Me11e 05

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Me11e 05

  1. 1. CHAPTER4—DEMAND ELASTICITY MULTIPLE CHOICE1. Point elasticity measures elasticity: a. over a given range of a function.b.at a spot on a function.c.over a given range along a function.d.before non-price effects. ANS: B Arc elasticity is measured: a.over a given range of a function.b.at a spot on a function.c.over a given range along a function.d.before non-price effects. ANS: C With elastic demand, a price increase will: a.decrease marginal revenue.b.decrease total revenue.c.increase total revenue.d.decrease marginal revenue and total revenue. ANS: B With unitary elasticity of demand, a price increase will: a.be associated with zero marginal revenue.b.decrease total revenue.c.increase total revenue.d.decrease marginal and total revenue. ANS: A With inelastic demand, a price increase produces: a.a less than proportionate decline in quantity demanded.b.lower total revenue.c.lower marginal revenue.d.lower marginal and total revenue. ANS: A With inelastic demand, a price increase produces: a.higher profits.b.lower profits.c.lower marginal revenue.d.lower total revenue. ANS: A A direct relation exists between the price of one product and the demand for: a.complements.b.substitutes.c.normal goods.d.inferior goods. ANS: B The demand for a product tends to be inelastic if: a.it is expensive.b.a small proportion of consumers income is spent on the good.c.consumers are quick to respond to price changes.d.it has many substitutes. ANS: B Two products are complements if the: a.cross-price elasticity of demand is less than zero.b.cross-price elasticity of demand equals zero.c.cross-price elasticity of demand is greater than zero.d.price elasticity of demand for each good is greater than zero. ANS: A
  2. 2. If the income elasticity of demand for a good is greater than one, the good is:a.a noncyclical normal good.b.a cyclical normal good.c.neither a normal nor an inferiorgood.d.an inferior good.ANS: BA product that enjoys rapidly growing demand over time is likely to be:a.a noncyclical normal good.b.a cyclical normal good.c.neither a normal nor an inferiorgood.d.an inferior good.ANS: BThe point advertising elasticity reveals the:a.percentage change in demand following a change in advertising.b.percentage change inthe quantity demanded following a change in advertising.c.percentage change inadvertising following a change in the quantity demanded.d.percentage change inadvertising following a change in demand.ANS: AWhen the product demand curve is Q = 140 - 10P, and price is decreased from P 1 = $10 toP2 = $9, the arc price elasticity of demand is:a.-0.1b.-3c.-4d.-10ANS: BIf the point price elasticity of demand equals -2 and the marginal cost per unit is $5, theoptimal price is:a.$5b.$10c.$2d.impossible to determine without further information.ANS: BThe concept of cross-price elasticity is used to examine the responsiveness of demand:a.to changes in income.b.for one product to changes in the price of another.c.to changes in"own" price.d.to changes in income.ANS: BWhen the cross-price elasticity εPX = 3:a.demand rises by 3% with a 1% increase in the price of X.b.the quantity demanded risesby 3% with a 1% increase in the price of X.c.the quantity demanded rises by 1% with a3% increase in the price of X.d.demand rises by 1% with a 3% increase in the price of X.ANS: AGoods for which εI > 1 are often referred to as:a.cyclical normal goods.b.noncyclical normal goods.c.being relatively unaffected bychanging income.d.inferior goods.ANS: AIf εP = -3 and MC = $0.66, the profit-maximizing price is:a.$3b.$0.99c.$0.66d.$1.98ANS: B
  3. 3. In demand analysis, endogenous variables include:a.the weather.b.consumer incomes.c.interest rates.d.company advertising.ANS: DIn demand analysis, factors within the control of the firm are called:a.independent variables.b.exogenous variables.c.endogenous variables.d.nonrandomvariables.ANS: CArc elasticity:a.gives accurate estimates of the effect on Y of very small (less than 5%) changes inX.b.varies at different points along a function.c.measures the effect on a dependentvariable Y of a marginal change in an independent variable X.d.measures the effect ofchange in a dependent variable Y of more than a marginal amount on an independentvariable X.ANS: BIn terms of advertising, the expected change in demand following a one-unit ($1,000)change in advertising is:a.∂A/∂Qb.∂Q/∂Ac.εAd.εPANS: BWith elastic demand:a.a given percentage increase in price causes quantity to decrease by a larger percentage.b.|εP| > 1 and the relative change in quantity is smaller than the relative change in price.c.aprice increase raises total revenued.A price decrease causes total revenues to fall.ANS: AWhen marginal cost is greater than zero, the profit-maximizing point price elasticity ofdemand must be:a.greater than zero but less than one.b.equal to one.c.greater than one.d.equal to zero.ANS: CWhen the product demand curve is P = $5 - $0.05Q, and Q = 40, the point price elasticityof demand is:a.-2/3b.-3/2c.-8/3d.-3/8ANS: BPROBLEMElasticity. The demand for mini cassette players can be characterized by the followingpoint elasticities: price elasticity = -2, cross-price elasticity with AA Alkaline batteries =-1.5, and income elasticity = 3. Indicate whether each of the following statements is true orfalse, and explain your answer.A.A price increase for cassette players will decrease both the number of units demandedand the total revenue of sellers.B.The cross-price elasticity indicates that a 2% reduction inthe price of cassette players will cause a 3% increase in battery demand.C.Demand for
  4. 4. cassette players is price elastic and they are cyclical normal goods.D.Falling battery priceswill definitely increase revenues received by sellers of both cassette players andbatteries.E.A 3% price reduction in cassette players would be necessary to overcome theeffects of a 2% decline in income.ANS:A.True. A price increase will always decrease units sold, given a downward slopingdemand curve. The negative sign on the price elasticity indicates that this is indeed thecase here. The fact that price elasticity equals -2 indicates that demand is elastic withrespect to price, and therefore that a price increase will also decrease totalrevenues.B.False. The cross-price elasticity indicates that a 2% decrease in the price ofbatteries will have the effect of increasing cassette player demand by 3%.C.True. Demandis price elastic (see part a). Because the income elasticity is positive, cassette players are anormal good. Moreover, because the income elasticity is greater than one, cassette playerdemand is also cyclical.D.False. A negative cross-price elasticity indicates that cassetteplayers and batteries are compliments. Therefore, falling battery prices will increase thedemand for cassette players and resulting revenues for sellers. However, we have noinformation concerning the price elasticity of demand for batteries, and therefore do notknow the effect of falling battery prices on battery revenues.E.True. A 3% reduction inprice will cause a 6% increase in the quantity of cassette players demanded. A 2% declinein income will cause a 6% fall in demand. These changes will be mutually offsetting.Elasticity. The demand for Penns Oil motor oil can be characterized by the followingpoint elasticities: price elasticity = -2.5, cross-price elasticity with Value Lean motor oil =1.5, and income elasticity = 0.75. Indicate whether each of the following statements is trueor false, and explain your answer.A.A price increase for Penns Oil will decrease both the number of units demanded and thetotal revenue of sellers.B.The cross-price elasticity indicates that a 2% increase in theprice of Value Lean will cause a 3% increase in Penns Oil demand.C.Demand for PennsOil is price elastic and the motor oil is a cyclical, normal good.D.Falling Value Lean priceswill definitely increase revenues received by manufacturers of both brands of oil.E.A 0.9%price reduction for Penns Oil would be necessary to overcome the effects of a 3% declinein income.ANS:A.True. A price increase will always decrease units sold, given a downward slopingdemand curve. The negative sign on the price elasticity indicates that this is indeed thecase here. The fact that price elasticity equals -2.5 indicates that demand is elastic withrespect to price, and therefore that a price increase will also decrease totalrevenues.B.True. The positive cross-price elasticity indicates that a 2% increase in theprice of the substitute good Value Lean will have the effect of increasing Penns Oilsdemand by 3%.C.False. Demand is price elastic (see part a). Because the income elasticityis positive, Penns Oil is a normal good. However, because the income elasticity is lessthan one, Penns Oil demand is not cyclical.D.False. A positive cross-price elasticityindicates that the two motor oils are substitutes. Therefore, falling Value Lean prices willdecrease the demand for Penns Oil and resulting revenues for its manufacturers. However,we have no information concerning the own price elasticity of demand for Value Lean, andtherefore do not know the effect of falling prices on its revenues.E.True. A 0.9% reductionin price will cause a 2.25% increase in the quantity of Penns Oil demanded. A 3% declinein income will cause a 2.25% fall in demand. These changes will be mutually offsetting.
  5. 5. Demand Analysis. The Crank Yankers DVD (season two) has been a hot seller duringrecent weeks. An analysis of weekly demand shows:Q = 3,000 - 90Pwhere Q is DVD sales and P is price.A.How many DVDs could be sold at a $20 price?B.Calculate the point price elasticity ofdemand at a price of $20.ANS:A.Q = 3,000 - 90P = 3,000 - 90(20) = 1,200B.The point price elasticity of demand at aprice of $20 is calculated as follows: = -90 = -1.5 (elastic)Demand Analysis. The South Park DVD (season three) has been a slow seller duringrecent months. An analysis of monthly demand shows:Q = 5,000 - 160Pwhere Q is DVD sales and P is price.A.How many DVDs could be sold at a $25 price?B.Calculate the point price elasticity ofdemand at a price of $25.ANS:A.Q = 5,000 - 160P = 5,000 - 160(25) = 1,000B.The point price elasticity of demand at aprice of $25 is calculated as follows: = -160 = -4 (elastic)Demand Analysis. The CSI DVD (season four) has been a hot seller during recent weeks.An analysis of weekly demand shows:Q = 15,000 - 500P,where Q is DVD sales and P is price.A.How many DVDs could be sold at a $20 price?B.Calculate the point price elasticity ofdemand at a price of $20.ANS:A.Q = 15,000 - 500P = 15,000 - 500(20) = 5,000B.The point price elasticity of demand ata price of $20 is calculated as follows: = -500 = -2 (elastic)Demand Analysis. KRDY-FM is contemplating a T-shirt advertising promotion. Monthlysales data from T-shirt shops marketing the "Listen to KRDY-FM" design indicate that:Q = 15,000 - 800P,
  6. 6. where Q is T-shirt sales and P is price.A.How many T-shirts could KRDY-FM sell at $15 each?B.What price would KRDY-FMhave to charge to sell 5,000 T-shirts?C.At what price would T-shirt sales equal zero?D.How many T-shirts could be given away?E.Calculate the point price elasticity ofdemand at a price of $15.ANS:A.Q = 15,000 - 800P = 15,000 - 800(15) = 3,000B.Q = 15,000 - 800P5,000 = 15,000 -800P800P = 10,000P = $12.50C.Q = 15,000 - 800P0 = 15,000 - 800P800P = 15,000P =$18.75D.Q = 15,000 - 800PQ = 15,000 - 800(0)Q = 15,000E.The point price elasticity ofdemand at a price of $15 is calculated as follows: = -800 = -4(elastic)Demand Analysis. The San Diego Zoo is contemplating a stuffed panda bear advertisingpromotion. Annualized sales data from local shops marketing the "Cant Bear it WhenYoure Away" bear indicate that:Q = 50,000 - 1,000Pwhere Q is Panda bear sales and P is price.A.How many pandas could the zoo sell at $30 each?B.What price would the zoo have tocharge to sell 25,000 pandas?C.At what price would panda sales equal zero?D.How manybears could be given away?E.Calculate the point price elasticity of demand at a price of$10.ANS:A.Q = 50,000 - 1,000P = 50,000 - 1,000(30) = 20,000B.Q = 50,000 - 1,000P25,000 =50,000 - 1,000P1,000P = 25,000P = $25C.Q = 50,000 - 1,000P0 = 50,000 - 1,000P1,000P= 50,000P = $50D.Q = 50,000 - 1,000PQ = 50,000 - 1,000(0)Q = 50,000E.The point priceelasticity of demand at a price of $30 is calculated as follows: = -1,000 = -1.5 (elastic)Demand Analysis. Robert E. Lee Grade School is contemplating a chocolate bar fundraiser. Weekly sales data from Mrs. Grants fifth grade class indicate that:Q = 4,000 - 1,000P,where Q is chocolate bar sales and P is price.A.How many chocolate bars could be sold at $2 each?B.What price would have to becharged to sell 2,500 chocolate bars?C.At what price would sales equal zero?D.How manychocolate bars could be given away?E.Calculate the point price elasticity of demand at aprice of $2.
  7. 7. ANS:A.Q = 4,000 - 1,000P = 4,000 - 1,000(2) = 2,000B.Q = 4,000 - 1,000P2,500 = 4,000 -1,000P1,000P = 1,500P = $1.50C.Q = 4,000 - 1,000P0 = 4,000 - 1,000P1,000P = 4,000P =$4D.Q = 4,000 - 1,000PQ = 4,000 - 1,000(0)Q = 4,000E.The point price elasticity ofdemand at a price of $2 is calculated as follows: = -1,000 = -1(unitary elastic)Demand Analysis. Aspen, Colorado is engaging in a bumper-sticker advertisingcampaign. Monthly sales data from ski shops selling the "Dont Worry-Be Happy (inAspen)" bumper-stickers indicate that:Q = 6,000 - 2,000Pwhere Q is bumper-sticker sales and P is price.A.How many bumper-stickers could Aspen sell at $2 each?B.What price would Aspenhave to charge to sell 5,000 bumper-stickers?C.At what price would bumper-sticker salesequal zero?D.How many bumper-stickers could be given away?E.Calculate the point priceelasticity of demand at a price of $1.ANS:A.Q = 6,000 - 2,000P= 6,000 - 2,000(2)= 2,000B.Q = 6,000 - 2,000P5,000 = 6,000 -2,000P2,000P = 1,000P = $0.50C.Q = 6,000 - 2,000P0 = 6,000 - 2,000P2,000P = 6,000P =$3D.Q = 6,000 - 2,000PQ = 6,000 - 2,000(0)Q = 6,000E.The point price elasticity ofdemand at a price of $2 is calculated as follows: = -2,000 = -2(elastic)Optimal Price. Last week, Discount Food Stores, Inc. reduced the average price on the 22ounce size of Dishwashing Liquid by 1%. In response, sales jumped by 8%.A.Calculate the point price elasticity of demand for Dishwashing Liquid.B.Calculate theoptimal price for Dishwashing Liquid if marginal cost is 70¢ per unit.ANS:A. = = -8 (elastic)B.The optimal price isfound setting MC = MR and solving for P where:MC = MR = P 0.7 = P0.7 = 0.875PP = 0.8 or 80¢Optimal Price. Last week, Wallys Burgers, Inc. reduced the average price on the 1/2-pound Papa burger by 1%. In response, sales jumped by 2%.A.Calculate the point price elasticity of demand for Papa burgers.B.Calculate the optimalprice for Papa burgers if marginal cost is $1 per unit.
  8. 8. ANS:A. = = -2 (elastic)B.The optimal price isfound setting MC = MR and solving for P where:MC = MR = P $1.00 = P $1.00 = 0.50PP = $2Optimal Price. Last month, Forest Lumber, Inc. reduced the average price on the eight-foot pine 2×4s by 1%. In response, sales jumped by 4%.A.Calculate the point price elasticity of demand for eight-foot 2×4s.B.Calculate theoptimal price for eight-foot 2×4s if marginal cost is $1.50 per unit.ANS:A. = = -4 (elastic)B.The optimal price isfound setting MC = MR and solving for P where:MC = MR = P $1.50 = P $1.50 = 0.75PP = $2Optimal Price. Last month, Ricks Bike Shop, Inc. increased the price on the 24 ouncecan of bearing grease by 1%. In response, sales dropped by 4%.A.Calculate the point price elasticity of demand for bearing grease.B.Calculate the optimalprice for bearing grease if marginal cost is $4.50 per unit.ANS:A. = = -4 (elastic)B.The optimal price isfound setting MC = MR and solving for P where:MC = MR = P $4.50 = P $4.50 = 0.75PP = $6Arc Price Elasticity. Assume that amazon.com dropped the price on a mens Seiko watch(SGF719) from $120 to $60, and sales jumped from 50 to 100 units per day.A.Calculate the implied arc price elasticity of demand.B.Is a further price decreasewarranted? Why or why not?ANS:
  9. 9. A. = = -1B.No further price decrease iswarranted. At P = $60, the EP = -1. This means that $60 is the revenue-maximizing priceand any further decrease in price would cause demand to fall into the inelastic region ofthe demand curve. In the inelastic region of the demand curve prices are too low becauseboth revenues and profits would rise with an increase in price.Arc Price Elasticity. Assume that amazon.com cut the price on a 1.10ct Princess CutDiamond Solitaire engagement ring from $4,500 to $2,500, and sales rose from 50 to 75units per week.A.Calculate the implied arc price elasticity of demand.B.Is a further price decreasewarranted? Why or why not?ANS:A. = = -0.7B.No further pricedecrease is warranted. At P = $2,500, the EP = -0.7. This means that demand is already inthe price inelastic region, and any further decrease in price would cause demand to fallfurther into the inelastic region of the demand curve. In the inelastic region of the demandcurve, prices are too low because revenues and profits would rise with an increase in price.Price should be increased.Arc Income Elasticity. Glenco Motors sells an average of 20 Toyota Camry XLE four-door sedans per month. Evanston Toyota sells twice as many. Based upon data obtained inthe financing process, Glenco customers earn an average household income of $100,000per year, while Evanston customers earn $125,000 per year.A.Calculate the implied arc income elasticity of demand.B.How would you characterizedemand for these Toyota Camrys?ANS:A. = = 3B.ToyotaCamry XLE four-door sedans appear to be cyclical normal goods. Goods for which 0 < εI< 1 are referred to as noncyclical normal goods, because demand is relatively unaffectedby changing income. Sales of most convenience goods, such as toothpaste, candy, soda,and movie tickets, account for only a small share of the consumers overall budget, andspending on such items tends to be relatively unaffected by changing economic conditions.For goods having εI > 1, referred to as cyclical normal goods, demand is strongly affectedby changing economic conditions. Purchase of "big ticket" items such as homes,automobiles, boats, and recreational vehicles can be postponed and tend to be put off byconsumers during economic downturns.Cross-Price Elasticity. During the past year, the average price of lots along LakeMichigan in Carol Beach rose from $2,500 to $3,000 per foot of lakefront. At the sametime, sales of new homes located off the Lake rose from 40 to 70 units.
  10. 10. A.Calculate the implied cross-price elasticity of demand.B.Are lakefront lots and newhomes complements or substitutes? Why?ANS:A. = = 3B.A direct relationbetween the price of one product and the demand for a second product holds for allsubstitutes. A price increase for a given product will increase demand for substitutes; aprice decrease for a given product will decrease demand for substitutes. In this case, newhomes and lakefront property appear to be substitute goods.Elasticity Analysis. Bloomingtons, Inc. is a retailer of distinctive clothing. At the end ofthe companys fiscal year, you have been asked to evaluate sales of traditional wool suitsand classic blazers using the following data: Month Number of Suits Sold, QSuit Advertising Expenditures A Suit Price P Blazer PricePBJuly400$50,000$700$350August50050,000650350September70055,000650350October 90055,000650450November1,00065,000700450December60065,000700350January5006 0,000800350February70060,000700350March80060,000650300April90063,000600300M ay70057,000600300June50057,000750300In particular, you have been asked to estimate relevant demand elasticities. Remember thatin order to estimate the required elasticities, you should only consider months when theother important factors considered above have not changed. Note also that by restrictingyour analysis to consecutive months, changes in any additional factors not explicitlyincluded in the analysis are less likely to affect estimated elasticities. Finally, the averagearc elasticity of demand for each factor is simply the average of monthly elasticitiescalculated over the past year.A.Indicate whether there was a change or no change in each respective variable for eachmonth-pair during the past year. Month-PairSuit Advertising Expentitures A Suit Price
  11. 11. P Blazer Price PBJuly-Aug.______________________________Aug.- Sept.______________________________Sept- Oct.______________________________Oct.- Nov.______________________________Nov.- Dec.______________________________Dec.- Jan.______________________________Jan.- Feb.______________________________Feb.- March______________________________March- April______________________________April- May______________________________May- June______________________________B.Calculate and interpret the average arc advertising elasticity of demand for suits.C.Calculate and interpret the average arc price elasticity of demand for suits.D.Calculate and interpret the average arc cross-price elasticity of demand between suits and blazers.ANS:A. Month-PairSuit Advertising Expentitures, A Suit Price P Blazer Price,PBJuly-Aug.No change.Change.No change.Aug.-Sept.Change.No change.No change.Sept-Oct.No change.No change.Change.Oct.-Nov.Change.Change.No change.Nov.-Dec.Nochange.No change.Change.Dec.-Jan.Change.Change.No change.Jan.-Feb.Nochange.Change.No change.Feb.-MarchNo change.Change.Change.March-AprilChange.Change.No change.April-MayChange.No change.No change.May-JuneNochange.Change.No change.B.In the calculation of the arc advertising elasticity of demand, only consider consecutivemonths when there was a change in advertising but no change in the prices of suits andblazers:Aug.-Sept. = =3.5April-May = = 2.5Onaverage, EA = (3.5 + 2.5)/2 = 3 and demand will rise 3%, with a 1% increase inadvertising. Thus, demand appears quite sensitive to advertising.C.In the calculation of the arc price elasticity of demand only consider consecutive monthswhen there was a change in the price of suits, but not a change in advertising nor the priceof blazers:July-Aug. = = -3Jan.-Feb.
  12. 12. = = -2.5May-June= = -1.5On average, EP = [(-3) + (-2.5) + (-1.5)]/3 = -2.33. A1% increase (decrease) in price will head to a 2.33% decrease (increase) in the quantitydemanded. The demand for suits is, therefore, elastic with respect to price.D.In the calculation of the arc cross-price elasticity of demand only consider consecutivemonths when there was a change in the price of blazers, but no change in advertising northe price of suits:Sept.-Oct. = =1Nov.-Dec. = = 2On average, EPX =(1 + 2)/2 = 1.5. Because EPX > 0, suits and dress blazers are substitutes.Elasticity Analysis. Almost Famous Footwear, Inc., is a retailer of bargain-priced shoes.At the end of the companys fiscal year, you have been asked to evaluate sales of itstraditional business wing-tip and loafer dress shoes using the following data: MonthPairs of Wing-Tips Sold QWing-Tip Advertising Expenditures A Wing-Tips Price P Loafer Price PLJuly30,000$100,000$110$70August50,000100,0009070September60,000120,0009070 October100,000120,0009090November120,000140,00010090December80,000140,00010 070January45,000125,00012070February75,000125,00010070March85,000125,0009060 April105,000130,0008060May75,000110,0008060June45,000110,00012060In particular, you have been asked to estimate relevant demand elasticities. Remember thatin order to estimate the required elasticities, you should only consider months when theother important factors considered above have not changed. Note also that by restrictingyour analysis to consecutive months, changes in any additional factors not explicitlyincluded in the analysis are less likely to affect estimated elasticities. Finally, the averagearc elasticity of demand for each factor is simply the average of monthly elasticitiescalculated over the past year.A.Indicate whether there was a change or no change in each respective variable for eachmonth-pair during the past year. Month-PairWing-Tip
  13. 13. Advertising Expentitures A Wing-Tip Price P Loafer Price PBJuly-Aug.______________________________Aug.- Sept.______________________________Sept- Oct.______________________________Oct.- Nov.______________________________Nov.- Dec.______________________________Dec.- Jan.______________________________Jan.- Feb.______________________________Feb.- March______________________________March- April______________________________April- May______________________________May- June______________________________B.Calculate and interpret the average arc advertising elasticity of demand for wing-tips.C.Calculate and interpret the average arc price elasticity of demand for wing-tips.D.Calculate and interpret the average arc cross- price elasticity of demand between wing-tips and loafers.ANS:A. Month-PairWing-Tip Advertising Expentitures A Wing-Tip Price P Loafer PricePBJuly-Aug.No change.Change.No change.Aug.-Sept.Change.No change.No change.Sept-Oct.No change.No change.Change.Oct.-Nov.Change.Change.No change.Nov.-Dec.Nochange.No change.Change.Dec.-Jan.Change.Change.No change.Jan.-Feb.Nochange.Change.No change.Feb.-MarchNo change.Change.Change.March-AprilChange.Change.No change.April-MayChange.No change.No change.May-JuneNochange.Change.No change.B.In the calculation of the arc advertising elasticity of demand,only consider consecutive months when there was a change in advertising but no changein the prices of wing-tips and loafers:Aug.-Sept. = = 1April-May = = 2On average, EA = (1 + 2)/2 = 1.5 anddemand will rise 1.5%, with a 1% increase in advertising. Thus, demand appears sensitive
  14. 14. to advertising.C.In the calculation of the arc price elasticity of demand only considerconsecutive months when there was a change in the price of wing-tips, but no change inadvertising and the price of loafers:July-Aug. = = -2.5Jan.-Feb. = = -2.75May-June = = -1.25On average, EP = [(-2.5) + (-2.75) + (-1.25)]/3= -2.17. A 1% increase (decrease) in price will lead to a 2.17% decrease (increase) in thequantity demanded. The demand for wing-tips is, therefore, elastic with respect toprice.D.In the calculation of the arc cross-price elasticity of demand only considerconsecutive months when there was a change in the price of loafers, but no change inadvertising nor the price of wing-tips:Sept.-Oct. = = 2Nov.-Dec. = = 1.6On average, EPX = (2 + 1.6)/2 = 1.8. BecauseEPX > 0, wing-tips and loafers are substitutes.Income Elasticity. Deluxe Carpeting, Inc., is a leading manufacturer of stain-resistantcarpeting. Demand for Deluxe products is tied to the overall pace of building andremodeling activity and, therefore, is sensitive to changes in national income. The carpetmanufacturing industry is highly competitive, so Deluxes demand is also very price-sensitive.During the past year, Deluxe sold 28 million square yards (units) of carpeting at anaverage wholesale price of $16 per unit. This year, GNP per capita is expected to fall from$19,000 to $17,000 as the nation enters a steep recession. Without any price change,Deluxe expects current-year sales to fall to 20 million units.A.Calculate the implied arc income elasticity of demand.B.Given the projected fall inincome, the sales manager believes that current volume of 28 million units could only bemaintained with a price cut of $2 per unit. On this basis, calculate the implied arc priceelasticity of demand.C.Holding all else equal, would a further increase in price result inhigher or lower total revenue?ANS:A. = = 3B.Without a pricedecrease, sales this year would total 20 million units. Therefore, it is appropriate toestimate the arc price elasticity from a (before-price-decrease) base of 20 million units: = = -2.5 (elastic)C.Lower. Because carpet
  15. 15. demand is in the elastic range, EP = -2.5, an increase (decrease) in price will result in lower(higher) total revenues.Income Elasticity. The Electronics Warehouse, Inc. is a leading retailer of home theatersystems. Demand for home theater systems is sensitive to changes in national income.Electronics retailing is highly competitive, so retail demand for home theater systems isalso very price-sensitive. During the past year, the Electronics Warehouse sold 550,000home theater systems at an average retail price of $4,000 per unit. This year, GDP perhousehold is expected to fall from $58,800 to $53,200 as the nation enters a steeprecession. Without any price change, the Electronics Warehouse expects current-year salesto fall to 450,000 units.A.Calculate the implied arc income elasticity of demand.B.Given the projected fall inincome, the sales manager believes that current volume of 550,000 units could only bemaintained with a price cut of $500 per unit. On this basis, calculate the implied arc priceelasticity of demand.C.Holding all else equal, would a further increase in price result inhigher or lower total revenue?ANS:A. = = 2B.Without a pricedecrease, sales this year would total 450,000 units. Therefore, it is appropriate to estimatethe arc price elasticity from a (before-price-decrease) base of 450,000 units: = = -1.5 (elastic)C.Lower.Because personal computer demand is in the elastic range, E P = -1.5, an increase(decrease) in price will result in lower (higher) total revenues.Income Elasticity. CarZone, Inc., is a leading retailer of replacement car parts andaccessories. Demand for replacement car parts and accessories is tied to the overall paceof new car sales and, therefore, is sensitive to changes in national income. Thereplacement car parts and accessories industry is also very price sensitive. During the pastyear, CarZone sold 150,000 pairs of brake shoes at an average wholesale price of $13 perpair. This year, per capita income is expected to fall from $33,600 to $30,400 as the nationenters a steep recession. Without any price change, CarZone expects current-year sales tofall to 100,000 units.A.Calculate the implied arc income elasticity of demand.B.Given the projected fall inincome, the sales manager believes the current volume of 150,000 units could only bemaintained with a price cut of $1 per unit. On this basis, calculate the implied arc priceelasticity of demand.C.Holding all else equal, would a further increase in price result inhigher or lower total revenue?ANS:A. = = 4B.Without a pricedecrease, sales this year would total 100,000 units. Therefore, it is appropriate to estimatethe arc price elasticity from a (before-price-decrease) base of 100,000 units:
  16. 16. = -5 (elastic)C.Lower.Because brake shoe demand is in the elastic range, E P = -5, an increase (decrease) in pricewill result in lower (higher) total revenues.Income Elasticity. Environmental Interiors, Inc. is a leading distributor of potted plantsand their maintenance for business environments. Demand for Environmental Interiorservices is tied to the overall pace of business activity and, therefore, is sensitive tochanges in national income. The greenery service sector is highly competitive, soEnvironmental Interiors demand is also very price-sensitive. During the past year,Environmental Interiors sold 10,500 potted plants at an average wholesale price of $25 perplant. This year, per capita income is expected to fall from $34,200 to $30,600 as thenation enters a steep recession. Without any price change, Interiors expects current-yearsales to fall to 7,500 potted plants.A.Calculate the implied arc income elasticity of demand.B.Given the projected fall inincome, the sales manager believes the current volume of 10,500 plants could only bemaintained with a price cut of $5 per unit. On this basis, calculate the implied arc priceelasticity of demand.C.Holding all else equal, would a further increase in price result inhigher or lower total revenue?ANS:A. = = 3B.Without a pricedecrease, sales this year would total 7,500 plants. Therefore, it is appropriate to estimatethe arc price elasticity from a (before-price-decrease) base of 7,500 plants: = = -1.5 (elastic)C.Lower.Because potted plant demand is in the elastic range, EP = -1.5, an increase (decrease) inprice will result in lower (higher) total revenues.Price Elasticity. Z-Best Pizza recently decided to raise its regular price on medium pizzasfrom $9 to $12 following increases in the costs of labor and materials. Unfortunately, salesdropped sharply from 8,100 to 4,500 pizzas per month. In an effort to regain lost sales, Z-Best ran a coupon promotion featuring $5 off the new regular price. Coupon printing anddistribution costs totaled $100, and caused only a modest increase in the typicaladvertising budget of $2,400 per month. The promotion was judged a success as it provedhighly popular with consumers. In the period prior to expiration, coupons were used on40% of all purchases and monthly sales rose to 7,500 pizzas.A.Calculate the arc price elasticity implied by the initial response to Z-Bests priceincrease.B.Calculate the effective price reduction resulting from the couponpromotion.C.In light of this price reduction, and assuming no change in the price elasticityof demand, calculate Z-Bests arc advertising elasticity.D.Why might the true arcadvertising elasticity differ from that calculated in Part C?ANS:
  17. 17. A. = = -2B.The effective pricereduction is $2, because when X percent of sales are accompanied by a coupon:∆P = -$5(0.4) = -$2orP2 = $12 - $5X = $12 - $5(0.4) = $10∆P = $10 - $12 = -$2C.In order to calculate the arc advertising elasticity, the effect of the $2 price cut implicitin the coupon promotion must first be reflected. With just a price cut, the quantitydemanded would rise to 6,500, because: -2 = -2 = -2(Q* + 4,500) = -11(Q* - 4,500)-2Q* -9,000 = -11Q* + 49,5009Q* = 58,500Q* = 6,500Then, the arc advertising elasticity can becalculated as: = = 3.5D.It is important to recognize that a coupon promotion can involve more than just theindependent effects of a price cut plus advertising as is implied in part C. Synergistic orinteractive effects may increase advertising effectiveness when the promotion isaccompanied by a price cut. Similarly, price reductions can have a much larger impactwhen advertised. In addition, a coupon is a price cut for only the most price sensitive(coupon-using) customers, and may spur sales by much more than a dollar equivalentacross-the-board price cut.Synergy between advertising and the implicit price reductionwhich accompanies a coupon promotion can cause the estimate in part C to overstate thetrue advertising elasticity. Similarly, this advertising elasticity will be overstated to theextent that targeted price cuts have a bigger influence on the quantity demanded thansimilar across-the-board price reductions (as seems likely).Price and Advertising Elasticity. EZ Auto Wash recently decided to raise its regular priceon wash and wax cycles from $5 to $7 following increases in the costs of equipment andmaterials. Unfortunately, sales dropped sharply from 6,000 to 2,000 washes per month. Inan effort to regain lost sales, EZ ran a coupon promotion featuring $4 off the new regularprice. Coupon printing and distribution costs totaled $100, and caused only a modestincrease in the typical advertising budget of $1,650 per month. The promotion was judgeda success as it proved highly popular with consumers. In the period prior to expiration,coupons were used on 25% of all purchases and monthly sales rose to 3,600 washes.A.Calculate the arc price elasticity implied by the initial response to EZs priceincrease.B.Calculate the effective price reduction resulting from the couponpromotion.C.In light of this price reduction, and assuming no change in the price elasticityof demand, calculate EZs arc advertising elasticity.D.Why might the true arc advertisingelasticity differ from that calculated in part C?ANS:A. = = -3B.The effective pricereduction is $1, because when X percent of sales are accompanied by a coupon:∆P = -$4(0.25) = -$1orP2 = $7 - $4X = $7 - $4(0.25) = $6∆P = $6 - $7 = -$1C.To calculate thearc advertising elasticity, the effect of the $1 price cut implicit in the coupon promotionmust first be reflected. With just a price cut, the quantity demanded would rise to 3,200,
  18. 18. because: -3 = -3 = -3(Q* + 2,000) = -13(Q* - 2,000)-3Q* - 6,000 = -13Q* + 26,00010Q* = 32,000Q* =3,200Then, the arc advertising elasticity can be calculated as:= = 2D.It is important to recognize that a couponpromotion can involve more than just the independent effects of a price cut plusadvertising as is implied in part C. Synergistic or interactive effects may increaseadvertising effectiveness when the promotion is accompanied by a price cut. Similarly,price reductions can have a much larger impact when advertised. In addition, a coupon is aprice cut for only the most price sensitive (coupon-using) customers, and may spur salesby much more than a dollar equivalent across-the-board price cut.Synergy betweenadvertising and the implicit price reduction which accompanies a coupon promotion cancause the estimate in part C to overstate the true advertising elasticity. Similarly, thisadvertising elasticity will be overstated to the extent that targeted price cuts have a biggerinfluence on the quantity demanded than similar across-the-board price reductions (asseems likely).

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