Transcript Section 3B Putting Numbers in Perspective

Section 3D
Index Numbers
Pages 186-198
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
3-D
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
2005
231.0¢
407.4%
407.4
Where did these numbers come from?
- percent as a fraction based on a reference value
P1955 P1965 P1975 P1985 P1995 P2000 P2005
,
,
,
,
,
,
P1975 P1975 P1975 P1975 P1975 P1975 P1975
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
2005
231.0¢
407.4
Price Index
1985 = 100
Complete the Gasoline Price Index using the 1985
price as the reference value
P1955 P1965 P1975 P1985 P1995 P2000 P2005
,
,
,
,
,
,
P1985 P1985 P1985 P1985 P1985 P1985 P1985
3-D
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
2005
419.8
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 1985 price is 210.9 percent of the 1975 price.
The 1995 price is 212.5 percent of the 1975 price.
The 2000 price is 273.4 percent of the 1975 price.
3-D
Index numbers are primarily used for COMPARISONS
Ex2a/188 Suppose it cost $7.00 to fill a gas tank in 1975.
How much would it cost to fill the same tank in 2005?
Price index for 2005 is 407.4
The 2005 gas cost is 407.4% of the1975 gas cost.
P2005 = 407.4% x P1975
= 4.074 x $7.00
= $28.52
3-D
Ex2/184 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
3-D
Ex2/184 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
P1995
 P1975
212.5%
Price index for 1955 is 51.3 so P1955 = 51.3% x P1975
P1955
P1955
51.3%

(P1995 )
212.5%
51.3

($20)  $4.83
212.5
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?
P1965
55.0

($10)  $2.61
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
2003
2004
2005
184.0
188.9
195.3
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)
Pg186: How do 2005 prices compare to
those in 1995.
CPI2005 195.3 1.28
CPI1995 152.4
Prices in 2005 were about 1.28 times what
they were in 1995.
3-D
Consumer Price Index (CPI)
ex4/190 If you were making $30,000 in 2000,
how much would you have needed in 2005 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
P2005
I2005

(P2000 )
I 2000
P2005 = (195.3/172.2) x ($30000) = $34020.00
To maintain the 2000 standard of living, you would have needed to
make $34,020 in 2005.
3-D
More Practice
31/196 A loaf of bread cost $0.75 in 1979. What was its
price in 2004 dollars?
33/197 Admission to a movie cost $7.00 in 2000. What
was its price in 1975 dollars?
35/197 What was the purchasing power of $1 in 1973 in
terms of 2002 dollars?
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
30*/192 Find the rate of inflation from 2000
to 2001:
CPI2001-CPI2000
100%
CPI2000
 .0285 100%
 2.85%
 177.1-172.2 100%
172.2
3-D
Adjusting prices for inflation
pg187 Compare the 1981 gas price of $1.47 / gallon
to today’s price of $2.38 / gallon ( use 2004 CPI)
Relative change
$2.38  $1.47

100%  61.9%
$1.47
190.3  90.9
100%  109.35%
Inflation rate (1981 to 2004) =
90.9
Gas prices from 1981 to today have increased by 61.9%
The inflation rate from 1981 to today is 109.35%.
Thus today’s gas prices have not kept up with inflation!
3-D
More Practice
41/193 Total spending on health care in the US rose from
$80 billion in 1973 to $1.8 trillion in 2004. Compare this
rise in health care spending to the overall rate of
inflation as measured by the CPI.
43/193 The average cost of college (tuition, fees, room
and board) at four-year private universities rose from
$5900 in 1980 to $27516 in 2004. Calculate the relative
change in cost from 1980 to 2004, and compare it to the
overall rate of inflation as measured by the CPI.
Homework:
Pages 196-197
# 24, 28, 30, 34, 36, 42, 44