Inflation, Price Indexes and Real Values
A simple price index compares a fixed basket's cost with its base-year cost, setting the base index to 100. Inflation is the percentage change in the index. Divide a nominal amount by (index / 100) to express it in base-year money. Price adjustments help compare wages across years, while a household's spending may differ from the published index basket.
What a learner can do afterwards
- Calculate a simple basket price index and the inflation rate between two years
- Convert a wage from twenty years ago into today's money and say whether it rose in real terms
- Name a reason the published index misses what a particular household actually feels
1 · Read
Inflation is a rise in the general price level. Some prices can fall while the overall level rises. Deflation is a fall in the general price level. Hyperinflation is an extreme, rapid rise in prices that quickly reduces money's buying power. One shop changing one price does not establish inflation across an economy.
For a simple index, keep basket quantities fixed. Multiply each price by its quantity, then add. Two rides at $3 each and one $4 sandwich cost $10. Later, rides cost $4 each and the sandwich still costs $4, so the basket costs $12. Index = current basket cost / base basket cost x 100. The later index is 12 / 10 x 100 = 120. Index numbers have no dollar or percent sign.
Inflation rate = (new index - old index) / old index x 100. Use the old index as the denominator, even when it is not 100. If an index rises from 150 to 156, the increase is 6. Dividing 6 by 150 and multiplying by 100 gives 4 percent inflation, not 6 percent.
Nominal pay is the money amount. Real pay adjusts for prices. With a base-100 index, real pay in base-year money = nominal pay / (index / 100). To compare percentage changes, calculate (1 + pay rise / 100) / (1 + inflation / 100). A ratio below 1 means buying power fell. Subtract 1 from the ratio and multiply by 100 to find the percentage change in buying power.
To express an old wage in current money, multiply it by current index / old index. Twenty years ago, an hourly wage was $10 at index 80. At today's index of 120, that wage equals $10 x 120 / 80 = $15 in today's money. A current wage of $16 buys more than that old wage, before tax.
Unexpected inflation reduces the real value of loan payments fixed in money. The borrower repays less buying power than expected; the lender receives less. This does not guarantee an easier budget if the borrower's income fails to keep up. Savings lose buying power when their nominal return is below inflation. Deflation increases cash's buying power and the real value of payments fixed in money.
A consumer price index represents its covered population's spending. A household spending more of its budget on rapidly rising rent can face faster bill increases. Spending shares give some prices more weight. A fixed basket can overstate the cost of maintaining a living standard when shoppers switch to cheaper alternatives. Official methods may adjust for this substitution.
Calculate inflation from the old index. Adjust wages for prices before comparing buying power. A household's spending may differ from the index basket.
Lesson, questions, worked solutions and flashcards written for this dataset. OpenStax inflation material was consulted for facts and teaching structure.
Readings and flashcards written for this dataset, with OpenStax material consulted for facts and teaching structure. Video references identify Khan Academy material on YouTube. Video license terms have not been verified.
More to read
A price change and a price level
A shop's price tag describes one product. A broad price index combines prices across many goods and services. Those two measures need not move in the same direction. Computers might become cheaper while the combined price level rises.
Inflation is an increase in the general price level. Deflation is a decrease. A fixed amount of cash loses buying power during inflation and gains buying power during deflation.
Loan payments can also be fixed in money. When prices fall, those payments represent more buying power. When prices rise unexpectedly, they represent less buying power than the borrower and lender expected. Neither result tells us everything about the borrower's budget, since income and other expenses may change too.
Hyperinflation is an extreme, rapid increase in the general price level. Holding cash becomes costly because its buying power falls very quickly. An isolated price increase does not establish hyperinflation or general inflation.
Calculate the basket, then the rate
Choose basket quantities before comparing prices. At each date, multiply every price by its quantity and add the results. Keeping the quantities fixed lets the comparison isolate price changes.
Suppose the basket costs $40 in the base year and $48 later. Setting the base index to 100 gives a later index of 48 / 40 x 100 = 120. The number 120 has no money unit or percent sign. It says this basket costs 20 percent more than in the base year.
For inflation between any two dates, use (new index - old index) / old index x 100. A move from 160 to 168 is an increase of eight index points, but the inflation rate is 8 / 160 x 100 = 5 percent.
A fixed basket also has limits. Shoppers may switch to cheaper alternatives when prices change. Keeping the original basket can then overstate the increase in the cost of maintaining their living standard. Published index methods may make substitution adjustments.
Put wages into comparable money
An hourly wage tells you the money paid for an hour of work. To compare its buying power across years, you also need a price index.
One approach expresses both wages in base-year money. With an index based at 100, divide each nominal wage by its year's index divided by 100.
Another approach converts the earlier wage into later-year money. Multiply the earlier wage by the later index divided by the earlier index. An old wage of $12 at index 90 equals $18 when the index reaches 135, because 12 x 135 / 90 = 18. Compare the later wage with $18 to judge its buying power before tax.
For percentage increases, divide the wage growth factor by the price growth factor. If the result is below one, real hourly pay fell.
The index used also matters. A published consumer index represents spending across its covered population. A household that spends a different share on rent or transport may experience different changes in its own bills.
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