How far can your dollar go?

The Consumer Price Index (CPI) is an average measure of price changes over time to help determine the dollar’s purchasing power; this index is calculated by the Bureau of Labor Statistics (BLS). They define it as “…a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services” (BLS 1). In laymen’s terms the BLS picks a selection of commonly purchased goods, called a basket; the prices of each good are then weighted and averaged. When we look at changes in this measurement we can gather useful information about the dollar and its worth.

Before we do further analysis of the CPI we need to define how the BLS calculates it. They start by selecting the base year to compare our current prices to. The BLS uses an average of 1982-84’s prices as the base year for calculating the CPI.

After the base year has been established the BLS begins defining what goods are to be included in the basket. Taken directly from the BLS’ CPI page, “…[The] BLS has classified all expenditure items into more than 200 categories, arranged into eight major groups” (BLS 2).  For obvious reasons I won’t go into great detail about these categories, however a few examples of the major groups are housing, medical care, and food and beverage. Each one of these groups can be split up into sub-categories to encompass all types of consumer goods. It should also be noted that the BLS can calculate multiple CPIs by changing this basket. Since the most commonly reported measurement is the CPI-U (Consumer CPI) that will be the focus for this article. (Greenlees, McClelland 4)

The last component needed before the BLS estimates the CPI are the weights of each consumer good. It would not be enough just to include the prices in a CPI calculation as price per unit does not capture total expenditures of that product. Thus in order to truly represent spending for a given good we must assign weights. A great example is fuel; the unit price is rather small usually around \$3 to \$4; however, we usually purchase multiple units per transaction. More often than not, depending on your vehicle of choice, you will purchase between 10-30 units (gallons) at a time. The weight assigned to fuel helps capture the spending habits of the common consumer.

Once all three components are collected the BLS will use a geometric mean to calculate the CPI. Rather than going through complex functional forms it is better to run through an example adapted from the Greenlees and McClelland article. Take a single consumer in a simple economy with two goods A and B where the cost per unit is \$1. Suppose the consumer purchases two of both A and B for a total spending of \$4. If the price of A were to increase to \$4 how much would the consumer have to pay now to be just as well off as before? There are two ‘extreme’ answers to this question which are based on the consumer’s preferences. For the first scenario let’s assume that the goods are not substitutable thus the consumer must purchase the same number of A and B as before. If this were true than the consumer would need to pay \$10 total to purchase two units of each good and remain indifferent. Conversely if A and B were perfect substitutes then the consumer would cease purchasing A and buy four units of B spending \$4. As stated previously these two answers represent the extremes, in reality the answer should lay between these two values. The geometric mean serves this very purpose as it will obtain a value between these two answers. (Greenlees McClelland 6)

In the previous example the actual geometric mean calculation ends up being \$8. The CPI is reported as an index not in dollars or percent so there is one last step. Recall our consumer started off paying \$4, but ended up spending \$8 to be just as well off, thus her spending has increased by \$4 or 100%. Note by definition our base year CPI is 100 and given that our consumer must spend 100% more our new CPI is 200.

This 100% increase in the amount of money required to remain just as well off as before is actually the inflation rate. Similarly we can calculate the percent change in CPI to get the inflation rate. The graph below taken from FRED shows the CPI and the CPI’s percent change from a year ago. First let’s focus on the blue line or the index values. As mentioned before the base year for the CPI is 1982-84 so we expect the value to be 100 in this time range, a visual inspection can confirm this. What this means is that all index values we see are being compared to the average of 1982-84’s prices. The red line shows the percent change in the CPI from the past year, here is where we can glean some useful information. As stated before this percent change is actually the inflation rate for the past year. Take note from the 80’s we had very high levels of inflation, thus the percent change in the CPI is very high.

Thus far we have used the CPI to calculate inflation, but how does this affect our dollar’s purchasing power? Take for example a comparison of two individuals one had a salary of \$40,000 in 1990, and the other individual had \$60,000 in 2010. They both seek to compare whose salary has the higher purchasing power adjusted for inflation. There are two ways to approach this example, we can either inflate the salary from 1990 to 2010’s dollar value or deflate the 2010 salary to 1990’s dollar value. For this example we will inflate to 2010’s dollar value. In order to calculate this, consider the following formula:

Inflated Salary = (Salary1990 * CPI2010) / CPI1990

In our example we are given the two salaries and two years to compare. In order to inflate 1990’s value we need both the CPI from 2010 and 1990. To obtain these values we can refer back to our CPI graph from above. At the start of the year in 1990 the CPI was approximately 128 and in 2010 it was 217 therefore we get the following.

Inflated Salary = (\$40,000 * 217) / 128 = \$67812.5

From this we can say that \$40,000 in 1990 would be worth \$67,812.50 in 2010. Going back to our original example the individual making \$40,000 in 1990 was in real terms able to purchase more goods and services in 1990 than the one with \$60,000 in 2010.

The CPI calculated and published by the BLS helps individuals and businesses alike get perspective on average prices across the U.S. We can also use the index to gather information on inflation rates and purchasing power of the dollar. All of these applications help people make comparisons and informed decisions. For further examples there is a tool on BLS’ webpage to experiment with different CPI levels found at the link below.