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Readings Readings Baye 6th edition or 7th edition, Chapter 3 BA 445 Lesson A.3 Elasticity 1 Overview Overview BA 445 Lesson A.3 Elasticity 2 Overview 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. BA 445 Lesson A.3 Elasticity 3 Own Price Elasticity Own Price Elasticity BA 445 Lesson A.3 Elasticity 4 Own Price Elasticity 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 5 Own Price Elasticity Two extremes of own price elasticity are: • Perfect inelasticity, demand is perfectly insensitive • Demand for an artificial limb may be perfectly inelastic for some range of prices. • Perfect elasticity, demand is perfectly sensitive • Demand for Farmer Smith’s apples. Price Perfect Inelasticity Perfect Elasticity Price Demand Demand Quantity BA 445 Lesson A.3 Elasticity Quantity 6 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. • Unprofitable Apple products include the Apple III computer and the Newton tablet computer. BA 445 Lesson A.3 Elasticity 7 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. • New product demand may be higher or lower than generic demand. (Higher demand means higher profit.) Price Profitable innovation Price iPod Demand Generic MP3 Player Demand Quantity Unprofitable innovation Generic Tablet Computer Demand Newton Demand BA 445 Lesson A.3 Elasticity Quantity 8 Own Price Elasticity The Simplest Definition of Elasticity • The simplest precise elasticity measure EQ,P of how much the demand Q for a good X responds to a change in price P (either the price Px of the same good X or the price Py of another good Y) is a ratio of changes DQ / DP • For one example, if demand Qx for cars decreases 10 in response to a $20 increase in the price Px of cars, then elasticity DQx/DPx = -10/20 = -0.5 • That definition is unacceptable, however, because it depends on units of measure. If the $20 increase in the price Px of cars were measured as a 2000 cent increase, then DQx/DPx changes from -0.5 to -10/2000 = -0.005 BA 445 Lesson A.3 Elasticity 9 Own Price Elasticity The Percent Definition of Elasticity • One acceptable precise elasticity measure EQ,P of how much the demand Q for a good X responds to a change in price P is a ratio of percentages EQ,P = %DQ / %DP • For one example, if demand Qx for cars decreases 10% in response to a 20% increase in the price Px of cars, then elasticity EQx,Px = %DQx/%DPx = -10/20 = -0.5 • For another example, if demand Qx for cars increases 6% in response to a 2% increase in the price Py of motorcycles 5%, then EQx,Py = %DQx/%DPy = 6/2 = 3 BA 445 Lesson A.3 Elasticity 10 Own Price Elasticity The Sign of Elasticity tells the direction of a relationship: • If EQ,P < 0, then Q and P are negatively (or inversely) related. 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, EQx,Px < 0. • If EQ,P > 0, then Q and P are positively (or directly) related. • If EQ,P = 0, then Q and P are unrelated. BA 445 Lesson A.3 Elasticity 11 Own Price Elasticity 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. 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. 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 12 Own Price Elasticity The Derivative Definition of Elasticity • An alternative acceptable elasticity measure uses derivatives EQ,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 avoids the inaccuracy of the percentage definition. The derivative definition of elasticity does not depend on whether price increases or decreases Elasticity EQ,P is the same whether P increases (dP > 0), or P decreases (dP < 0) BA 445 Lesson A.3 Elasticity 13 Own Price Elasticity Own Price Elasticity of Demand EQx,Px = %DQx / %DPx or EQx,Px = dQx/dPx . Px/Qx is classified into three categories, according to its magnitude: • Elastic (sensitive demand): | EQx,Px | > 1 • Inelastic (insensitive demand): | EQx,Px | < 1 • Unit elastic: | EQx,Px | = 1 BA 445 Lesson A.3 Elasticity 14 Elasticity and Revenue Elasticity and Revenue BA 445 Lesson A.3 Elasticity 15 Elasticity and Revenue 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 16 Elasticity and Revenue 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. Price Price Setting Quantity Setting Price Demand P P Q Quantity Q BA 445 Lesson A.3 Elasticity Demand Quantity 17 Elasticity and Revenue First, consider firms that choose price. Predicting revenue change from a price change follows the formula DR = Rx(1+EQx,Px) . %DPx where DR is the change in revenue Rx is the initial revenue from good X EQx,Px is the own price elasticity of demand for good X %DPx is the change in the price Px of good X expressed as a fraction. BA 445 Lesson A.3 Elasticity 18 Elasticity and Revenue 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 DR = Rx(1+EQx,Px) . %DPx implies revenue changes DR = ($100(1-0.5)) . (0.10) = $5 That is, revenue increases $5. BA 445 Lesson A.3 Elasticity 19 Elasticity and Revenue When demand is inelastic, revenue moves in the same direction of a change in price. DR = Rx(1+EQx,Px) . %DPx • When demand is inelastic, |EQx,Px| < 1 EQ ,P > -1, so 1+ EQ ,P > 0, so if price increases, x x x x %DP > 0 and DR > 0. Increased price implies increased total revenue. 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 20 Elasticity and Revenue When demand is elastic, revenue moves in the opposite direction of a change in price. DR = Rx(1+EQx,Px) . %DPx • When demand is elastic, |EQx,Px| > 1 EQ ,P < -1, so 1+ EQ ,P < 0, so if price increases, x x x x %DP > 0 and DR < 0. Increased price implies decreased total revenue. 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 21 Elasticity and Revenue 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 increases Price decreases because of the law of demand. So, revenue increases since revenue and price move in opposite directions. Marginal revenue MR is the change in revenue as quantity increases, so MR < 0 • When demand is elastic, as quantity increases Price decreases. Revenue decreases. Marginal revenue is positive. • When demand is unit elastic, marginal revenue is 0 BA 445 Lesson A.3 Elasticity 22 Elasticity and Revenue Graphing elasticity and revenue when demand is linear P 100 TR 0 10 20 30 40 50 Q 0 BA 445 Lesson A.3 Elasticity Q 23 Elasticity and Revenue Graphing elasticity and revenue when demand is linear P 100 TR 80 800 0 10 20 30 40 50 Q 0 10 BA 445 Lesson A.3 Elasticity 20 30 40 50 Q 24 Elasticity and Revenue Graphing elasticity and revenue when demand is linear P 100 TR 80 1200 60 800 0 10 20 30 40 50 Q 0 10 BA 445 Lesson A.3 Elasticity 20 30 40 50 Q 25 Elasticity and Revenue Graphing elasticity and revenue when demand is linear P 100 TR 80 1200 60 40 800 0 10 20 30 40 50 Q 0 10 BA 445 Lesson A.3 Elasticity 20 30 40 50 Q 26 Elasticity and Revenue Graphing elasticity and revenue when demand is linear P 100 TR 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 BA 445 Lesson A.3 Elasticity 20 30 40 50 Q 27 Elasticity and Revenue 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). P 100 TR Elastic 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elastic BA 445 Lesson A.3 Elasticity 28 Elasticity and Revenue 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). P 100 TR Elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 20 Elastic BA 445 Lesson A.3 Elasticity 30 40 50 Q Inelastic 29 Elasticity and Revenue Unit elasticity divides elasticity from inelasticity. P 100 TR Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 20 Elastic BA 445 Lesson A.3 Elasticity 30 40 50 Q Inelastic 30 Elasticity and Revenue 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. P 100 TR Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 20 Elastic BA 445 Lesson A.3 Elasticity 30 40 50 Q Inelastic 31 Elasticity and Revenue P 100 Elastic 80 60 40 20 0 10 20 For any linear inverse demand function, P(Q) = a - bQ, then MR(Q) = a - 2bQ. So, Unit elastic • MR > 0, where demand is elastic Inelastic • MR = 0, where demand is unit elastic • MR < 0, where demand is inelastic 40 50 Q MR BA 445 Lesson A.3 Elasticity 32 Elasticity and Revenue Example: To maximize revenue when demand is Q = 12 – 0.2 P, first invert demand, to TR 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. Unit elastic Q 0 Elastic BA 445 Lesson A.3 Elasticity Inelastic 33 Cross Elasticity Cross Elasticity BA 445 Lesson A.3 Elasticity 34 Cross Elasticity 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 35 Cross Elasticity Cross Price Elasticity of Demand is defined like own price elasticity EQx,Py = %DQx / %DPy or EQx,Py = dQx/dPy . Px/Qy Unlike the negative own price elasticity EQx,Px < 0, cross price elasticity can be positive or negative, depending on how good relate. If EQx,Py > 0, then X and Y are (gross) substitutes. If EQx,Py < 0, then X and Y are (gross) complements. BA 445 Lesson A.3 Elasticity 36 Cross Elasticity Predicting revenue change from a price change follows the formula for multiple products DR = (Rx(1+EQx,Px) + RyEQy,Px) . %DPx where DR is the change in revenue from the two products Rx is the initial revenue from good X EQx,Px is the own price elasticity of demand for good X Ry is the initial revenue from good Y EQy,Px is the cross elasticity of demand for good Y %DPx is the change in the price Px of good X expressed as a fraction. BA 445 Lesson A.3 Elasticity 37 Cross Elasticity For example, suppose You sell only burgers and fries. Current revenue is $100 from burgers, $50 from fries. 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 DR = (Rx(1+EQx,Px) + RyEQy,Px) . %DPx implies revenue changes DR = ($100(1-.5) + $50(-2)) . (0.20) = -$10 That is, revenue decreases $10. BA 445 Lesson A.3 Elasticity 38 Demand Functions Demand Functions BA 445 Lesson A.3 Elasticity 39 Demand Functions 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 40 Demand Functions Interpreting Linear Demand Example: QX = 10 – 2PX + 3PY + 5M • Law of demand holds (coefficient of PX is negative). • X and Y are gross substitutes (coefficient of PY is positive). • X is a normal good (coefficient of income M is positive). BA 445 Lesson A.3 Elasticity 41 Demand Functions Computing Elasticity from Linear Demand Use the derivative definition of elasticity: QX = 10 – 2PX + 3PY + 5M • Own price elasticity (depends on price and quantity): EQx,Px = dQx/dPx . Px/Qx = - 2 Px/Qx • Cross price elasticity (depends on price and quantity): EQx,Py = dQx/dPy . Py/Qx = 3 Py/Qx BA 445 Lesson A.3 Elasticity 42 Demand Functions Computing Elasticity from Log-Linear Demand Use the derivative definition of elasticity: ln(QX) = 10 – 2ln(PX) + 3ln(PY) + 5ln(M) • Own price elasticity (not depend on price and quantity): EQx,Px = dQx/dPx . Px/Qx = - 2 • Cross price elasticity (not depend on price and quantity): EQx,Py = dQx/dPy . Py/Qx = 3 BA 445 Lesson A.3 Elasticity 43 Demand Functions Graphs of Linear and Log-Linear Demand Price Price Linear Demand Log Linear Demand Quantity BA 445 Lesson A.3 Elasticity Quantity 44 Summary Summary BA 445 Lesson A.3 Elasticity 45 Summary Applications of Elasticity • Pricing and managing cash flows. • Effect of changes in competitors’ prices. BA 445 Lesson A.3 Elasticity 46 Summary 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 Elasticity 47 Summary 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 Elasticity 48 Summary 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 Elasticity 49 Summary Answer • Calls would increase by 25.92 percent. EQX , PX %DQX 8.64 %DPX d %DQX 8.64 3% d 3% 8.64 %DQX d %DQX 25.92% d BA 445 Lesson A.3 Elasticity 50 Summary 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 Elasticity 51 Summary Answer • AT&T’s demand would fall by 36.24 percent. EQX , PY %DQX 9.06 %DPY d %DQX 9.06 4% d 4% 9.06 %DQX d %DQX 36.24% d BA 445 Lesson A.3 Elasticity 52 Review Questions 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. BA 445 Lesson A.3 Elasticity 53 BA 445 Managerial Economics End of Lesson A.3 BA 445 Lesson A.3 Elasticity 54