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Readings

Readings. Readings. Baye 6 th edition or 7 th edition, Chapter 3. Overview. Overview. Overview. Own Price Elasticity. Own Price Elasticity. 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.

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Readings

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

  2. Overview • Overview BA 445 Lesson A.3 Elasticity

  3. Overview BA 445 Lesson A.3 Elasticity

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

  5. 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

  6. 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. Perfect Inelasticity Perfect Elasticity Price Price Demand Demand Quantity Quantity BA 445 Lesson A.3 Elasticity

  7. Own Price Elasticity The primary factordetermining 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

  8. 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.) Profitable innovation Unprofitable innovation Price Price iPod Demand Generic Tablet Computer Demand Generic MP3 Player Demand Newton Demand Quantity Quantity BA 445 Lesson A.3 Elasticity

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Elasticity and Revenue • Elasticity and Revenue BA 445 Lesson A.3 Elasticity

  16. 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 elastic but revenue decreases if demand is inelastic. Likewise, when quantity increases, revenue decreases if demand is elastic but revenue increases if demand is inelastic. — So, elasticity affects whether to increase or decrease price or quantity. BA 445 Lesson A.3 Elasticity

  17. 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 Demand P P Quantity Quantity Q Q BA 445 Lesson A.3 Elasticity

  18. 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

  19. 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

  20. 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 • EQx,Px > -1, so 1+EQx,Px > 0, so if price increases, %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

  21. 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 • EQx,Px < -1, so 1+EQx,Px < 0, so if price increases, %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

  22. 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

  23. Elasticity and Revenue Graphing elasticity and revenue when demand is linear P TR 100 30 40 50 Q Q 0 10 20 0 BA 445 Lesson A.3 Elasticity

  24. Elasticity and Revenue Graphing elasticity and revenue when demand is linear P TR 100 80 800 30 40 50 Q Q 0 10 20 10 30 40 50 0 20 BA 445 Lesson A.3 Elasticity

  25. Elasticity and Revenue Graphing elasticity and revenue when demand is linear P TR 100 80 1200 60 800 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 BA 445 Lesson A.3 Elasticity

  26. Elasticity and Revenue Graphing elasticity and revenue when demand is linear P TR 100 80 1200 60 40 800 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 BA 445 Lesson A.3 Elasticity

  27. Elasticity and Revenue Graphing elasticity and revenue when demand is linear P TR 100 80 1200 60 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 BA 445 Lesson A.3 Elasticity

  28. 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 TR 100 Elastic 80 1200 60 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic BA 445 Lesson A.3 Elasticity

  29. 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 TR 100 Elastic 80 1200 60 Inelastic 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic Inelastic BA 445 Lesson A.3 Elasticity

  30. Elasticity and Revenue Unit elasticity divides elasticity from inelasticity. P TR 100 Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic Inelastic BA 445 Lesson A.3 Elasticity

  31. 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 TR 100 Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic Inelastic BA 445 Lesson A.3 Elasticity

  32. Elasticity and Revenue 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 P 100 Elastic Unit elastic 80 60 Inelastic 40 20 Q 40 50 0 10 20 MR BA 445 Lesson A.3 Elasticity

  33. Elasticity and Revenue Example: To maximize revenue when demand is Q = 12 – 0.2 P,first invert demand, to0.2 P = 12 – Q and P = 60 – 5Q.Then, compute marginal revenueMR = 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. TR Unit elastic Q 0 Elastic Inelastic BA 445 Lesson A.3 Elasticity

  34. Cross Elasticity Cross Elasticity BA 445 Lesson A.3 Elasticity

  35. Cross Elasticity OverviewCross 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

  36. Cross Elasticity • Cross Price Elasticity of Demandis 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

  37. 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

  38. 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

  39. Demand Functions • Demand Functions BA 445 Lesson A.3 Elasticity

  40. Demand Functions OverviewDemand 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

  41. 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

  42. 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

  43. 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

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

  45. Summary • Summary BA 445 Lesson A.3 Elasticity

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

  47. 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

  48. 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

  49. 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

  50. Summary • Answer • Calls would increase by 25.92 percent. BA 445 Lesson A.3 Elasticity

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