通货膨胀：先审计指数，再看权衡

The tax nobody voted for

• Aurora's 2021 headline read "inflation 6.0%". A tenant heard "rent up 6%". A saver watched a 5% deposit rate lose money. All three readings were about the same number — and only one was right.
• This lesson audits the index, then meets the oldest trade-off in macro.

Price a fixed basket

• The consumer price index 消费者价格指数 prices an unchanged basket: 10 loaves, one month of rent, 40 bus rides.
• The basket cost £920 last year and £975 this year: index $975/920 \times 100 = 106.0$, so inflation 通货膨胀 is 6.0% ✓.

Weights turn items into a headline

• Contributions are weighted item rates: bread $2.17\% \times 10.0 = 0.22$ points; rent $86.96\% \times 6.0 = 5.22$; bus $10.87\% \times 5.0 = 0.54$ — total $5.98 \approx 6.0$ ✓.
• So rent was 5.2 of the 6 points: the tenant's rent did NOT rise 6% "like everything" — the basket did, mostly BECAUSE of rent.

Real rates: the Fisher equation

• The Fisher equation 费雪方程: $(1 + i) = (1 + r)(1 + \pi)$, so $r = (1+i)/(1+\pi) - 1$.
• At 5% nominal and 3% inflation: $r = 1.05/1.03 - 1 = \mathbf{1.94}$% — not the naive 2%. If inflation surprises at 6%: $1.05/1.06 - 1 = -0.94$% — the saver paid for the surprise.

Jobs: read the rate properly

• The unemployment rate 失业率 = unemployed ÷ labour force, and "unemployed" requires active search.
• A falling rate can mean jobs — or discouraged workers leaving the force. Always ask what participation did.

The trade-off that expires

• The Phillips curve 菲利普斯曲线: $\pi = \pi^e - 0.8(u - 5)$ with natural rate 5%. With $\pi^e = 4$: u = 7 → 2.4; u = 5 → 4.0; u = 3 → 5.6 ✓.
• Each point of unemployment below 5 buys 0.8 of inflation — until expectations catch up and the whole line shifts. The trade-off is a lease, not a deed.

Three index slips

Recap