商务与经济统计习题答案（第8版中文版）SBE8-SM17.doc

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1、Index NumbersChapter 17Index NumbersLearning Objectives1.Know how to compute price relatives and understand how they represent price changes over time.2.Know how to compute aggregate price indexes and understand how the choice of a base period affects the index.3.Become familiar with the Consumer Pr

2、ice Index, the Producer Price Index and the Dow Jones averages.4.Learn how to deflate a time series to measure changes over time in constant dollars.5.Learn how to compute an aggregate quantity index and how to interpret it.Solutions:1.a.ItemPrice RelativeA103 = (7.75/7.50)B238 = (1500/630)b.c.d.2.a

3、.From the price relative we see the percentage increase was 32%.b.Divide the current cost by the price relative and multiply by 100.1990 cost =(100) = $8.14 3.a.Price RelativesA = (6.00 / 5.45) 100= 110B = (5.95 / 5.60) 100= 106C = (6.20 / 5.50) 100= 113b.c.9% increase over the two year period.4.5.P

4、aasche index6. ItemPrice RelativeBase PeriodPriceBase PeriodUsageWeightWeighted Price RelativesA15022.0020 440 66,000B 90 5.0050 250 22,500C12014.0040 560 67,2001250155,7007.a.Price RelativesA = (3.95 / 2.50) 100= 158B = (9.90 / 8.75) 100= 113C = (.95 /.99) 100= 96b.ItemPrice RelativesBasePriceQuant

5、ityWeightPi0QiWeighted Price RelativesA1582.5025 62.5 9875B1138.7515131.3 14837C 96 .9960 59.4 5702253.230414Cost of raw materials is up 20% for the chemical.8.StockPrice RelativesBasePriceQuantityWeightWeighted Price RelativesHoliday11015.50500 7750 852500NY Electric10918.50200 3700 403300KY Gas 97

6、26.7550013375 1297375PQ Soaps10842.2530012675 136890037500 3922075Portfolio up 5%9.ItemPrice RelativesBasePriceQuantityWeightWeighted Price RelativesBeer10815.0035,000 525,000 56,700,000Wine10760.00 5,000 300,000 32,100,000Soft Drink102 9.8060,000 588,000 59,976,0001,413,000148,776,00010.a.Deflated

7、1980 wages: Deflated 2000 wages: b. The percentage increase in actual wages is 97.5%.c. The change in read wages is a decrease of 5.7%.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)=8.01 the increase in real wages and

8、salaries from 1998 to 2000 is 2%.12.a.19973929 (100/160.5)=244819984052 (100/163.0)=248619994260 (100/166.6)=2557Manufacturers shipments are increasing slightly in constant dollars when deflated using the CPI.b.19973929 (100/131.8)=298119984052 (100/130.7)=310019994260 (100/133.0)=3203c.The PPI is a

9、 better deflator since manufacturing shipments reflect prices paid by manufacturers.13.YearRetail Sales ($)CPIDeflatedRetail Sales ($)1982380,00096.5393,7821987520,000113.6457,7461992700,000140.3498,93119972000870,000940,000160.5172.6542,056544,612In terms of constant dollars, the firms sales are in

10、creasing moderately.14.15.Quantities are down slightly.16.ModelQuantity RelativesBaseQuantityPrice ($)WeightWeighted Quantity RelativesSedan8520015,2003,040,000 258,400,000Sport8010017,0001,700,000136,000,000Wagon80 7516,8001,260,000100,800,0006,000,000495,200,00017.a/b. Price IndexYear1996 Base1997

11、 Base1996100.095.91997104.3100.01998108.9104.51999114.3109.618.a.Price RelativesA = (15.90 / 10.50) (100)= 151B = (32.00 / 16.25) (100)= 197C = (17.40 /12.20) (100)= 143D = (35.50 / 20.00) (100)= 178b.19.20.Market is down compared to 1999.21.Price Relatives: Jan MarOil(32.75 / 31.50) (100)= 104103Co

12、mputer(59.00 / 65.00) (100)= 91 88Steel(42.00 / 40.00) (100)= 105 99Real Estate(16.5 / 18.00) (100)= 92 76IJan = 96 IMar = 9222.Product RelativesBasePriceQuantityWeightWeighted Price RelativesCorn1132.3014273282370,866Soybeans1235.51 3501929237,2675211608,13323.a.Fruit Price RelativesBananas (.51/.4

13、1) (100) = 124.4Apples (.85/.71) (100) = 119.7Oranges (.61/.56) (100) = 108.9Pears(.98/.64) (100) = 153.1b.Weights (PioQio)Price RelativeProduct 9.963124.41239.3972 14.129119.71691.2413 7.784108.9847.6776 2.048153.1313.5488Totals 33.9244091.8649Fruit prices have increased by 20.6% over the 10-year p

14、eriod according to the index.24.Salaries in constant (1982-84) dollars are computed as follows:1970$14,000 (100 / 38.8)= $36,0821975$17,500 (100 / 53.8)= $32,5281980$23,000 (100 / 82.4)= $27,9131985$37,000 (100 / 107.6)= $34,3871990$53,000 (100 / 130.7)= $40,5511995$65,000 (100 / 152.4)= $42,6512000

15、$80,000 (100 / 172.6) = $46,350In constant dollar terms, real starting salaries have increased about 28% over this period.25.The stock market prices in constant (1982-84) dollars are computed as follows:1996$51.00 (100 / 156.9)= $32.501997$54.00 (100 / 160.5)= $33.641998$58.00 (100 / 163.0)= $35.581999$59.50 (100 / 166.6)= $35.712000$59.00 (100 / 172.6)= $34.18The value of the stock, in real dollars, is only slightly more in 2000 than it is in 1996. Of course, if the stock paid a high dividend it may still have been a good investment over this period.26.Quantity is up 43%.17 - 7