Measuring Price Levels and Inflation

• Food and beverages
• Housing
• Apparel
• Transportation
• Medical care
• Recreation
• Education and communication
• Other goods and services

The Role of the Base Year

To compare prices across different years, economists select a base year to serve as a benchmark or point of reference. The CPI for the base year is always set to $100$. This makes it very easy to see percentage changes in subsequent years. For example, if the CPI in a later year is $150$, you immediately know that prices have risen by $50%$ compared to the base year.

Calculating the CPI

To determine the CPI for any given year, you compare the cost of the market basket in that year to the cost of the same basket in the base year using this formula:

$\text{CPI} = \left( \frac{\text{Price of market basket in current year}}{\text{Price of market basket in base year}} \right) \times 100$

Exam Tip: If you are asked to identify the base year in a data set, look for the year where the CPI is exactly $100$.

Measuring Inflation

Inflation is defined as an increase in the price level. While the CPI tells us the level of prices, the inflation rate tells us the speed at which those prices are rising. Specifically, the inflation rate is the positive percentage change in the price level over a specific period.

To calculate the inflation rate between two years, use the following formula:

$\text{Inflation Rate} = \left( \frac{\text{CPI}_{\text{later year}} - \text{CPI}_{\text{earlier year}}}{\text{CPI}_{\text{earlier year}}} \right) \times 100$

Worked Example: Calculating Inflation

Suppose the CPI in 2010 was $218$ and the CPI in 2016 was $241$. To find the inflation rate:

1. Subtract the earlier CPI from the later CPI: $241 - 218 = 23$
2. Divide that difference by the earlier CPI: $\frac{23}{218} \approx 0.1055$
3. Multiply by $100$ to get the percentage: $10.55%$

Nominal vs. Real Income

Understanding inflation is vital for understanding your own financial health. Economists distinguish between two types of income:

1. Nominal Income: The current dollar amount of a person's income (the number written on your paycheck).
2. Real Income: Nominal income adjusted for price changes. This represents your actual purchasing power—what you can actually buy with your money.

If your nominal income increases by $3%$, but the inflation rate is $5%$, your real income has actually decreased. You are making more dollars, but those dollars buy fewer goods and services than they did before.

Converting Dollars Across Time

If you want to compare how much a salary from the past is worth in today's terms, you can use the ratio of the two CPIs:

$\text{Salary in current dollars} = \text{Salary in earlier year} \times \left( \frac{\text{CPI}_{\text{current year}}}{\text{CPI}_{\text{earlier year}}} \right)$

Example: If you earned $$10,000$ in 1960 and the CPI in 1960 was $29.6$, while the CPI in 2016 was $241.353$, your 1960 salary in 2016 dollars would be: $\$10,000 \times \left( \frac{241.353}{29.6} \right) = \$81,538$ This tells us that to have the same purchasing power in 2016 that $$10,000$ provided in 1960, you would need to earn $$81,538$.

Summary Checklist

• Price Level: The average price of all goods/services.
• CPI: The tool used to measure the price level via a market basket.
• Inflation: The rate at which the price level increases.
• Real Income: Your income after accounting for inflation.