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Measuring Inflation The Consumer Price Index

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Background The Bureau of Labor Statistics (BLS) surveys 30,000 households on their spending habits. It uses this information to construct a market basket of 211 types of goods and services purchased by the typical urban family of four.

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Background Each month the BLS visits 23,000 stores in 87 cities and collects price information for the goods and services in the market basket.

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Definition This information is weighted to construct the Consumer Price Index (CPI): An average of the prices of the goods and services purchased by the typical urban family of four, or a measure of the overall average price level faced by consumers.

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Movieville Suppose we live in Movieville and our hypothetical market basket is made up of movie related goods and services.

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Caclulating Our “CPI” We first need to determine the base year. We first need to determine the base year. Suppose we choose the base-year to be 2006 Suppose we choose the base-year to be 2006 The quantities purchased in 2007 and 2008 are irrelevant, because we are assuming the household buys the same market basket of goods each month. The quantities purchased in 2007 and 2008 are irrelevant, because we are assuming the household buys the same market basket of goods each month.

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Calculate Expenditures on Base- Year Quantities (2006) For the CPI we use “Current Prices” and “Constant Quantities”. P 2006 x Q 2006 = (12 x $8.00) Movie Tickets (6 x $4.00) Popcorn (10 x $2.50) Soda = $145.00

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Calculate the Cost of the Market Basket in 2007 For the CPI we use “Current Prices” and “Constant Quantities”. P 2007 x Q 2006 = (12 x $10.00) Movie Tickets (6 x $5.00) Popcorn (10 x $3.00) Soda = $180.00

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Calculate the Cost of the Market Basket in 2008 For the CPI we use “Current Prices” and “Constant Quantities”. P 2008 x Q 2006 = (12 x $12.00) Movie Tickets (6 x $5.50) Popcorn (10 x $3.50) Soda = $212.00

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To calculate the CPI we use the following formula:

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Calculate the CPI for 2006 CPI 2006 = (Cost of Basket 2006 /Cost of Basket 2006 ) x 100 CPI 2006 = (145/145) x 100 = 100 The value of the CPI is always equal to 100 in the base- year. As with the GDP deflator, the CPI gives us an index number, there are no units.

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Calculate the CPI for 2007 and 2008 CPI 2007 = (Cost of Basket 2007 /Cost of Basket 2006 ) x 100 CPI 2007 = (180/145) x 100 = 124.14 CPI 2008 = (Cost of Basket 2008 /Cost of Basket 2006 ) x 100 CPI 2008 = (212/145) x 100 = 146.21

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Calculating the Inflation Rate from the CPI Remember, the CPI is a measure of the average overall price-level, not the inflation rate. To Calculate the inflation rate we use our growth rate formula.

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Calculate the inflation rate from 2006 to 2007 and from 2007 to 2008 Inflation 06-07 = [(CPI 2007 – CPI 2006 )/CPI 2006 ] x 100 Inflation 06-07 = [(124.14 – 100)/100] x 100 Inflation 06-07 = 24.14% Inflation 07-08 = [(CPI 2008 – CPI 2007 )/CPI 2007 ] x 100 Inflation 07-08 = [(146.21 – 124.14)/124.14] x 100 Inflation 07-08 = 17.78%

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The CPI Over Time

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Two Types of Inflation Top-Line (Headline) Inflation: The inflation rate as calculated from the CPI for all urban consumers for All Items. Top-Line (Headline) Inflation: The inflation rate as calculated from the CPI for all urban consumers for All Items. Core Inflation: The inflation rate as calculated from the CPI for all urban consumers Less Food and Energy. Core Inflation: The inflation rate as calculated from the CPI for all urban consumers Less Food and Energy.

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Top-Line and Core Inflation, 1957 to 2009

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Using the CPI to adjust for inflation Example: Babe Ruth was paid $80,000 in 1930. How much would that be worth in 2009 dollars? The CPI in 1930 was approximately 16.5 and the CPI in 2009 is 215.8.

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Converting to “Today’s Dollars” General Formula Value in Year X Dollars = (Value in Year Z Dollars) x (CPI in Year X/CPI in Year Z)

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Our Example Value in 2009 Dollars = Value in 1930 Dollars x (CPI 2009 /CPI 1930 ) Value in 2009 Dollars = $80,000 x (215.8/16.5) = $1,046,303.03

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Interpretation This tells us that if you were paid $1,046,303.03 today, you would be able to purchase roughly the same amount of goods and services Babe Ruth could have purchased in 1930 with a salary of $80,000. This calculation adjusts a nominal variable, the Babe’s salary for the effects of inflation.

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Nominal and Real Values We can also use the CPI to convert nominal values to real values using the following formula: Real Value in Base Year Dollars = [(Nominal Value in Year X)/(CPI in Year X)] x 100

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Our Base Year Note that our current CPI uses the “base- year” 1982-84, so everything is in 1982-84 dollars. The basket used to be updated every 10 years and is now updated every 2 years, but the “base-year” 1982-84 remains.

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Historical Gasoline Prices

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Converting the Price of Gasoline We can use the formula from above to convert the price of gasoline to the “real” price of gasoline in 1982-84 dollars. We can use the formula from above to convert the price of gasoline to the “real” price of gasoline in 1982-84 dollars. We can also convert all of the gasoline prices to 2009 dollars. We can also convert all of the gasoline prices to 2009 dollars.

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Calculate the Real Price of Gasoline for 1950 Real Price in Base Year Dollars = [(Nominal Value in 1950)/(CPI in 1950)] x 100 The 1950 Real Price of Gas in 1982-84 Dollars = [($0.27/24.0)] x 100 = $1.13

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Convert the 1950 Price of Gasoline to 2009 Dollars Price of Gas in 2009 Dollars = (Price of Gas in 1950) x (CPI in 2009/CPI in 1950) Price of Gas in 2009 Dollars = ($0.27) x (215.8/24) = $2.43

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Historical Gasoline Prices

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