Your Balance Versus Your Buying Power

How much can your paycheck buy?

Suppose you receive $500 a week. One basket of groceries costs $100. Divide your pay by the basket price: $500 ÷ $100 = 5 baskets.

Later, the same groceries cost $125. Your pay stays at $500. Now $500 ÷ $125 = 4 baskets. Your paycheck covers one fewer basket.

The price rose by $25. Compare that with the starting $100: 25 ÷ 100 = 0.25, or a 25 percent price increase.

Your buying power fell by one basket out of the five you could buy before. 1 ÷ 5 = 0.20, or a 20 percent drop. The percentages differ because one starts with the old price and the other starts with your old buying power.

Now suppose your pay rises to $625. $625 ÷ $125 = 5 baskets. You have more dollars, but they buy the same amount as before. These are made-up numbers to show the steps.

The dollar amount is your nominal income. What it can buy is your real income. A raise improves your buying power only if your pay grows faster than the prices you face. If both rise at the same rate, you keep up.

One price does not tell the whole story

A poor harvest may leave fewer oranges for sale, pushing their price up. That tells us about oranges. It does not tell us what happened to bread, rent, or bus fares.

A broad rise in prices over time is called inflation. Some prices can fall while the average rises.

Prices may rise when shoppers want more than businesses can supply, or when a shortage leaves less to buy. Changes in money and borrowing can also give people more to spend. Expectations matter too: a shop expecting higher costs may raise prices, while workers expecting higher bills may ask for more pay.

One shopping trip cannot tell us which forces caused a price rise. Nor does every household face the same bills. A family paying for childcare may see different increases from a family without that cost.

The Consumer Price Index, or CPI, tracks prices across a broad mix of goods and services. Think of a large shopping basket that includes things like rent and haircuts. It represents common spending, not every family’s exact shopping list.

What does 200 to 210 mean?

The US Bureau of Labor Statistics, or BLS, collects prices and spending information to produce the CPI. A main version is CPI-U, which covers urban consumers.

It combines many price changes into a number called an index. This gives us a common scale for comparing prices over time. The index number is not a dollar price or an inflation rate.

Suppose a made-up index rises from 200 to 210. That is a rise of 10 points. Compare the rise with the starting number: 10 ÷ 200 = 0.05. Multiply by 100 to get 5 percent. A rise of 10 points is not necessarily a rise of 10 percent.

You can also divide the new number by the old one: 210 ÷ 200 = 1.05. Subtract 1 to leave the increase, then multiply by 100. Written in one line: inflation rate = (new index ÷ old index − 1) × 100.

Use the same type of index for both numbers. Comparing two months gives the change between those months. Comparing the same month a year apart gives the twelve-month change.

What about your $500 paycheck? In this example, prices are now 1.05 times as high. Divide your pay by 1.05: $500 ÷ 1.05 = about $476.19. The same calculation is $500 × 200 ÷ 210 = about $476.19.

Today’s $500 therefore buys about what $476.19 bought before, using this index. No money has left your account. We have changed the price scale to make a fair comparison. Your own bills may rise at a different rate.

Start with two tubs of ice cream

Let’s build a tiny index. Imagine buying one tub of brand A and one tub of brand B. Both stay the same size and quality. At $10 each, the basket costs $10 + $10 = $20.

Brand A then rises to $12, while B stays at $10. Buying one of each now costs $12 + $10 = $22. These prices are made up.

Divide the new cost by the old cost: $22 ÷ $20 = 1.10. The basket costs 10 percent more. If the starting index is 100, the new index is 100 × 1.10 = 110.

We kept the shopping list and quantities the same. For a larger basket, price those same quantities at the new prices. Add the costs, divide by the old total, then multiply by 100.

Each brand made up half our starting spending. That share is called its weight. A larger share counts more in the total. This small example helps explain baskets and weights; the official CPI has more steps.

How the official CPI puts prices together

Imagine collecting prices for several ice-cream products in one city area. First, BLS combines them into a result for that small group. Then it combines the groups into the wider index.

First, measure each group. Most groups use an average that allows for shoppers switching between similar products as prices change. It is called a geometric mean. We will work through an ice-cream example below.

Some groups, including certain utilities and medical services, use a different method. It keeps estimated quantities fixed while prices change. That method is called modified Laspeyres.

Next, combine the groups. Spending surveys show how much people spend in each category and area. A category that takes more of the budget gets more weight. Think of your own bills: a 10 percent rise in rent matters more than a 10 percent rise in something you rarely buy.

CPI-U combines these groups using modified Laspeyres. It keeps the estimated quantities fixed between weight updates. Their share of spending can still change as prices change. So the whole CPI-U is not one geometric average of every price.

BLS also tries to compare the same quality over time. If a product improves, some of its higher price may pay for that improvement. BLS tries to separate this from the price rise it is measuring.

1983 and 1985: measuring the cost of a home

A home you own is both an asset you could sell and a place to live. Its sale price and the cost of having a place to live are different things.

The older CPI included home purchases, mortgage interest, property taxes, insurance, and repairs. BLS changed this part of the index to ask: what would a similar home cost to rent? That helps measure the housing service the owner receives.

This approach is called rental equivalence. It started in January 1983 for CPI-U and January 1985 for CPI-W, which covers urban wage earners and clerical workers. These were two start dates for the same reform.

For owners living in their homes, the measure is called owners’ equivalent rent, or OER. It estimates rental value; it does not mean owners actually pay rent.

Spending surveys help set housing’s weight in the index. Rents observed at rental homes help measure its price change. The monthly change is not simply owners guessing what rent would be.

Housing was not removed from CPI. Rent and OER still form a major part of it. Home sale prices and mortgage interest are no longer directly counted as spending on the housing service. Your mortgage bill still matters to your budget; this measure answers a different question.

1999: two ways to average the prices

Our ice cream still costs $12 for A and $10 for B. Buying one of each costs $22. But a shopper might choose more B and less A after A becomes more expensive.

In January 1999, BLS began using geometric means in most basic groups. This allows for switching between similar products within a category. It does not track every shopper or mean replacing steak with hamburger across separate categories.

Let’s compare the two methods. First divide each new price by its old price: 12 ÷ 10 = 1.2 for A and 10 ÷ 10 = 1.0 for B. The first rose 20 percent; the second did not change.

Keep buying one of each. Both brands had half the starting spending. Give each number half the weight: 0.5 × 1.2 + 0.5 × 1.0 = 1.10. Subtract 1, then multiply by 100: (1.10 − 1) × 100 = 10 percent. This is the arithmetic average, matching our basket’s rise from $20 to $22.

Allow for switching brands. With equal starting weights, the geometric average multiplies the two numbers: 1.2 × 1.0 = 1.2. Then take the square root on a calculator. That means finding the positive number that gives 1.2 when multiplied by itself.

The answer is about 1.095445. Subtract 1 and multiply by 100: (1.095445 − 1) × 100 = about 9.54 percent.

The first method keeps quantities fixed. The second keeps spending shares fixed and allows quantities to change. Both use the same prices, including A’s higher price. Neither makes the shop charge less.

These are small examples within one group, not the full US CPI calculation. The difference is not something to subtract from every inflation report.

In its 1998 announcement, BLS estimated that the coming change would lower annual CPI growth by about 0.2 percentage point. For example, 3.0 percent to 2.8 percent is a difference of 0.2 point. That was a research estimate at the time, not a fixed deduction from every later report.

2002 and 2023: keeping up with how people spend

People can switch brands within one group. They can also change how much of their budget goes to different groups. A separate measure called chained CPI-U, or C-CPI-U, tries to capture that wider change.

BLS introduced it in August 2002 alongside CPI-U. It did not replace CPI-U.

The final chained calculation uses spending shares from both months being compared. Suppose a category took 20 percent of spending before and 18 percent after. Its average share is (20 + 18) ÷ 2 = 19 percent. The calculation uses that share to give the category its weight.

This method is called Törnqvist. Each month’s result links to the next, which explains “chained.” BLS needs later spending information to finish the calculation, so early estimates can be revised.

A different change began in January 2023. CPI-U and CPI-W started updating spending weights every year instead of every two years. The 2023 update used 2021 spending; the earlier weights used 2019 and 2020 spending. These dates describe that update, not today’s weights.

Annual updates give CPI more recent shopping patterns. They do not turn CPI-U into chained CPI. And CPI has changed more than twice: the housing reform, the 1999 averages, the separate chained index, and yearly weight updates do different jobs.

Inflation still means a broad rise in consumer prices. These changes affect how it is measured. They do not change what your shop or landlord charges.

Small price rises add up

A $100 grocery basket rises by 2 percent in a year. It now costs $100 × 1.02 = $102.

The next 2 percent rise applies to $102, not the old $100: $102 × 1.02 = $104.04. Each increase builds on the last. This is called compounding.

After ten years at that rate, the basket costs about $121.90. Your $100 buys about 82 percent of it: $100 ÷ $121.90 is about 0.82. This is a made-up example, not a forecast.

Now suppose prices first rise 5 percent, taking the basket from $100 to $105. Then inflation slows to 2 percent. Prices are still rising: $105 × 1.02 = $107.10. Slower inflation does not mean prices return to where they started.

No dollars need to leave your account for their buying power to fall. People sometimes call this a “hidden tax.” It is a comparison, not a claim that every price rise is money paid to the government.

Give your money a job

The baker needs flour tomorrow, money for unexpected repairs, and a better oven later. Those are three different jobs for her money.

Money for tomorrow’s flour cannot wait for an investment to recover from a fall. The bill is due now, even if the investment might grow over several years.

She has 100 units. Set aside 30 for flour and 20 for repairs: 100 − 30 − 20 = 50. Only 50 remains without a job. The whole 100 is not free to invest.

Rising prices give her a reason to plan, but do not pick an investment for her. A token with a fixed supply can still fall in price. Can she sell or use it in time? Will the miller accept the payment? Will it buy enough flour?

Borrowing needs care too. If the dollars you owe stay fixed while prices rise, that debt may shrink in buying-power terms. But payments are still due, and your pay may not rise. A changing interest rate, fees, or a lost job can make repayment harder.

Inflation alone does not make a loan a good idea. Check the terms and your income. For any money decision, ask what the money is for, when you need it, and what it must buy.

Review: the baker’s money

The baker sells bread, then uses the money to buy flour. Her bread buyer does not also have to be a miller. Money connects the trades so each person can focus on their work. The bread and flour still have to be made.

Of her 100 units, 30 is for flour and 20 for repairs. That leaves 50. An oven costing 80 is still out of reach unless she takes money from those other jobs.

A seller says a scarce token will buy the oven later. But its supply rule cannot tell her whether people will want it then or whether its price will fall. She must also check selling fees and anything that could block access when she needs the money.

Review: what do you own?

A stone on Yap could get a new owner without moving. Ownership changed; its location did not.

A bank payment changes records too. After an approved payment, one balance falls and another rises. The bank keeps the records. A stranger should not be able to order that change without permission.

A gold receipt can change hands while the gold stays in a vault. The new holder has a claim on the keeper’s promise to hand over gold.

Also remember the bank with valuable loans but too little cash for withdrawals today. Having enough value overall does not mean having ready cash now.

Ask: who owns what, who keeps the record, and does anyone owe the holder something? These answers matter more than what the money looks like.

Review: choose for the job

Money may last well but be hard to carry. A bank balance may be easy to spend but rely on the bank completing the payment. A scarce asset can still have a price that moves sharply. The right questions depend on the job and deadline.

If something used as money becomes easier to make, its supply may grow and it may become less scarce. Prices also depend on demand, acceptance, goods for sale, and how the new money reaches people. More money does not cause the same percentage rise in every price.

Finally, remember your paycheck: $500 buys five $100 baskets, or four $125 baskets. Your balance and the price together tell you what you can afford.