasticity = -1**-0.5 -0.75 -1 -1.25 -1.5 -1.75 Quantity Sold Maximum Revenue a/2 Less Revenue Price per Unit a/2b TJM**Revenue looks like R = aP - bP2**Revenue Price Elasticity -0.5 -0.75 -1 - 1.25 -1.5 -1.75 0 Price Optimal price, Pr = a/2b TJM**We remember that the price**• That maximizes revenueis the first derivative of the revenue function • R = P(a-bP) • R = aP – bP2 • dR/dP = a – 2bP • Set equal to zero to solve for the optimal price • a - 2bP = 0 • P = a/2b**Convenient to consider price elasticity constant in the**current region e is the price elasticityand it is same for every price k is a scaling constant Q Q Q = a-bP Q = kPe P P