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
Trang 1Index Numbers
Learning Objectives
1 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 Price 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:
17 - 1
Trang 21 a.
Item Price Relative
b 2009
7.75 1500.00 1507.75
7.50 630.00 637.50
+
+
c 2009
7.75(1500) 1500.00(2) 14,625.00
7.50(1500) 630.00(2) 12,510.00
+
+
d 2009
7.75(1800) 1500.00(1) 15, 450.00
7.50(1800) 630.00(1) 14,130.00
+
+
2 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 =$10.75
132 (100) = $8.14
3 a Price Relatives A = (6.00 / 5.45)100 = 110
B = (5.95 / 5.60)100 = 106
C = (6.20 / 5.50)100 = 113
b 2009
6.00 5.95 6.20
5.45 5.60 5.50
+ +
+ +
c 2009
6.00(150) 5.95(200) 6.20(120)
5.45(150) 5.60(200) 5.50(120)
+ +
+ +
9% increase over the two year period
20.15(35) 118.00(5) 8.80(60)
17.50(35) 100.00(5) 8.00(60)
+ +
+ +
5 .19(500) 1.80(50) 4.20(100) 13.20(40)
.15(500) 1.60(50) 4.50(100) 12.00(40)
+ + +
+ + +
Paasche index
Item
Price Relative
Base Period Price
Base Period
Weighted Price Relatives
Trang 3A 150 22.00 20 440 66,000
155,700
1250
= =
7 a Price Relatives A = (3.95 / 2.50) 100 = 158
B = (9.90 / 8.75) 100 = 113
C = (.95 /.99) 100 = 96
b
Item
Price Relatives
Base
Weight
Pi0Qi
Weighted Price Relatives
30414
253.2
= =
Cost of raw materials is up 20% for the chemical
8
Stock
Price Relatives
Base
Weighted Price Relatives
3922075
37500
= =
Portfolio up 5%
9
Item
Price Relatives
Base
Weighted Price Relatives
182, 237,500
1,592,500
10 a Deflated 1996 wages: $11.86
(100) $7.66 154.9 =
17 - 3
Trang 4Deflated 2009 wages: $18.55(100) $8.74
212.2 =
b 18.55
(100) 156.4 11.86 = The percentage increase in actual wages is 56.4%
(100) 114.1
7.66 = The change in real wages is an increase of 14.1%
2003 18.95 (100/184.0) = 10.30
2004 19.23 (100/188.9) = 10.18
2005 19.46 (100/195.3) = 9.96
9.96
.97 10.30= the decrease in real wages and salaries from 2003 to 2005 is 3%
2006 5020 (100/201.6) = 2490
2007 5081 (100/207.3) = 2451
Manufacturers' shipments have increased slightly in constant dollars when deflated using the CPI
2006 5020 (100/160.3) = 3132
2007 5081 (100/166.6) = 3050
c The PPI is a better deflator since manufacturing shipments reflect prices paid by manufacturers 13
Deflated Retail Sales ($)
1997 2002 2007
870,000 940,000 990,000
160.5 179.9 207.3
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)(100) 20,110(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
Quantity Relatives
Base
Weighted Quantity Relatives
Trang 5Wagon 80 75 16,800 1,260,000 100,800,000
495, 200,000
6,000,000
18 a 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
b 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)
22.75(100) 49(150) 32(75) 6.5(50)
31.50(100) 65(150) 40(75) 18(50)
+ + +
+ + +
Mar
22.50(100) 47.5(150) 29.5(75) 3.75(50)
31.50(100) 65(150) 40(75) 18(50)
+ + +
Market is down compared to 2007
Real Estate (6.50 / 18.00) (100) = 36.1 20.8
IJan = 73.5 IMar = 70.1
22
Base
Weighted Price Relatives
17 - 5
Trang 6952, 214.49
5210.6
23 a
Fruit Price Relatives
b
Weights (PioQio) Price Relative Product
5187.5
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 $14,000 (100 / 38.8) = $36,082
1975 $17,500 (100 / 53.8) = $32,528
1980 $23,000 (100 / 82.4) = $27,913
1985 $37,000 (100 / 107.6) = $34,387
1990 $53,000 (100 / 130.7) = $40,551
1995 $65,000 (100 / 152.4) = $42,651
2000 $80,000 (100 / 172.2) = $46,458
2005 $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 $51.00 (100 / 188.9) = $27.00
2005 $54.00 (100 / 195.3) = $27.65
2006 $58.00 (100 / 201.6) = $28.77
2007 $59.50 (100 / 207.3) = $28.70
2008 $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 1200(30) 500(20) 500(25)
800(30) 600(20) 200(25)
+ +
+ +
Quantity is up 43%