Transcript Section 3B Putting Numbers in Perspective

Section 3D
Index Numbers
Pages 182-191
3-D
Index Numbers
An index number provides a simple way
to compare measurements made at
different times or in different places.
The value at one particular time (or
place) must be chosen as the
reference value. The index number for
any other time (or place) is
value
index number =
 100
reference value
Average Gasoline Prices (per gallon)
Year
Price
Price as a Percentage of
1975 Price
Price Index
1975 = 100
1955
29.1¢
51.3%
51.3
1965
31.2¢
55.0%
55.0
1975
56.7¢
100.0%
100.0
1985
119.6¢
210.9%
210.9
1995
120.5¢
212.5%
212.5
2000
155.0 ¢
273.4%
273.4
2006
257.2¢
453.6%
453.6
Where did these numbers come from?
- percent as a fraction based on a reference value
P1955 P1965 P1975 P1985 P1995 P2000 P2006
,
,
,
,
,
,
P1975 P1975 P1975 P1975 P1975 P1975 P1975
3-D
Gasoline Price Index
Year
Price
Price Index
1975 = 100
1955
29.1¢
51.3
1965
31.2¢
55.0
1975
56.7¢
100.0
1985
119.6¢
210.9
1995
120.5¢
212.5
2000
155.0¢
273.4
2006
257.2¢
453.6
3-D
Price Index
2006 = 100
Complete the Gasoline Price Index using the 2006
price as the reference value
P1955 P1965 P1975 P1985 P1995 P2000 P2006
,
,
,
,
,
,
P2006 P2006 P2006 P2006 P2006 P2006 P2006
Gasoline Price Index
Year
Price
Price Index
1975 = 100
1955
29.1¢
51.3
1965
31.2¢
55.0
1975
56.7¢
100.0
1985
119.6¢
210.9
1995
120.5¢
212.5
2000
155.0¢
273.4
2006
257.2¢
453.6
3-D
Price Index
2006 = 100
11.3
Complete the Gasoline Price Index using the 2000
price as the reference value
P1955 P1965 P1975 P1985 P1995 P2000 P2006
,
,
,
,
,
,
P2006 P2006 P2006 P2006 P2006 P2006 P2006
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
1985
119.6¢
210.9
1995
120.5¢
212.5
2000
155.0¢
273.4
2006
257.2¢
453.6
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
22.0
1985
119.6¢
210.9
1995
120.5¢
212.5
2000
155.0¢
273.4
2006
257.2¢
453.6
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
22.0
1985
119.6¢
210.9
46.5
1995
120.5¢
212.5
2000
155.0¢
273.4
2006
257.2¢
453.6
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
22.0
1985
119.6¢
210.9
46.5
1995
120.5¢
212.5
46.9
2000
155.0¢
273.4
2006
257.2¢
453.6
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
22.0
1985
119.6¢
210.9
46.5
1995
120.5¢
212.5
46.9
2000
155.0¢
273.4
60.3
2006
257.2¢
453.6
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
3-D
Year
Price
Price Index
1975 = 100
Price Index
2000 = 100
1955
29.1¢
51.3
11.3
1965
31.2¢
55.0
12.1
1975
56.7¢
100.0
22.0
1985
119.6¢
210.9
46.5
1995
120.5¢
212.5
46.9
2000
155.0¢
273.4
60.3
2006
257.2¢
453.6
100
Complete the Gasoline Price Index using the 2000
price as the reference value
Gasoline Price Index
What do these
numbers mean?
Year
Price Index
1975 = 100
1955
51.3
1965
55.0
1975
100.0
1985
210.9
1995
212.5
2000
273.4
2006
453.6
The 1955 price is 51.3 percent of the 1975 price.
The 1965 price is 55.0 percent of the 1975 price.
The 1975 price is 100 percent of the 1975 price.
The 1995 price is 212.5 percent of the 1975 price.
The 2006 price is 453.6 percent of the 1975 price.
3-D
Index numbers are primarily used for
COMPARISONS
Example: Suppose it cost $7.00 to fill a gas tank
in 1975. How much would it cost to fill the
same tank in 1995?
Price index for 1995 is 212.5
The 1995 gas cost is 212.5% of the 1975 gas cost.
P1995 = 212.5% x P1975
= 2.125 x $7.00
= $14.875
= $14.88
3-D
Example: Suppose it cost $20.00 to fill a gas
tank in 1995. How much would it have cost to
fill the tank in 1955?
Price index for 1995 is 212.5
P1995 = 2.125 x P1975
$20 = 2.125 x P1975
$20/2.125 = P1975
$9.41 = P1975
Price index for 1955 is 51.3
P1955 = .513 x P1975
P1955 = .513 x $9.41
P1955 = $4.83
So the tank cost in 1955 is $4.83
Another way: Suppose it cost $20.00 to fill a gas
tank in 1995. How much would it have cost to fill the
tank in 1955?
Price index for 1995 is 212.5 so P1995 = 212.5% x P1975
Price index for 1955 is 51.3 so P1955 = 51.3% x P1975
P1995
 P1975
212.5%
P1995
P1955

212.5% 51.3%
P1955
 P1975
51.3%
51.3%
(P1995 )  P1955
212.5%
51.3
($20)  P1955  $4.83
212.5
3-D
To compare prices in year X and year Y,
use the index numbers directly.
IX
PX 
 PY
IY
Example. Suppose it cost $10 to fill a gas tank
in 1985. How much would it have cost to fill
the same tank in 1965? How much would it
cost in 2006?
P1965
P2006
55.0

($10)  $2.61
210.9
453.6

($10)  $21.51
210.9
3-D
Consumer Price Index (CPI)
•Intended to measure the overall rate of
inflation
•Computed and reported monthly by U.S.
Bureau of Labor Statistics
•More than 60,000 items each month
•Current reference value is an average of
prices during 1982-1984
3-D
Consumer Price Index
2004
188.9 | 2005
195.3
|
2006
201.6
The 1973 price is 44.4 percent of the 1982-84 price.
The 1974 price is 49.3 percent of the 1982-84 price.
The 1983 price is 99.6 percent of the 1982-84 price.
The 1991 price is 136.2 percent of the 1982-84 price.
The 2000 price is 172.2 percent of the 1982-84 price.
3-D
Consumer Price Index (CPI)
How do ‘today’s’ prices compare to those
in 1986?
CPI2006  201.6 1.839
CPI1986 109.6
Prices ‘today’ are about 1.84 times what
they were in 1986.
Consumer Price Index (CPI)
3-D
Ex: If you were making $30,000 in 1995, how
much would you need now to maintain the same
standard of living? [Assume the average price of your
typical purchases has risen at the same rate as the CPI.]
IX
PX 
 PY
IY
P2006
I 2006

(P1995 )
I1995
P2006 = (201.6/152.4) x ($30,000) = $39,685.04
To maintain the 1995 standard of living, you would need to make
about $39,700 today.
More Practice
A loaf of bread cost $0.75 in 1979. What was its price
in 2000 dollars?
P2000
I 2000

(P1979 )
I1979
172.2
 $.75
72.6
 $1.78
3-D
3-D
More Practice
Admission to a movie cost $7.00 in 2000. What was
its price in 1975 dollars?
P1975
I1975

($7.00)
I 2000
53.8

 $7.00
172.2
 $2.19
3-D
More Practice
What was the purchasing power of $1 in 1973 in terms
of 2006 dollars?
P2006
I 2006

($1.00)
I1973
201.6

 $1.00
44.4
 $4.54
3-D
Rate of Inflation
The rate of inflation refers to the relative
change in the CPI from one year to the
next.
 CPInew year  CPIold year 100%
CPIold year
3-D
Rate of Inflation
Find the rate of inflation from 2004 to
2005:
CPI2005 -CPI2004
100%
CPI2004
 .033880 100%
 3.39%
 195.3-188.9 100%
188.9
Adjusting prices for inflation
3-D
Compare the 1981 gas price of $1.47 / gallon
to today’s price of $2.57 / gallon ( use 2006 CPI)
Relative change

$2.57  $1.47
100%  74.8%
$1.47
Inflation rate (1981 to 2006) =
201.6  90.9
100%  121.78%
90.9
Gas prices from 1981 to today have increased by 74.8%
The inflation rate from 1981 to today is 121.78%.
Thus today’s gas prices have not kept up with inflation!
More Practice
3-D
Total spending on health care in the US rose from $80
billion in 1973 to $1.5 trillion in 2002. Compare this
rise in health care spending to the overall rate of
inflation as measured by the CPI.
Relative change =1.5 1012
 80 109
100%  1775%
9
80 10
Inflation rate:
179.9  44.4
100%  305.18%
44.4
More Practice
The average cost of college (tuition, fees, room and
board) at four-year private universities rose from
$5900 in 1980 to $25100 in 2002. Calculate the
relative change in cost from 1980 to 2002, and
compare it to the overall rate of inflation as
measured by the CPI.
25,100  5,900
Relative change =
100%  325.4%
5,900
Inflation rate =
179.9  82.4
 100%  116.14%
82.4
3-D
Homework:
Pages 192-193
# 14, 18, 20, 24, 26, 32, 34