Section 3DSection 3DIndex NumbersIndex Numbers

Pages 186-198Pages 186-198

Index NumbersIndex Numbers

An An index number provides a simple way provides a simple way to compare measurements made at to compare measurements made at different times or in different places. The different times or in different places. The value at one particular time (or place) value at one particular time (or place) must be chosen as the must be chosen as the reference valuereference value. . The The index numberindex number for any other time (or for any other time (or

place) is place) is

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value

index number = 100reference value

Average Gasoline Prices (per gallon)Average Gasoline Prices (per gallon)3-D

YearYear PricePricePrice as a Percentage Price as a Percentage

of of

1975 Price1975 Price

Price IndexPrice Index

1975 = 1001975 = 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?Where did these numbers come from?- percent as a fraction based on a reference value- percent as a fraction based on a reference value

1955 1965 1975 1985 1995 2000 2005

1975 1975 1975 1975 1975 1975 1975

P P P P P P P, , , , , ,

P P P P P P P

Gasoline Price IndexGasoline Price Index3-D

Year PricePricePrice Index

1975 = 100

Price Index

1985 = 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

Complete the Gasoline Price Index using the 1985 Complete the Gasoline Price Index using the 1985 price as the reference valueprice as the reference value

1955 1965 1975 1985 1995 2000 2005

1985 1985 1985 1985 1985 1985 1985

P P P P P P P, , , , , ,

P P P P P P P

YearYearPrice IndexPrice Index

1975 = 1001975 = 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 1955 price is 51.3 percent of the 1975 price.

The 1965 price is 55.0 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 1975 price is 100 percent of the 1975 price.

The 1985 price is 210.9 percent of the 1975 The 1985 price is 210.9 percent of the 1975 price.price.

The 1995 price is 212.5 percent of the 1975 The 1995 price is 212.5 percent of the 1975 price.price.

The 2000 price is 273.4 percent of the 1975 The 2000 price is 273.4 percent of the 1975 price.price.

What do these What do these numbers mean?numbers mean?

Gasoline Price Index

Index numbers are primarily used for are primarily used for COMPARISONSCOMPARISONS

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Ex2a/188Ex2a/188 Suppose it cost $7.00 to fill a gas tank in 1975. Suppose it cost $7.00 to fill a gas tank in 1975. How much would it cost to fill the same tank in 2005?How much would it cost to fill the same tank in 2005?

Price index for 2005 is 407.4The 2005 gas cost is 407.4% of the1975 gas cost.

P2005 = 407.4% x P1975

= 4.074 x $7.00= 4.074 x $7.00= $28.52= $28.52

Ex2/184Ex2/184 Suppose it cost $20.00 to fill a gas tank Suppose it cost $20.00 to fill a gas tank in 1995. How much would it have cost to fill the in 1995. How much would it have cost to fill the tank in 1955?tank in 1955?

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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

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

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19951975

PP

212.5%

1955 1995

51.3%P (P )

212.5%

1955

51.3P ($20) $4.83

212.5

Ex2/184Ex2/184 Suppose it cost $20.00 to fill a gas tank in Suppose it cost $20.00 to fill a gas tank in 1995. How much would it have cost to fill the tank in 1995. How much would it have cost to fill the tank in 1955?1955?

XX Y

Y

IP P

I

To compare prices in year X and year Y, use To compare prices in year X and year Y, use the index numbers directly.the index numbers directly.

Example.Example. Suppose it cost $10 to fill a gas tank in Suppose it cost $10 to fill a gas tank in 1985. How much would it have cost to fill the 1985. How much would it have cost to fill the same tank in 1965?same tank in 1965?

1965

55.0P ($10) $2.61

210.9

Consumer Price Index (CPI)Consumer Price Index (CPI)3-D

•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

Consumer Price IndexConsumer Price Index3-D

2003 184.0 2004 188.9 2005 195.3

The 1973 price is 44.4 percent of the 1982-84 The 1973 price is 44.4 percent of the 1982-84 price.price.

The 1974 price is 49.3 percent of the 1982-84 The 1974 price is 49.3 percent of the 1982-84 price.price.

The 1983 price is 99.6 percent of the 1982-84 The 1983 price is 99.6 percent of the 1982-84 price.price.

The 1991 price is 136.2 percent of the 1982-84 The 1991 price is 136.2 percent of the 1982-84 price.price.

The 2000 price is 172.2 percent of the 1982-84 The 2000 price is 172.2 percent of the 1982-84 price.price.

Consumer Price Index (CPI)Consumer Price Index (CPI)3-D

Pg186: How do 2005 prices compare Pg186: How do 2005 prices compare to those in 1995. to those in 1995.

Prices in 2005 were about 1.28 times Prices in 2005 were about 1.28 times what they were in 1995.what they were in 1995.

2005

1995

CPI 195.3 1.28152.4CPI

Consumer Price Index (CPI)Consumer Price Index (CPI)3-D

ex4/190ex4/190 If you were making $30,000 in If you were making $30,000 in 2000, how much would you have needed 2000, how much would you have needed in 2005 to maintain the same standard of in 2005 to maintain the same standard of living? [living? [Assume the average price of your typical Assume the average price of your typical purchases has risen at the same rate as the CPI.]purchases has risen at the same rate as the CPI.]

XX Y

Y

IP P

I 2005

2005 20002000

IP (P )

I

PP20052005 = (195.3/172.2) x ($30000) = $34020.00 = (195.3/172.2) x ($30000) = $34020.00

To maintain the 2000 standard of living, you would have needed to To maintain the 2000 standard of living, you would have needed to make $34,020 in 2005.make $34,020 in 2005.

More PracticeMore Practice

31/19631/196 A loaf of bread cost $0.75 in 1979. What was its A loaf of bread cost $0.75 in 1979. What was its price in 2004 dollars?price in 2004 dollars?

33/19733/197 Admission to a movie cost $7.00 in 2000. What was its price in 1975 dollars?

35/19735/197 What was the purchasing power of $1 in 1973 in terms of 2002 dollars?

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Rate of InflationRate of Inflation

The The rate of inflation refers to the refers to the relative relative changechange in the CPI from one year to the next. in the CPI from one year to the next.

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new year old year

old year

100%CPI CPICPI

Rate of InflationRate of Inflation

30*/19230*/192 Find the rate of inflation from 2000 Find the rate of inflation from 2000 to 2001:to 2001:

2001 2000

2000

CPI -CPI 100%CPI

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.0285 100%

2.85%

100%177.1-172.2 172.2

Adjusting prices for inflationAdjusting prices for inflationpg187pg187 Compare the 1981 gas price of $1.47 / gallon Compare the 1981 gas price of $1.47 / gallonto today’s price of $2.38 / gallon ( use 2004 CPI)to today’s price of $2.38 / gallon ( use 2004 CPI)

Relative changeRelative change

Inflation rate (1981 to 2004) = Inflation rate (1981 to 2004) =

Gas prices from 1981 to today have increased by 61.9%Gas prices from 1981 to today have increased by 61.9%The inflation rate from 1981 to today is 109.35%.The inflation rate from 1981 to today is 109.35%.

Thus today’s gas prices have not kept up with inflation!

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$2.38 $1.47100% 61.9%

$1.47

190.3 90.9100% 109.35%

90.9

More PracticeMore Practice

41/19341/193 Total spending on health care in the US rose from Total spending on health care in the US rose from $80 billion in 1973 to $1.8 trillion in 2004. Compare this $80 billion in 1973 to $1.8 trillion in 2004. Compare this rise in health care spending to the overall rate of rise in health care spending to the overall rate of inflation as measured by the CPI.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.

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Homework:Homework:

Pages 196-197Pages 196-197

# 24, 28, 30, 34, 36, 42, 44