Price Indices and Household Purchasing Power

The CPI assembles a basket of representative consumer goods and services, weighted by how much households actually spend. Because families weight things differently, one and the same wave of price changes lands differently on different pockets. A housing transaction price belongs to asset prices, not consumption; what goes into the consumption statistics for housing is the service side, paying to live somewhere.

To estimate the change in your own cost of living, hold last period's basket fixed, same items, same quality, same amounts, and reprice it at today's prices. Then compare the totals. If you move into a bigger place or add a second computer, that raises your spending too, but it's a change in your lifestyle or your quantities, and it deserves its own entry, not mixed into inflation.

A teaching example: a household spends 2,000 yuan a month on food, 3,000 on rent, 5,000 on everything else. Quantities and quality stay put; food prices rise 10%, rent rises 5%, everything else is flat. The new bill is 2,200 + 3,150 + 5,000 = 10,350, so the basket costs 3.5% more. Now take another household spending 5,000 on food, 3,000 on rent, 2,000 on the rest. The identical price moves push its total to 10,650, up 6.5%. The same price changes produce different increases in living costs because the baskets differ.

Money statistics count what exists at a moment; GDP counts production over a period. Nominal GDP values that production at current prices; real GDP strips the price movement out. Held to the same definition, the money stock times its speed of circulation corresponds to nominal output:

M × V = P × Y.

M is the money stock you've chosen, V is the velocity that goes with that stock, P is the price level of output, Y is real output. Stated across periods:

Price growth factor = money growth factor × velocity growth factor ÷ real output growth factor.

Run the numbers. Money grows 10%, real output grows 5%, velocity holds steady, and prices rise 1.10 ÷ 1.05 − 1 ≈ 4.76%. Now let velocity fall 5% over the same stretch: 1.10 × 0.95 ÷ 1.05 − 1 ≈ −0.48%. The numbers are there to display the relationship, not to forecast anything.

Subtracting GDP growth from M2 growth to guess at inflation skips velocity entirely, and you still have to know which GDP you're holding, nominal or real. Even once the output-price relation is fully drawn, the price index implied by GDP covers output broadly, while the CPI covers the consumption basket, and the two don't overlap completely. For a household, the prices that matter are the prices on the things it actually buys.

Say the basket you care about rises 3% a year, and you hold exactly 100,000 yuan in an account. Ten years on, the same money buys what 100,000 ÷ 1.03^10 ≈ 74,409 bought at the start. If after fees and tax your account earns 2% a year net, the same comparison gives 100,000 × (1.02 ÷ 1.03)^10 ≈ 90,705.

Those calculations compare one lump of money against one basket of prices. Money you keep depositing enters the record at its actual dates; the long-horizon arithmetic lives in Compounding, Fees, and Real Purchasing Power, and the tie between account balances and net wealth is in Money, Income, and Wealth.

A specific target like a house down payment gets its own tracking: the price of that house, and your progress toward it. If you borrow, the true weight depends on your income, the rate, and the monthly payment, covered in Borrowing Costs and Leverage Payoffs.

Applied version: Money Feels Like It Lasts Less, How to Measure Your Purchasing Power. Reading route: How Investment Returns Become Real Gains.