Your grandfather bought a movie ticket for 50 cents. You paid $16. Is film sixteen times more valuable now — or is the dollar just smaller? Inflation is the shrinking of the measuring stick itself, which is why it corrupts every naive comparison across time: wages, interest rates, GDP, your allowance. This lesson builds the tool that re-standardizes the stick (the CPI), the vocabulary that separates real from nominal, and the surprisingly precise accounting of who gets hurt when prices rise unexpectedly — and who quietly benefits. Spoiler: if you owe money at a fixed rate, inflation is your friend.
The Consumer Price Index tracks the cost of a fixed market basket of goods a typical urban consumer buys.
CPI = (cost of basket in current year ÷ cost of basket in base year) × 100
The base year's CPI is always 100.
Inflation rate = [(CPI₂ − CPI₁) ÷ CPI₁] × 100
Apply It: Basket costs $200 in the base year, $250 this year. CPI now? → 125. If next year's CPI is 130, the inflation rate between those years = (130 − 125)/125 = 4%.
Vocabulary triple: - Inflation: price level rising. - Disinflation: price level rising more slowly (inflation falls from 6% to 3% — prices still rising!). - Deflation: price level actually falling (inflation negative).
CPI's known biases (it tends to overstate true inflation): substitution bias (the fixed basket ignores consumers switching to cheaper alternatives), new-product bias (baskets update slowly), and quality-change bias (a pricier but better phone isn't pure inflation). The GDP deflator (Lesson 2) differs by covering all domestically produced goods, not a fixed consumer basket.
Real value = nominal value ÷ (price index/100)
Real income tells you what your paycheck actually buys. If your salary rises 4% while inflation runs 6%, your real income fell ~2% — you got a pay cut wearing a raise costume.
The Fisher relationship (memorize):
Real interest rate ≈ nominal interest rate − inflation rate
A 7% CD during 5% inflation yields 2% real. Lenders set nominal rates as: desired real return + expected inflation. This little equation is the hinge for the winners/losers analysis — and it returns in Lessons 10–11 as the bridge between the money market (nominal) and loanable funds (real).
The key word is unanticipated — inflation that surprises. (Perfectly anticipated inflation gets built into contracts and mostly just imposes nuisance costs.)
| Hurt by surprise inflation | Helped by surprise inflation |
|---|---|
| Lenders/savers at fixed rates (repaid in shrunken dollars) | Borrowers at fixed rates (repay with cheaper dollars) |
| Workers with fixed wages / fixed-income retirees | Employers who locked in those wages |
| Holders of cash | Governments with large fixed-rate debt |
If inflation comes in below expectations (or turns to deflation), flip every row: lenders win, borrowers lose.
Even anticipated inflation has real costs: menu costs (repricing everything), shoe-leather costs (economizing on cash holdings), and distorted price signals.
Apply It: You borrow at a fixed 6% expecting 2% inflation (expected real cost 4%). Inflation turns out to be 7%. Your realized real rate = 6 − 7 = −1% — the lender effectively paid you to borrow.
M × V = P × Y
where M = money supply, V = velocity (how many times a dollar turns over per year), P = price level, Y = real output. If V and Y are stable, growth in the money supply translates directly into growth in the price level — the classical explanation of sustained inflation ("too much money chasing too few goods"). This equation resurfaces in Lessons 9–10 and 13 as the long-run anchor: printing money faster than output grows ultimately buys inflation, not output.
Apply It: M = $4 trillion, V = 5, Y = 10 trillion units of real output. Price level? → P = MV/Y = 20/10 = 2.0. If M doubles with V, Y fixed → P doubles.
No new curve today — but a numerical exhibit the AP loves:
[GRAPH/TABLE: CPI Timeline
X-axis: Year (1, 2, 3, 4)
Y-axis: CPI (100, 110, 121, 118.6)
Annotations: Year 1→2: inflation 10%; Year 2→3: inflation 10%;
Year 3→4: inflation −2% (deflation)
Reading: a RISING CPI = inflation; a rising-but-flattening CPI = disinflation;
a FALLING CPI = deflation. The price LEVEL and the inflation RATE are
different objects — one is a stock of accumulated increases, the other a speed.]
AP labeling requirements: when the exam shows a CPI table, it asks for the inflation rate between two specific years — always divide by the earlier year's CPI, and never subtract index points and call the difference a percentage (121 − 110 = 11 points but 10%). When a price-level graph appears in AD-AS form (Lesson 7), inflation = the equilibrium price level rising between equilibria.
1. E. CPI = 650/500 × 100 = 130. A: uses a $100 basket assumption. B: inverts the ratio (500/650 ≈ 77 is C's error too, differently scaled). C: base ÷ current, upside down. D: subtracts then misscales.
Fix: CPI = (current ÷ base) × 100 — current on top, always.
2. C. (147 − 140)/140 = 7/140 = 5%. A: uses the 7-point change as a percent. B: divides by 147 (the ending CPI). D/E: arithmetic slips.
Fix: Inflation = index change ÷ starting index — points are not percent.
3. A. Falling rate of still-positive inflation = disinflation. B/D: deflation needs a negative rate/falling level — 4% is still rising prices. C: stagflation is high inflation plus high unemployment (and isn't described). E: real income isn't addressed.
Fix: Check the sign of the inflation rate: positive-but-smaller = disinflation; negative = deflation.
4. D. Real wage change ≈ 3% − 5% = −2%. A: nominal ≠ real. B: added instead of subtracted. C: subtracted backwards. E: unchanged would need equal rates.
Fix: Real change ≈ nominal change − inflation; a raise below inflation is a real pay cut.
5. B. Realized real = 6 − 5 = 1%. A: uses expected inflation (that's the expected real rate). C: added. D: subtracted 7 (misread). E: splits the difference.
Fix: Expected real uses expected inflation; realized real uses actual — keep the two calculations separate.
6. C. The borrower repaid with dollars worth less than either side expected; the bank's real return fell from 4% expected to 1%. A: unchanged nominal repayment is exactly why the bank lost in real terms. B: surprise inflation is a zero-sum transfer, not neutral. D/E: unrelated or backwards.
Fix: Surprise inflation transfers real wealth from fixed-rate lenders to fixed-rate borrowers.
7. E. Fixed nominal pensions buy less as prices rise — the textbook victim. A/D: fixed-rate borrowers gain. B: firms that locked in wages pay workers in shrinking dollars — the firms gain. C: governments with fixed-rate debt repay in cheaper dollars — they gain.
Fix: Find who receives fixed nominal payments (they lose) and who owes them (they win).
8. A. Substitution bias: real consumers dodge price hikes; the frozen basket can't. B: describes the GDP deflator's coverage, not the CPI. C: it's computed continuously. D: quality changes are imperfectly captured — and that failure biases CPI up, the reverse of "fully captured." E: CPI includes consumer imports.
Fix: Fixed basket = no substitution = overstated inflation; remember substitution, new-product, and quality biases.
9. D. With V, Y pinned, %ΔM ≈ %ΔP: 10% money growth → ~10% price growth. A: Y was held constant by assumption. B: V constant too. C: direction reversed. E: nominal GDP (PY) rises with P.
Fix: In MV = PY with V, Y fixed, money growth passes one-for-one into the price level.
10. B. P = MV/Y = (2 × 6)/8 = 12/8 = 1.5. A: inverted (8/12). C: forgot to divide. D/E: arithmetic slips.
Fix: Solve P = MV/Y mechanically; write the equation before plugging numbers.
11. A. A falling CPI (120 → 117) is a falling price level: deflation. B: disinflation. C: inflation. D: nominal outpacing real signals inflation. E: that's just any positive-inflation year.
Fix: Deflation = the index actually declines — look at the level's direction, not the rate's.
12. C. Menu costs and shoe-leather costs survive even perfect anticipation. A: anticipated inflation is priced into rates — no systematic transfer. B: wages renegotiate to expectations. D: no such requirement. E: anticipated inflation triggers COLAs and adjusted contracts for those who can index.
Fix: Anticipation kills the transfers but not the friction costs (repricing, cash management).
13. D. Real wage = nominal − actual inflation; with inflation 2 points below expectation, workers' real wage exceeds the intended level — the surprise ran in labor's favor. A: backwards. B: real wages rose, hurting employers. C: voluntariness doesn't immunize against forecast errors. E: fixed contracts don't auto-adjust — that's the point.
Fix: Below-expected inflation reverses the usual story: fixed-payment receivers win, payers lose.
The nation of Corvia uses a CPI with base year 1. The basket: 10 pizzas and 4 backpacks.
| Price of pizza | Price of backpack | |
|---|---|---|
| Year 1 | $8 | $30 |
| Year 2 | $9 | $33 |
(a) Calculate the cost of the market basket in Year 1 and in Year 2. Show your work.
(b) Calculate the CPI in Year 2 and the inflation rate between Year 1 and Year 2. Show your work.
(c) Rina lent money in Year 1 at a fixed nominal interest rate of 9%, expecting the Year 2 inflation you calculated to be only 5%. (i) Calculate the real interest rate Rina expected. (ii) Calculate the real interest rate Rina actually received. (iii) Did the inflation surprise benefit Rina or her borrower? Explain.
(d) Corvia's central bank claims that, with velocity and real output fixed, limiting money-supply growth to the growth rate of real output would achieve approximately zero inflation. Use the quantity theory of money to explain the claim.
1. E. CPI = 650/500 × 100 = 130. A: uses a $100 basket assumption. B: inverts the ratio (500/650 ≈ 77 is C's error too, differently scaled). C: base ÷ current, upside down. D: subtracts then misscales. Fix: CPI = (current ÷ base) × 100 — current on top, always.
2. C. (147 − 140)/140 = 7/140 = 5%. A: uses the 7-point change as a percent. B: divides by 147 (the ending CPI). D/E: arithmetic slips. Fix: Inflation = index change ÷ starting index — points are not percent.
3. A. Falling rate of still-positive inflation = disinflation. B/D: deflation needs a negative rate/falling level — 4% is still rising prices. C: stagflation is high inflation plus high unemployment (and isn't described). E: real income isn't addressed. Fix: Check the sign of the inflation rate: positive-but-smaller = disinflation; negative = deflation.
4. D. Real wage change ≈ 3% − 5% = −2%. A: nominal ≠ real. B: added instead of subtracted. C: subtracted backwards. E: unchanged would need equal rates. Fix: Real change ≈ nominal change − inflation; a raise below inflation is a real pay cut.
5. B. Realized real = 6 − 5 = 1%. A: uses expected inflation (that's the expected real rate). C: added. D: subtracted 7 (misread). E: splits the difference. Fix: Expected real uses expected inflation; realized real uses actual — keep the two calculations separate.
6. C. The borrower repaid with dollars worth less than either side expected; the bank's real return fell from 4% expected to 1%. A: unchanged nominal repayment is exactly why the bank lost in real terms. B: surprise inflation is a zero-sum transfer, not neutral. D/E: unrelated or backwards. Fix: Surprise inflation transfers real wealth from fixed-rate lenders to fixed-rate borrowers.
7. E. Fixed nominal pensions buy less as prices rise — the textbook victim. A/D: fixed-rate borrowers gain. B: firms that locked in wages pay workers in shrinking dollars — the firms gain. C: governments with fixed-rate debt repay in cheaper dollars — they gain. Fix: Find who receives fixed nominal payments (they lose) and who owes them (they win).
8. A. Substitution bias: real consumers dodge price hikes; the frozen basket can't. B: describes the GDP deflator's coverage, not the CPI. C: it's computed continuously. D: quality changes are imperfectly captured — and that failure biases CPI up, the reverse of "fully captured." E: CPI includes consumer imports. Fix: Fixed basket = no substitution = overstated inflation; remember substitution, new-product, and quality biases.
9. D. With V, Y pinned, %ΔM ≈ %ΔP: 10% money growth → ~10% price growth. A: Y was held constant by assumption. B: V constant too. C: direction reversed. E: nominal GDP (PY) rises with P. Fix: In MV = PY with V, Y fixed, money growth passes one-for-one into the price level.
10. B. P = MV/Y = (2 × 6)/8 = 12/8 = 1.5. A: inverted (8/12). C: forgot to divide. D/E: arithmetic slips. Fix: Solve P = MV/Y mechanically; write the equation before plugging numbers.
11. A. A falling CPI (120 → 117) is a falling price level: deflation. B: disinflation. C: inflation. D: nominal outpacing real signals inflation. E: that's just any positive-inflation year. Fix: Deflation = the index actually declines — look at the level's direction, not the rate's.
12. C. Menu costs and shoe-leather costs survive even perfect anticipation. A: anticipated inflation is priced into rates — no systematic transfer. B: wages renegotiate to expectations. D: no such requirement. E: anticipated inflation triggers COLAs and adjusted contracts for those who can index. Fix: Anticipation kills the transfers but not the friction costs (repricing, cash management).
13. D. Real wage = nominal − actual inflation; with inflation 2 points below expectation, workers' real wage exceeds the intended level — the surprise ran in labor's favor. A: backwards. B: real wages rose, hurting employers. C: voluntariness doesn't immunize against forecast errors. E: fixed contracts don't auto-adjust — that's the point. Fix: Below-expected inflation reverses the usual story: fixed-payment receivers win, payers lose.
Exam tip: Three formulas do all the work: CPI = current/base × 100; inflation = ΔCPI/old CPI; real ≈ nominal − inflation. The conceptual questions all reduce to one sorting task — who's locked into fixed nominal payments, and did inflation surprise up or down? Sort the players; the answer falls out. Next lesson we start building the course's flagship graph: aggregate demand.