# Consumer Price Index. What prices have changed over your lifetime? What items cost more? What items cost less?

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Consumer Price Index

What prices have changed over your lifetime? What items cost more? What items cost less?

Question: How do we know if something really costs more?

First, we need correct terminology.

Nominal price: list or actual cost given current value of money

Nominal price: Useful for comparisons within same time period and in same location

Problem with nominal prices: Cannot make meaningful comparisons of prices across time periods or locations.

Prices of products in 1962: \$0.05 for a Hershey bar \$0.05 for a Hershey bar \$0.05 for a copy of New York Times \$0.05 for a copy of New York Times \$0.04 for first class postage stamp \$0.04 for first class postage stamp \$0.31 for gallon of regular gas \$0.31 for gallon of regular gas \$0.28 for McDonalds double hamburger \$0.28 for McDonalds double hamburger \$2,529.00 for full-size Chevrolet \$2,529.00 for full-size Chevrolet

Why cant one compare 1962 prices with prices for same or similar products today? More precisely, why are such comparisons meaningless?

Real price: Cost relative to general economic conditions in a place and time.

Why? Because the price of an item only has meaning in terms of what one passes up to buy it.

Similarly with wages: Income only can be evaluated in terms of what can be purchased with it.

Inflation: A general rise in prices in an economy.

Deflation: A general decrease in prices in an economy.

Inflation and deflation create disparities between real and nominal prices.

Suppose a young person gets an allowance of \$10 per week. Her allowance allows her a certain level of consumption.

Suppose that the prices of goods she normally buys increase by 20% and her father increases her allowance to \$11.

Has her allowance increased?

Answer: Her nominal allowance has increased but her real allowance has decreased.

Key Question: Are people better off now than they used to be?

To answer this, you need a way to standardize prices (and wages), so that you can compare across time. To answer this, you need a way to standardize prices (and wages), so that you can compare across time.

CPI: Consumer Price Index Economists use Consumer Price Index [CPI] to estimate real wages and costs from nominal wages and costs. Economists use Consumer Price Index [CPI] to estimate real wages and costs from nominal wages and costs.

Computation of CPI An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year) An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year)

Computation of CPI An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year). An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year). The prices of the baskets is compared. The prices of the baskets is compared.

Computation of CPI An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year). An army of economists gathers prices on a standard market basket of goods at fixed time periods (month, year). The prices of the baskets is compared. The prices of the baskets is compared. The prices are converted to index numbers. The prices are converted to index numbers.

Whats in the CPI? Housing (41.4%) Housing (41.4%) Transportation (17.8%) Transportation (17.8%) Food (16.2%) Food (16.2%) Energy (8.2%) Energy (8.2%) Medical Care (6.4%) Medical Care (6.4%) Apparel & Upkeep (6.1%) Apparel & Upkeep (6.1%) Other (3.9%) Other (3.9%)

Current CPI NYTimes Graphic NYTimes Graphic NYTimes Graphic NYTimes Graphic

Creating the CPI Cost of bundle in a base year = 100 (on index) Cost of bundle in a base year = 100 (on index) Cost of the bundle for other years is then calculated Cost of the bundle for other years is then calculated Ex: 1982 = base year; bundle = \$1103.46 Ex: 1982 = base year; bundle = \$1103.46 In 1983, bundle = \$1138.91 In 1983, bundle = \$1138.91 SO: \$1138.91 (1983) = SO: \$1138.91 (1983) = \$1103.46 (1982) \$1103.46 (1982)

OR: \$1138.91 (1983) = \$1103.46 (1982) \$1138.91 (1983) = \$1103.46 (1982) Then 1 (1982\$) = 1138.91/1103.46 Then 1 (1982\$) = 1138.91/1103.46 =1.032 (1983\$) =1.032 (1983\$) So…1 (1982\$) = 1.032 (1983\$) So…1 (1982\$) = 1.032 (1983\$) 1982 = base year; index = 100 1982 = base year; index = 100 1983; index = 103.2 1983; index = 103.2

And we get an INDEX Year Year 1980 1980 1981 1981 1982 1982 1983 1983 1984 1984 1985 1985 1986 1986 1987 1987 CPI CPI 85.4 85.4 94.2 94.2 100.0 100.0 103.2 103.2 107.7 107.7 111.5 111.5 113.6 113.6 117.7 117.7

FORMULA for the Conversion Factor Notice that those relative values can be computed using this formula: CPI of base year / CPI of object year (Object year is the year being compared to the base year) Notice that those relative values can be computed using this formula: CPI of base year / CPI of object year (Object year is the year being compared to the base year)

Conversion factor = CPI of base year / CPI of object year

Use the conversion factor to adjust the prices: Price * conversion factor = adjusted price

An Example 1990, gas costs \$1.16/gallon (on avg) 1990, gas costs \$1.16/gallon (on avg) 1997, gas costs \$1.23/gallon (on avg) 1997, gas costs \$1.23/gallon (on avg) Was gas more or less expensive in 1997? Was gas more or less expensive in 1997? Nominal price (current price) = MORE Nominal price (current price) = MORE But, what about in constant/real \$? But, what about in constant/real \$?

Converting Prices From the CPI table, we know that From the CPI table, we know that \$130.70 (1990) = \$160.50 (1997) \$130.70 (1990) = \$160.50 (1997) If something costs \$1.16 in 1990, what would that amount to in 1997? 160.50 (1997) = x (1997 \$) 130.70 (1990) 1.16 (1990 \$)

Another way to think of this Conversion Factor Conversion Factor = CPI of base year/CPI of object year = CPI of base year/CPI of object year160.50130.70 (how much more one dollar in 1990 is worth in 1997) =1.228 * \$1.16 = \$1.42 So, \$1.16 in 1990 = \$1.42 in 1997

Using previous terminology: Nominal price * conversion factor = real price (relative to base year)

Combining the formula for adjusted price with that for the conversion factor: Nominal price * (CPI base year / CPI object year) = real price

Another Example

Converting Prices in Excel

Freezing the Cell Remember that you can freeze the value in a cell so that the reference stays the same Remember that you can freeze the value in a cell so that the reference stays the same When you convert prices, you want to freeze the value of the base year (1998) When you convert prices, you want to freeze the value of the base year (1998) F4 freezes the value – B2*\$C\$10/C2 F4 freezes the value – B2*\$C\$10/C2

Additional terminology: Current values (prices, wages, etc.) are prices (nominal values) at the value of the currency at that time Current values (prices, wages, etc.) are prices (nominal values) at the value of the currency at that time Constant values (prices, etc.) are prices in real values, i.e., as if the currency had the value of the base year. Constant values (prices, etc.) are prices in real values, i.e., as if the currency had the value of the base year.

Inflation Rate Percentage Change in the annual CPI Percentage Change in the annual CPI Ex: Inflation Rate in 1996: Ex: Inflation Rate in 1996: