# 1 1 BA 445 Lesson A.3 Elasticity ReadingsReadings Baye 6 th edition or 7 th edition, Chapter 3.

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1 1 BA 445 Lesson A.3 Elasticity ReadingsReadings Baye 6 th edition or 7 th edition, Chapter 3

2 2 BA 445 Lesson A.3 Elasticity OverviewOverview

3 3Overview Own Price Elasticity measures how much the demand for a good responds to a change in its own price. Demand is more inelastic (less responsive) when products are distinguished from competitors. Elasticity and Revenue are inversely related: If demand is elastic, then increasing price decreases revenue from that product; if inelastic, increasing price increases revenue. — So, elasticity affects optimal prices and quantities. Cross Elasticity measures how the demand for one good responds to a change in the price of another good. Cross elasticity affects the optimal choice of prices and quantities for firms supplying multiple products. Demand Functions are typically linear or log-linear. Linear demand simplifies computing equilibrium price, quantity and surplus. Log-linear demand simplifies computing elasticity.

4 4 BA 445 Lesson A.3 Elasticity Own Price Elasticity

5 5 Overview Own Price Elasticity of Demand measures how much the demand for a good responds to a change in its own price.  For example, elasticity measures how much demand for cars responds to a change in the price of cars.  Demand is more inelastic (less responsive) when products are distinguished from competitors. Elasticity can also measure how much demand for a good responds to a change in the price of any other good.  For example, how much the demand for cars responds to a change in the price of motorcycles. BA 445 Lesson A.3 Elasticity Own Price Elasticity

6 6 Demand Price Quantity Price Quantity BA 445 Lesson A.3 Elasticity Own Price Elasticity Two extremes of own price elasticity are: Perfect inelasticity, demand is perfectly insensitivePerfect inelasticity, demand is perfectly insensitive Demand for an artificial limb may be perfectly inelastic for some range of prices.Demand for an artificial limb may be perfectly inelastic for some range of prices. Perfect elasticity, demand is perfectly sensitivePerfect elasticity, demand is perfectly sensitive Demand for Farmer Smith’s apples.Demand for Farmer Smith’s apples. Perfect Inelasticity Perfect Elasticity Demand

7 7 BA 445 Lesson A.3 Elasticity Own Price Elasticity The primary factor determining own-price elasticity is the number of substitutes competing against that good.  Fewer substitutes implies lower demand elasticity.  Innovating or distinguishing a product (making it different) from competing goods reduces substitutes.  Distinguishing a product may raise demand and profit, or lower demand and profit.  Google and Apple Inc. are innovative firms, with many distinguished products. All have inelastic demand, but not all have been profitable. Profitable Apple products include the Apple II computer, iPod, iPhone, and the iPad tablet computer.Profitable Apple products include the Apple II computer, iPod, iPhone, and the iPad tablet computer. Unprofitable Apple products include the Apple III computer and the Newton tablet computer.Unprofitable Apple products include the Apple III computer and the Newton tablet computer.

8 8 iPod Demand Price Quantity Price Quantity BA 445 Lesson A.3 Elasticity Own Price Elasticity Graphing distinguished successes and failures The new product is more innovative or distinguished than the generic product, and so has lower elasticity.The new product is more innovative or distinguished than the generic product, and so has lower elasticity. New product demand may be higher or lower than generic demand. (Higher demand means higher profit.)New product demand may be higher or lower than generic demand. (Higher demand means higher profit.) Generic MP3 Player Demand Profitable innovation Generic Tablet Computer Demand Newton Demand Unprofitable innovation

9 9 The Simplest Definition of Elasticity The simplest precise elasticity measure E Q,P of how much the demand Q for a good X responds to a change in price P (either the price P x of the same good X or the price P y of another good Y) is a ratio of changesThe simplest precise elasticity measure E Q,P of how much the demand Q for a good X responds to a change in price P (either the price P x of the same good X or the price P y of another good Y) is a ratio of changes  Q /  P For one example, if demand Q x for cars decreases 10 in response to a \$20 increase in the price P x of cars, then elasticity  Q x /  P x = -10/20 = -0.5For one example, if demand Q x for cars decreases 10 in response to a \$20 increase in the price P x of cars, then elasticity  Q x /  P x = -10/20 = -0.5 That definition is unacceptable, however, because it depends on units of measure.That definition is unacceptable, however, because it depends on units of measure. If the \$20 increase in the price P x of cars were measured as a 2000 cent increase, then  Q x /  P x changes from -0.5 to -10/2000 = -0.005 If the \$20 increase in the price P x of cars were measured as a 2000 cent increase, then  Q x /  P x changes from -0.5 to -10/2000 = -0.005 BA 445 Lesson A.3 Elasticity Own Price Elasticity

10 The Percent Definition of Elasticity One acceptable precise elasticity measure E Q,P of how much the demand Q for a good X responds to a change in price P is a ratio of percentagesOne acceptable precise elasticity measure E Q,P of how much the demand Q for a good X responds to a change in price P is a ratio of percentages E Q,P = %  Q / %  P For one example, if demand Q x for cars decreases 10% in response to a 20% increase in the price P x of cars, then elasticity E Q x,P x = %  Q x /%  P x = -10/20 = -0.5For one example, if demand Q x for cars decreases 10% in response to a 20% increase in the price P x of cars, then elasticity E Q x,P x = %  Q x /%  P x = -10/20 = -0.5 For another example, if demand Q x for cars increases 6% in response to a 2% increase in the price P y of motorcycles 5%, then E Q x,P y = %  Q x /%  P y = 6/2 = 3For another example, if demand Q x for cars increases 6% in response to a 2% increase in the price P y of motorcycles 5%, then E Q x,P y = %  Q x /%  P y = 6/2 = 3 BA 445 Lesson A.3 Elasticity Own Price Elasticity

11 The Sign of Elasticity tells the direction of a relationship: If E Q,P < 0, then Q and P are negatively (or inversely) related.If E Q,P < 0, then Q and P are negatively (or inversely) related. n For example, the observed law of demand for all goods considered in this class is that demand is negatively related to its own price, so own-price elasticity of demand is negative, E Q x,P x < 0. If E Q,P > 0, then Q and P are positively (or directly) related.If E Q,P > 0, then Q and P are positively (or directly) related. If E Q,P = 0, then Q and P are unrelated.If E Q,P = 0, then Q and P are unrelated. BA 445 Lesson A.3 Elasticity Own Price Elasticity

12 Percentages in the Definition of Elasticity have both good and bad properties. One good property of percentages: they do not depend on units of measure.One good property of percentages: they do not depend on units of measure. n Doubling price from \$1 to \$2 in dollars, or from 100c to 200c in cents, is the same percent increase. One bad property of percentages: they are inaccurate.One bad property of percentages: they are inaccurate. n 100 to 200 is a 100% increase, but 200 to 100 is only a 50% decrease. So, the percent definition of elasticity depends on whether price increases or decreases. BA 445 Lesson A.3 Elasticity Own Price Elasticity

13 The Derivative Definition of Elasticity An alternative acceptable elasticity measure uses derivativesAn alternative acceptable elasticity measure uses derivatives E Q,P = dQ/dP. P/Q The derivative definition shares the good property of the percentage definition (elasticity does not depend on the units of measure).The derivative definition shares the good property of the percentage definition (elasticity does not depend on the units of measure). The derivative definition avoids the inaccuracy of the percentage definition. The derivative definition of elasticity does not depend on whether price increases or decreasesThe derivative definition avoids the inaccuracy of the percentage definition. The derivative definition of elasticity does not depend on whether price increases or decreases n Elasticity E Q,P is the same whether P increases (dP > 0), or P decreases (dP 0), or P decreases (dP < 0) BA 445 Lesson A.3 Elasticity Own Price Elasticity

14 Own Price Elasticity of Demand E Q x,P x = %  Q x / %  P x or E Q x,P x = dQ x /dP x. P x /Q x is classified into three categories, according to its magnitude: Elastic (sensitive demand): | E Q x, P x | > 1Elastic (sensitive demand): | E Q x, P x | > 1 Inelastic (insensitive demand): | E Q x, P x | < 1Inelastic (insensitive demand): | E Q x, P x | < 1 Unit elastic: | E Q x, P x | = 1Unit elastic: | E Q x, P x | = 1 BA 445 Lesson A.3 Elasticity Own Price Elasticity

15 BA 445 Lesson A.3 Elasticity Elasticity and Revenue

16 Overview Elasticity and Revenue are related when a supplier changes either price or quantity. When price increases, revenue increases if demand is inelastic but revenue decreases if demand is elastic. Likewise, when quantity increases, revenue decreases if demand is inelastic but revenue increases if demand is elastic. — So, elasticity affects whether to increase or decrease price or quantity. BA 445 Lesson A.3 Elasticity Elasticity and Revenue

17 Choosing price or output quantity is the simplest management decision. Each firm chooses one variable, with the other variable defined by demand.  Examples of choosing price include choosing the advertised price first, then producing just enough to satisfy demand at that price.  Examples of choosing output quantity include choosing the output first, then adjusting price just enough to sell all output. BA 445 Lesson A.3 Elasticity Elasticity and Revenue Price Quantity Price Quantity Demand Setting Price Setting Quantity P Q Demand P Q

18 First, consider firms that choose price. Predicting revenue change from a price change follows the formula  R = R x (1+E Q x,P x ). %  P x where   R is the change in revenue  R x is the initial revenue from good X  E Q x,P x is the own price elasticity of demand for good X  %  P x is the change in the price P x of good X expressed as a fraction. BA 445 Lesson A.3 Elasticity Elasticity and Revenue

19 For example, suppose  You only sell burgers.  Your current revenue from burgers is \$100.  The own price elasticity is -0.5  You increase price 10% Then, the formula  R = R x (1+E Q x,P x ). %  P x implies revenue changes  R = (\$100(1-0.5)). (0.10) = \$5  That is, revenue increases \$5. BA 445 Lesson A.3 Elasticity Elasticity and Revenue

20 When demand is inelastic, revenue moves in the same direction of a change in price.  R = R x (1+E Q x,P x ). %  P x When demand is inelastic, |E Q x,P x | < 1When demand is inelastic, |E Q x,P x | < 1 E Q x,P x > -1, so 1+ E Q x,P x > 0, so if price increases, %  P > 0 and  R > 0. E Q x,P x > -1, so 1+ E Q x,P x > 0, so if price increases, %  P > 0 and  R > 0. n Increased price implies increased total revenue. n It is definitely profitable to raise price since raising price increases revenue and decreases as higher price leads to lower supply quantity.) BA 445 Lesson A.3 Elasticity Elasticity and Revenue

21 revenue moves in the When demand is elastic, revenue moves in the opposite direction of a change in price.  R = R x (1+E Q x,P x ). %  P x E Q x,P xWhen demand is elastic, |E Q x,P x | > 1 E Q x,P x E Q x,P x E Q x,P x 0 and  R < 0. n Increased price implies decreased total revenue. n It may be profitable to lower price since lowering price increases revenue. (Profit also depends on how much cost increases as lower price leads to higher supply quantity.) BA 445 Lesson A.3 Elasticity Elasticity and Revenue

22 Now consider firms that choose quantity. Revenue change from a quantity change is the opposite of the revenue change from a price change. When demand is inelastic, as quantity increasesWhen demand is inelastic, as quantity increases n Price decreases because of the law of demand. n So, revenue increases since revenue and price move in opposite directions. n Marginal revenue MR is the change in revenue as quantity increases, so MR < 0 When demand is elastic, as quantity increasesWhen demand is elastic, as quantity increases n Price decreases. n Revenue decreases. n Marginal revenue is positive. When demand is unit elastic, marginal revenue is 0When demand is unit elastic, marginal revenue is 0 BA 445 Lesson A.3 Elasticity Elasticity and Revenue

23 Graphing elasticity and revenue when demand is linear QQ P TR 100 001020 304050 BA 445 Lesson A.3 Elasticity Elasticity and Revenue

24 QQ P TR 100 01020 304050 80 800 0 10 20 304050 BA 445 Lesson A.3 Elasticity Elasticity and Revenue Graphing elasticity and revenue when demand is linear

25 QQ P TR 100 80 800 60 1200 01020 304050 01020 304050 BA 445 Lesson A.3 Elasticity Elasticity and Revenue Graphing elasticity and revenue when demand is linear

26 QQ P TR 100 80 800 60 1200 40 01020 304050 01020 304050 BA 445 Lesson A.3 Elasticity Elasticity and Revenue Graphing elasticity and revenue when demand is linear

27 QQ P TR 100 80 800 60 1200 40 20 01020 304050 01020 304050 BA 445 Lesson A.3 Elasticity Elasticity and Revenue Graphing elasticity and revenue when demand is linear

28 QQ P TR 100 80 800 60 1200 40 20 Elastic 01020 304050 01020 304050 BA 445 Lesson A.3 Elasticity Where quantity is less than 25, a price decrease causes a quantity increase and an increase in revenue. So, demand is elastic since price and revenue are negatively related (and quantity and revenue are positively related). Elasticity and Revenue

29 QQ P TR 100 80 800 60 1200 40 20 Inelastic Elastic Inelastic 01020 304050 01020 304050 BA 445 Lesson A.3 Elasticity Where quantity is greater than 25, a price decrease causes a quantity increase and a decrease in revenue. So, demand is inelastic since price and revenue are positively related (and quantity and revenue are negatively related). Elasticity and Revenue

30 QQ P TR 100 80 800 60 1200 40 20 Inelastic Elastic Inelastic 01020 304050 01020 304050 Unit elastic BA 445 Lesson A.3 Elasticity Unit elasticity divides elasticity from inelasticity. Elasticity and Revenue

31 Elasticity and Revenue QQ P TR 100 80 800 60 1200 40 20 Inelastic Elastic Inelastic 01020 304050 01020 304050 Unit elastic BA 445 Lesson A.3 Elasticity Marginal Revenue is the extra revenue from increasing output. It is positive when output is less than 25 and demand is elastic, and is negative when output is greater than 25 and demand is inelastic.

32 For any linear inverse demand function, P(Q) = a - bQ, then MR(Q) = a - 2bQ. So, MR > 0, where demand is elastic MR = 0, where demand is unit elastic MR < 0, where demand is inelastic Q P 100 80 60 40 20 Inelastic Elastic 01020 4050 Unit elastic MR BA 445 Lesson A.3 Elasticity Elasticity and Revenue

33 Elasticity and Revenue Q TR Elastic Inelastic 0 Unit elastic BA 445 Lesson A.3 Elasticity Example: To maximize revenue when demand is Q = 12 – 0.2 P, first invert demand, to 0.2 P = 12 – Q and P = 60 – 5Q. Then, compute marginal revenue MR = 60 – 10Q. Then, set MR = 0, to get Q = 6. Then, set P = 60 – 5(6) = 30. Demand is unit elastic when revenue is maximized.

34 BA 445 Lesson A.3 Elasticity Cross Elasticity

35 Overview Cross Price Elasticity measures how the demand for one good responds to a change in the price of another good. Cross elasticity affects the optimal choice of prices and quantities for firms supplying multiple products. BA 445 Lesson A.3 Elasticity Cross Elasticity

36 is defined like own Cross Price Elasticity of Demand is defined like own price elasticity price elasticity E Q x,P y = %  Q x / %  P y or E Q x,P y = dQ x /dP y. P x /Q y  Unlike the negative own price elasticity E Q x,P x < 0, cross price elasticity can be positive or negative, depending on how good relate.  If E Q x,P y > 0, then X and Y are (gross) substitutes.  If E Q x,P y < 0, then X and Y are (gross) complements. BA 445 Lesson A.3 Elasticity Cross Elasticity

37 Predicting revenue change from a price change follows the formula for multiple products  R = (R x (1+E Q x,P x ) + R y E Q y,P x ). %  P x where   R is the change in revenue from the two products  R x is the initial revenue from good X  E Q x,P x is the own price elasticity of demand for good X  R y is the initial revenue from good Y  E Q y,P x is the cross elasticity of demand for good Y  %  P x is the change in the price P x of good X expressed as a fraction. BA 445 Lesson A.3 Elasticity Cross Elasticity

38 For example, suppose  You sell only burgers and fries.  Current revenue is \$100 from burgers, \$50 from fries.  T  The own price elasticity of burgers is -0.5 (inelastic).  The cross price elasticity of fries when the price of burgers changes is -2 (gross complements).  You increase burger price 20% Then, the formula  R = (R x (1+E Q x,P x ) + R y E Q y,P x ). %  P x implies revenue changes  R =. = -\$10  R = (\$100(1-.5) + \$50(-2)). (0.20) = -\$10  That is, revenue decreases \$10. BA 445 Lesson A.3 Elasticity Cross Elasticity

39 BA 445 Lesson A.3 Elasticity Demand Functions

40 Overview Demand Functions are typically linear or log-linear. Linear demand simplifies computing equilibrium price, quantity and surplus. Log-linear demand simplifies computing elasticity. BA 445 Lesson A.3 Elasticity Demand Functions

41 Interpreting Linear Demand Example: Q X = 10 – 2P X + 3P Y + 5M Law of demand holds (coefficient of P X is negative).Law of demand holds (coefficient of P X is negative). X and Y are gross substitutes (coefficient of P Y is positive).X and Y are gross substitutes (coefficient of P Y is positive). X is a normal good (coefficient of income M is positive).X is a normal good (coefficient of income M is positive). BA 445 Lesson A.3 Elasticity Demand Functions

42 Computing Elasticity from Linear Demand Use the derivative definition of elasticity: Q X = 10 – 2P X + 3P Y + 5M Own price elasticity (depends on price and quantity):Own price elasticity (depends on price and quantity): E Q x,P x = dQ x /dP x. P x /Q x = - 2 P x /Q x Cross price elasticity (depends on price and quantity):Cross price elasticity (depends on price and quantity): E Q x,P y = dQ x /dP y. P y /Q x = 3 P y /Q x BA 445 Lesson A.3 Elasticity Demand Functions

43 Computing Elasticity from Log-Linear Demand Use the derivative definition of elasticity: ln(Q X ) = 10 – 2ln(P X ) + 3ln(P Y ) + 5ln(M) Own price elasticity (not depend on price and quantity):Own price elasticity (not depend on price and quantity): E Q x,P x = dQ x /dP x. P x /Q x = - 2 Cross price elasticity (not depend on price and quantity):Cross price elasticity (not depend on price and quantity): E Q x,P y = dQ x /dP y. P y /Q x = 3 BA 445 Lesson A.3 Elasticity Demand Functions

44 Quantity Linear Demand Log Linear Demand Graphs of Linear and Log-Linear Demand BA 445 Lesson A.3 Elasticity Demand Functions Price Quantity Price

45 BA 445 Lesson A.3 Elasticity SummarySummary

46 Applications of Elasticity Pricing and managing cash flows.Pricing and managing cash flows. Effect of changes in competitors’ prices.Effect of changes in competitors’ prices. BA 445 Lesson A.3 ElasticitySummary

47 Example 1: Pricing and Cash Flows According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64. AT&T needs to boost revenues in order to meet it’s marketing goals. To accomplish this goal, should AT&T raise or lower it’s price? BA 445 Lesson A.3 ElasticitySummary

48 Answer: Lower price. Since demand is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T. BA 445 Lesson A.3 ElasticitySummary

49 Example 2: Quantifying the Change If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T? BA 445 Lesson A.3 ElasticitySummary

50 Answer Calls would increase by 25.92 percent. BA 445 Lesson A.3 ElasticitySummary

51 Example 3: Effect of a change in a competitor’s price According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services? BA 445 Lesson A.3 ElasticitySummary

52 Answer AT&T’s demand would fall by 36.24 percent. BA 445 Lesson A.3 ElasticitySummary

53 Review Questions BA 445 Lesson A.3 Elasticity Review Questions  You should try to answer some of the review questions (see the online syllabus) before the next class.  You will not turn in your answers, but students may request to discuss their answers to begin the next class.  Your upcoming Exam 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.

54 End of Lesson A.3 BA 445 Managerial Economics BA 445 Lesson A.3 Elasticity