Price Indices, the CPI, and the Costs of Inflation
Your grandparents say a movie ticket cost 50¢ when they were kids. Today it's $\$12$. Does that mean movies got 24 times more expensive in real terms? Not exactly. The $\$12$ is a nominal price, measured in today's dollars, and almost every price went up over those years. A real price adjusts for that general rise. To compare money across years, economists need one number that tracks the price level. That number is a price index, and the most famous one is the CPI. By the end of this page you'll be able to compute it, use it to measure inflation, and explain why inflation hurts even when paychecks go up.
The CPI and the market basket
The consumer price index (CPI) measures how the cost of a typical household's purchases changes over time. The Bureau of Labor Statistics (BLS) calculates it every month.
The idea is simple. The BLS picks a market basket: a fixed list of goods and services that a typical urban consumer buys (food, rent, gas, clothes, doctor visits, streaming subscriptions…). Then it tracks what that same basket costs each year. Because the basket stays fixed, any change in its cost comes from prices, not from buying more stuff.
One year is chosen as the base year. The index in the base year is always 100.
Why multiply by 100? It makes the base year equal 100, so any other value reads like a percentage: a CPI of 115 means prices are 15% higher than in the base year.
Define the consumer price index (CPI) and the market basket it uses. Name the US government agency that calculates the CPI.
Define the consumer price index (CPI) and the market basket it uses. Name the US government agency that calculates the CPI.
A fixed market basket costs $\$200$ in the base year and $\$230$ in the current year. Compute the CPI for the current year. Show the formula you use.
A fixed market basket costs $\$200$ in the base year and $\$230$ in the current year. Compute the CPI for the current year. Show the formula you use.
A college student's market basket contains 10 burgers and 5 movie tickets. In the base year, a burger costs $\$4$ and a ticket costs $\$10$. In the current year, a…
A college student's market basket contains 10 burgers and 5 movie tickets. In the base year, a burger costs $\$4$ and a ticket costs $\$10$. In the current year, a burger costs $\$5$ and a ticket costs $\$12$. Compute the cost of the basket in each year and the CPI for the current year. Then explain in words what that CPI value means.
Inflation, deflation, and disinflation
The CPI is a level. Inflation is how fast that level is changing: a sustained rise in the overall price level.
This is just the percent change formula applied to the CPI: new minus old, divided by old.
Three words are easy to mix up:
| Term | What happens | Example |
|---|---|---|
| Inflation | The price level rises | CPI goes from 250 to 260 |
| Deflation | The price level falls (negative inflation rate) | CPI goes from 260 to 255 |
| Disinflation | Prices still rise, but the inflation rate is lower than before | Inflation drops from 6% to 4% |
The CPI was 250 last year and is 260 this year. Compute the inflation rate between the two years. State whether the economy experienced inflation, deflation, or…
The CPI was 250 last year and is 260 this year. Compute the inflation rate between the two years. State whether the economy experienced inflation, deflation, or disinflation if last year's inflation rate had been 6%.
The CPI is 200 in year 1, 210 in year 2, and 220.5 in year 3. Sophia's annual salary is $\$50{,}000$ in year 1, $\$52{,}000$ in year 2, and $\$53{,}000…
The CPI is 200 in year 1, 210 in year 2, and 220.5 in year 3. Sophia's annual salary is $\$50{,}000$ in year 1, $\$52{,}000$ in year 2, and $\$53{,}000$ in year 3. (a) Compute the inflation rate in years 2 and 3. (b) Compute Sophia's salary in each year expressed in year 1 dollars. (c) Evaluate whether her purchasing power rose or fell over the period, and explain what this tells you about comparing nominal incomes across time.
Using the CPI to compare dollars across time
A $\$52{,}000$ salary in year 2 and a $\$50{,}000$ salary in year 1 are not directly comparable, because a dollar buys less when prices rise. To compare, convert to the dollars of one year:
$$\text{value in base-year dollars} = \frac{\text{nominal amount}}{\text{CPI}} \times 100$$The CPI is 200 in year 1, 210 in year 2, and 220.5 in year 3. Sophia's annual salary is $\$50{,}000$ in year 1, $\$52{,}000$ in year 2, and $\$53{,}000…
The CPI is 200 in year 1, 210 in year 2, and 220.5 in year 3. Sophia's annual salary is $\$50{,}000$ in year 1, $\$52{,}000$ in year 2, and $\$53{,}000$ in year 3. (a) Compute the inflation rate in years 2 and 3. (b) Compute Sophia's salary in each year expressed in year 1 dollars. (c) Evaluate whether her purchasing power rose or fell over the period, and explain what this tells you about comparing nominal incomes across time.
Problems with the CPI
Because the CPI is a fixed basket, it can overstate the true rise in the cost of living.
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Substitution bias. When beef gets expensive, people buy more chicken. The fixed basket keeps counting the same beef, so it overstates how much the cost of living rose for consumers who switch to cheaper goods.
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New products and quality changes. A new phone costs more than last year's, but it may be much better. The CPI can't fully separate a pure price rise from a better product.
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New goods and outlets. New items and discount stores take time to enter the basket.
A CPI-style basket in the base year contains 10 pounds of beef at $\$5$ per pound and 10 pounds of chicken at $\$3$ per pound. In the current year, beef costs $\$8…
A CPI-style basket in the base year contains 10 pounds of beef at $\$5$ per pound and 10 pounds of chicken at $\$3$ per pound. In the current year, beef costs $\$8$ per pound and chicken costs $\$3.30$ per pound. (a) Compute the CPI for the current year using the fixed basket. (b) Consumers respond by buying only 5 pounds of beef and 15 pounds of chicken. Compute the cost of this new bundle at base-year prices and at current prices, and the price index implied by those two costs. (c) Explain what these results show about substitution bias in the CPI, and name one other reason the CPI can overstate the true change in the cost of living.
The costs of inflation
If all prices and all incomes rose by the same percent at the same time, inflation would be harmless. In practice it has costs.
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Shoe-leather costs. When money loses value quickly, people hold less cash and make extra trips to the bank. The time and effort are wasted resources.
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Menu costs. Firms must spend money to change prices: reprinting menus, updating price tags and websites. These costs are bigger when prices change often.
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Redistribution from unexpected inflation. Fixed contracts don't adjust. Unexpected inflation helps borrowers and hurts lenders and people on fixed incomes.
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Loss of the dollar as a unit of account. When prices keep shifting, it's harder to compare prices and plan.
Expected inflation can be built into contracts, so the redistribution comes mostly from unexpected inflation. The real interest rate is approximately
$$r \approx i - \pi^e$$where $i$ is the nominal interest rate and $\pi^e$ is expected inflation. After the fact, use actual inflation $\pi$ to get the actual real rate.
When inflation reaches 12% per year, a restaurant chain must reprint its menus every month, and many households make extra trips to the bank so they hold less cash that…
When inflation reaches 12% per year, a restaurant chain must reprint its menus every month, and many households make extra trips to the bank so they hold less cash that loses value. Identify which cost of inflation each of these two situations illustrates (shoe-leather costs or menu costs), and explain each one. Then explain why these costs are larger when inflation is high.
Mateo borrows from a bank at a fixed nominal interest rate of 4%. At the time, both he and the bank expected inflation of 2% over the loan period. Actual inflation turns…
Mateo borrows from a bank at a fixed nominal interest rate of 4%. At the time, both he and the bank expected inflation of 2% over the loan period. Actual inflation turns out to be 5%. Compute the expected real interest rate and the actual real interest rate. Who gains and who loses from the unexpected inflation, and why?
Back to the start: the movie ticket went from 50¢ to $\$12$ in nominal dollars, but a price index lets us strip out general inflation and compare real purchasing power across time.