Chapter 17 Index Numbers Learning Objectives Know how to compute price relatives and understand how they represent price changes over time Know how to compute aggregate price indexes and understand how the choice of a base period affects the index Become familiar with the Consumer Price Index, the Producer Price Index and the Dow Jones averages Learn how to deflate a time series to measure changes over time in constant dollars Learn how to compute an aggregate quantity index and how to interpret it Solutions: 17 - © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 17 a Item Price Relative A 103 = (7.75/7.50)(100) B 238 = (1500/630)(100) b I 2009 = 7.75 + 1500.00 1507.75 (100) = (100) = 237 7.50 + 630.00 637.50 c I 2009 = 7.75(1500) + 1500.00(2) 14, 625.00 (100) = (100) = 117 7.50(1500) + 630.00(2) 12,510.00 d I 2009 = 7.75(1800) + 1500.00(1) 15, 450.00 (100) = (100) = 109 7.50(1800) + 630.00(1) 14,130.00 a From the price relative we see the percentage increase was 32% b Divide the current cost by the price relative and multiply by 100 1992 cost = a $10.75 (100) = $8.14 132 Price Relatives A = (6.00 / 5.45)100 = 110 B = (5.95 / 5.60)100 = 106 C = (6.20 / 5.50)100 = 113 b I 2009 = 6.00 + 5.95 + 6.20 (100) = 110 5.45 + 5.60 + 5.50 c I 2009 = 6.00(150) + 5.95(200) + 6.20(120) (100) = 109 5.45(150) + 5.60(200) + 5.50(120) 9% increase over the two year period I 2009 = I= 20.15(35) + 118.00(5) + 8.80(60) (100) = 114 17.50(35) + 100.00(5) + 8.00(60) 19(500) + 1.80(50) + 4.20(100) + 13.20(40) (100) = 104 15(500) + 1.60(50) + 4.50(100) + 12.00(40) Paasche index Item Price Relative Base Period Price 17 - Base Period Usage Weight Weighted Price Relatives © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Index Numbers A B C 150 90 120 22.00 5.00 14.00 I= a 20 50 40 440 250 560 1250 66,000 22,500 67,200 155,700 155, 700 = 125 1250 Price Relatives A = (3.95 / 2.50) 100 = 158 B = (9.90 / 8.75) 100 = 113 C = (.95 /.99) 100 = 96 b Item A B C Price Relatives 158 113 96 Base Price 2.50 8.75 99 Weight Pi0Qi 62.5 131.3 59.4 253.2 Quantity 25 15 60 I= Weighted Price Relatives 9875 14837 5702 30414 30414 = 120 253.2 Cost of raw materials is up 20% for the chemical Stock Holiday NY Electric KY Gas PQ Soaps Price Relatives 110 109 97 108 Base Price 15.50 18.50 26.75 42.25 Quantity 500 200 500 300 I= Weight 7750 3700 13375 12675 37500 Weighted Price Relatives 852500 403300 1297375 1368900 3922075 3922075 = 105 37500 Portfolio up 5% Item Beer Wine Soft Drink Price Relatives 115 118 110 Base Price 17.50 100.00 8.00 I= 10 a Deflated 1996 wages: Quantity 35,000 5,000 60,000 Weight 612,500 500,000 480,000 1,592,500 Weighted Price Relatives 70,437,500 59,000,000 52,800,000 182,237,500 182, 237,500 = 114 1,592,500 $11.86 (100) = $7.66 154.9 17 - © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 17 Deflated 2009 wages: $18.55 (100) = $8.74 212.2 b 18.55 (100) = 156.4 The percentage increase in actual wages is 56.4% 11.86 c 8.74 (100) = 114.1 The change in real wages is an increase of 14.1% 7.66 11 2002 2003 2004 2005 18.52 (100/179.9) = 10.29 18.95 (100/184.0) = 10.30 19.23 (100/188.9) = 10.18 19.46 (100/195.3) = 9.96 9.96 = 97 the decrease in real wages and salaries from 2003 to 2005 is 3% 10.30 12 a 2005 2006 2007 4742 (100/195.3) = 2428 5020 (100/201.6) = 2490 5081 (100/207.3) = 2451 Manufacturers' shipments have increased slightly in constant dollars when deflated using the CPI b 2005 2006 2007 4742 (100/155.8) = 3043 5020 (100/160.3) = 3132 5081 (100/166.6) = 3050 c The PPI is a better deflator since manufacturing shipments reflect prices paid by manufacturers 13 Year 1982 1987 1992 1997 2002 2007 Retail Sales ($) 380,000 520,000 700,000 870,000 940,000 990,000 CPI 96.5 113.6 140.3 160.5 179.9 207.3 Deflated Retail Sales ($) 393,782 457,746 498,931 542,056 522,513 477,569 In terms of constant dollars, the firm's sales were increasing moderately until 1997, then they decreased over the next two periods 14 I= 300(18.00) + 400(4.90) + 850(15.00) 20,110 (100) = (100) = 110 350(18.00) + 220(4.90) + 730(15.00) 18,328 15 I= 95(1200) + 75(1800) + 50(2000) + 70(1500) (100) = 99 120(1200) + 86(1800) + 35(2000) + 60(1500) Quantities are down slightly 16 Model Sedan Sport Quantity Relatives 85 80 Base Quantity 200 100 Price ($) 15,200 17,000 17 - Weight 3,040,000 1,700,000 Weighted Quantity Relatives 258,400,000 136,000,000 © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Index Numbers Wagon 80 75 16,800 Price Index 2004 Base 2005 Base 100.0 91.7 109.0 100.0 111.5 102.3 112.2 102.9 Year 2004 2005 2006 2007 18 a 100,800,000 495,200,000 495, 200, 000 = 83 6, 000, 000 I= 17 a/b 1,260,000 6,000,000 Price Relatives A = (15.90 / 10.50) (100) = 151 B = (32.00 / 16.25) (100) = 197 C = (17.40 /12.20) (100) = 143 D = (35.50 / 20.00) (100) = 178 I= 15.90(2000) + 32.00(5000) + 17.40(6500) + 35.50(2500) (100) = 170 10.50(2000) + 16.25(5000) + 12.20(6500) + 20.00(2500) 19 I= 15.90(4000) + 32.00(3000) + 17.40(7500) + 35.50(3000) (100) = 164 10.50(4000) + 16.25(3000) + 12.20(7500) + 20.00(3000) 20 I Jan = 22.75(100) + 49(150) + 32(75) + 6.5(50) (100) = 73.5 31.50(100) + 65(150) + 40(75) + 18(50) I Mar = 22.50(100) + 47.5(150) + 29.5(75) + 3.75(50) (100) = 70.1 31.50(100) + 65(150) + 40(75) + 18(50) b Market is down compared to 2007 21 Price Relatives: Oil Computer Steel Real Estate IJan = 73.5 Jan (22.75 / 31.50) (100) (49.00 / 65.00) (100) (32.00 / 40.00) (100) (6.50 / 18.00) (100) = = = = 72.2 75.4 80.0 36.1 Mar 71.4 73.1 73.8 20.8 IMar = 70.1 22 Product Corn Soybeans Relatives 173.9 197.8 Base Price 2.30 5.51 Quantity 1427 350 17 - Weight 3282.1 1928.5 5210.6 Weighted Price Relatives 570,757.19 381,457.30 952,214.49 © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 17 952, 214.49 = 182.7 5210.6 I= 23 a Fruit Bananas Apples Oranges Pears Price Relatives (.53/.41) (100) = 129.3 (1.12/.71) (100) = 157.7 (.91/.56) (100) = 162.5 (1.27/.64) (100) = 198.4 b Weights (PioQio) 9.963 14.129 7.784 2.048 Totals 33.924 I= Price Relative 129.3 157.7 162.5 198.4 Product 1288.2 2228.1 1264.9 406.3 5187.5 5187.5 = 152.9 33.924 Fruit prices have increased by 52.9% over the 19-year period according to the index 24 Salaries in constant (1982-84) dollars are computed as follows: 1970 1975 1980 1985 1990 1995 2000 2005 $14,000 (100 / 38.8) = $36,082 $17,500 (100 / 53.8) = $32,528 $23,000 (100 / 82.4) = $27,913 $37,000 (100 / 107.6) = $34,387 $53,000 (100 / 130.7) = $40,551 $65,000 (100 / 152.4) = $42,651 $80,000 (100 / 172.2) = $46,458 $110,000 (100 / 195.3) = $56,324 In constant dollar terms, real starting salaries have increased about 56% over this period 25 The stock market prices in constant (1982-84) dollars are computed as follows: 2004 2005 2006 2007 2008 $51.00 (100 / 188.9) = $27.00 $54.00 (100 / 195.3) = $27.65 $58.00 (100 / 201.6) = $28.77 $59.50 (100 / 207.3) = $28.70 $59.00 (100 / 215.3) = $27.40 The value of the stock, in real dollars, is 1.48% higher in 2008 than it was in 2004 This is not a big increase, but if the stock paid a high dividend it may still have been a good investment over this period 26 I= 1200(30) + 500(20) + 500(25) (100) = 143 800(30) + 600(20) + 200(25) Quantity is up 43% 17 - © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ... = $7.66 154.9 17 - © 2010 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 17 Deflated 2009... 000, 000 I= 17 a/b 1,260,000 6,000,000 Price Relatives A = (15.90 / 10.50) (100) = 151 B = (32.00 / 16.25) (100) = 197 C = (17. 40 /12.20) (100) = 143 D = (35.50 / 20.00) (100) = 178 I= 15.90(2000)... 178 I= 15.90(2000) + 32.00(5000) + 17. 40(6500) + 35.50(2500) (100) = 170 10.50(2000) + 16.25(5000) + 12.20(6500) + 20.00(2500) 19 I= 15.90(4000) + 32.00(3000) + 17. 40(7500) + 35.50(3000) (100) =