Consumer Price Index

The last topic of this chapter is the Consumer Price Index (CPI). CPI is a measurement that is often discussed in financial markets because it is used to adjust for inflation. Simply put, CPI is the percentage change in the cost of a basket of goods today compared to some base year. CPI represents some fixed-expenditure weighted index used to measure changes in the purchasing power of households. One drawback of CPI is that it suffers substitution bias, so it oftentimes overstates the impact of price changes. Regardless, it is the preferred measure of purchasing power. Mathematically, we calculate CPI as

CPI = Cost of Goods t Cost of Goods t n

where the subscript t is the current year and t − n is some base year n periods in the past. If we wanted to calculate the CPI for 2020 and use 2015 as the base year, then we would use the cost of some basket of goods for both 2020 and 2015. A “basket of goods” might be all purchases in the U.S. economy, for example, or it might be just the food purchased in the U.S. economy. It can be any group of assets for which we are worried about inflation. Plugging the years into the equation above gives us

CPI = Cost of Goods 2020 Cost of Goods 2015

We can also use CPI to estimate an inflation rate relative to some base year. The equation we would use is

Inflation Rate = CPI t CPI t n CPI t n

Using the same years as the previous example, if we wanted to see how much inflation an economy experienced from 2015 to 2020, we would simply plug the CPI for each of those years into the above equation as follows:

Inflation Rate = CPI 2020 CPI 2015 CPI 2015

Each of these equations gives us the decimal representation of the change. If we wanted to convert the value to a percentage, we would simply multiply the output by 100.

Example of CPI

Consider the gas example from the previous section where the gallon of gas you want to purchase went from $3 to $4.50. If you wanted to compute the CPI for that basket of goods, you would use the CPI equation, which is

CPI = Cost of Gas Now Cost of Gas Back Then = $ 4.50 $ 3.00 = 1.5

Example of Inflation Rate

Let’s say we had computed the CPI for the period before the jump in prices from $3 to $4.50, and it was 1.1. If we wanted to compute the inflation rate over the two different time periods, we would use the inflation rate equation, which equals

1.5 1.1 1.1 = 0.3636

Multiplying this result by 100, we get 36.36%.

Key Terms Review

Barter economy Financial instruments Monetary policy
Central banks Financial markets Money
Commodity money Income Money aggregates
Consumer Price Index (CPI) Inflation Net worth
Cryptocurrency Liquidity Regulatory agencies
Federal Reserve System M1 Store value
Fiat money M2 The Fed
Financial institutions Means of payment Unit of account
    Wealth