商务与经济统计习题答案（第8版，中文版）SBE8-SM17

17-1Chapter17IndexNumbersLearningObjectives1.Knowhowtocomputepricerelativesandunderstandhowtheyrepresentpricechangesovertime.2.Knowhowtocomputeaggregatepriceindexesandunderstandhowthechoiceofabaseperiodaffectstheindex.3.BecomefamiliarwiththeConsumerPriceIndex,theProducerPriceIndexandtheDowJonesaverages.4.Learnhowtodeflateatimeseriestomeasurechangesovertimeinconstantdollars.5.Learnhowtocomputeanaggregatequantityindexandhowtointerpretit.Chapter1717-2Solutions:1.a.ItemPriceRelativeA103=(7.75/7.50)B238=(1500/630)b.20017.751500.001507.75I(100)(100)2377.50630.00637.50c.20017.75(1500)1500.00(2)14,625.00I(100)(100)1177.50(1500)630.00(2)12,510.00d.20017.75(1800)1500.00(1)15,450.00I(100)(100)1097.50(1800)630.00(1)14,130.002.a.Fromthepricerelativeweseethepercentageincreasewas32%.b.Dividethecurrentcostbythepricerelativeandmultiplyby100.1990cost=$10.75132(100)=$8.143.a.PriceRelativesA=(6.00/5.45)100=110B=(5.95/5.60)100=106C=(6.20/5.50)100=113b.20016.005.956.20I(100)1105.455.605.50c.20016.00(150)5.95(200)6.20(120)I(100)1095.45(150)5.60(200)5.50(120)9%increaseoverthetwoyearperiod.4.200116.25(35,000)64.00(5,000)10.00(60,000)I(100)10515.00(35,000)60.00(5,000)9.80(60,000)5..19(500)1.80(50)4.20(100)13.20(40)I(100)104.15(500)1.60(50)4.50(100)12.00(40)PaascheindexIndexNumbers17-36.ItemPriceRelativeBasePeriodPriceBasePeriodUsageWeightWeightedPriceRelativesA15022.002044066,000B905.005025022,500C12014.004056067,2001250155,700155,700I12512507.a.PriceRelativesA=(3.95/2.50)100=158B=(9.90/8.75)100=113C=(.95/.99)100=96b.ItemPriceRelativesBasePriceQuantityWeightPi0QiWeightedPriceRelativesA1582.502562.59875B1138.7515131.314837C96.996059.45702253.23041430414I120253.2Costofrawmaterialsisup20%forthechemical.8.StockPriceRelativesBasePriceQuantityWeightWeightedPriceRelativesHoliday11015.505007750852500NYElectric10918.502003700403300KYGas9726.75500133751297375PQSoaps10842.253001267513689003750039220753922075I10537500Portfolioup5%9.ItemPriceRelativesBasePriceQuantityWeightWeightedPriceRelativesBeer10815.0035,000525,00056,700,000Wine10760.005,000300,00032,100,000SoftDrink1029.8060,000588,00059,976,0001,413,000148,776,000148,776,000I1051,413,000Chapter1717-410.a.Deflated1980wages:$7.27(100)$8.8282.4Deflated2000wages:$14.36(100)$8.32172.6b.14.36(100)197.57.27Thepercentageincreaseinactualwagesis97.5%.c.8.32(100)94.38.82Thechangeinreadwagesisadecreaseof5.7%.11.199611.76(100/156.9)=7.49199712.23(100/160.5)=7.62199812.84(100/163.0)=7.88199913.35(100/166.6)=8.01200013.82(100/172.6)=8.018.011.027.88theincreaseinrealwagesandsalariesfrom1998to2000is2%.12.a.19973929(100/160.5)=244819984052(100/163.0)=248619994260(100/166.6)=2557Manufacturers'shipmentsareincreasingslightlyinconstantdollarswhendeflatedusingtheCPI.b.19973929(100/131.8)=298119984052(100/130.7)=310019994260(100/133.0)=3203c.ThePPIisabetterdeflatorsincemanufacturingshipmentsreflectpricespaidbymanufacturers.13.YearRetailSales($)CPIDeflatedRetailSales($)1982380,00096.5393,7821987520,000113.6457,7461992700,000140.3498,93119972000870,000940,000160.5172.6542,056544,612Intermsofconstantdollars,thefirm'ssalesareincreasingmoderately.14.300(18.00)400(4.90)850(15.00)20,110I(100)(100)110350(18.00)220(4.90)730(15.00)18,32815.95(1200)75(1800)50(2000)70(1500)I(100)99120(1200)86(1800)35(2000)60(1500)IndexNumbers17-5Quantitiesaredownslightly.16.ModelQuantityRelativesBaseQuantityPrice($)WeightWeightedQuantityRelativesSedan8520015,2003,040,000258,400,000Sport8010017,0001,700,000136,000,000Wagon807516,8001,260,000100,800,0006,000,000495,200,000495,200,000I836,000,00017.a/b.PriceIndexYear1996Base1997Base1996100.095.91997104.3100.01998108.9104.51999114.3109.618.a.PriceRelativesA=(15.90/10.50)(100)=151B=(32.00/16.25)(100)=197C=(17.40/12.20)(100)=143D=(35.50/20.00)(100)=178b.15.90(2000)32.00(5000)17.40(6500)35.50(2500)I(100)17010.50(2000)16.25(5000)12.20(6500)20.00(2500)19.15.90(4000)32.00(3000)17.40(7500)35.50(3000)I(100)16410.50(4000)16.25(3000)12.20(7500)20.00(3000)20.Jan32.75(100)59(150)42(75)16.5(50)I(100)9631.50(100)65(150)40(75)18(50)Mar32.50(100)57.5(150)39.5(75)13.75(50)I(100)9231.50(100)65(150)40(75)18(50)Marketisdowncomparedto1999.21.PriceRelatives:JanMarOil(32.75/31.50)(100)=104103Computer(59.00/65.00)(100)=9188Steel(42.00/40.00)(100)=10599RealEstate(16.5/18.00)(100)=9276IJan=96IMar=92Chapter1717-622.ProductRelativesBasePriceQuantityWeightWeightedPriceRelativesCorn1132.3014273282370,866Soybeans1235.513501929237,2675211608,133608,133I117521123.a.FruitPriceRelativesBananas(.51/.41)(100)=124.4Apples(.85/.71)(100)=119.7Oranges(.61/.56)(100)=108.9Pears(.98/.64)(100)=153.1b.Weights(PioQio)PriceRelativeProduct9.963124.41239.397214.129119.71691.24137.784108.9847.67762.048153.1313.5488Totals33.9244091.86494091.8649I120.633.924Fruitpriceshaveincreasedby20.6%overthe10-yearperiodaccordingtotheindex.24.Salariesinconstant(1982-84)dollarsarecomputedasfollows:1970$14,000(100/38.8)=$36,0821975$17,500(100/53.8)=$32,528