Your income over a lifetime is lumpy. It climbs, peaks, and stops at retirement. Your spending is not — you eat, heat a home and take holidays at a steady rate for decades. Reconciling a smooth consumption path with a jagged income path is one of the oldest questions in macroeconomics, and it sits early in the intermediate sequence at New York University (NYU). This page builds the two classic answers from the arithmetic up.
1 · The puzzle: smooth spending, lumpy income
Start with the benchmark you already know. The Keynesian consumption function says C = a + cY: consumption tracks current income through a fixed marginal propensity to consume c. It fits the very short run well.
It fails two obvious tests. A retiree earns almost nothing yet keeps spending. A student earns little now but borrows against a large future salary. Neither behaves as C = a + cY predicts, because neither looks only at this year’s income.
That is the puzzle. People smooth consumption across a lumpy income path; the question is how far they look ahead. Two economists gave the canonical answers: Franco Modigliani and Milton Friedman.
2 · Modigliani’s life-cycle model
The life-cycle hypothesis starts from one idea: you plan consumption over your whole remaining life, not one year at a time.
Take the cleanest case. A graduate starts work at 25, earns a flat salary for 40 years, retires at 65 and lives to 85 — 20 years of retirement. Set the interest rate to zero, with no inheritance and no bequest.
The plan has three moving parts:
- Lifetime resources. Add up every pound you will ever earn. With a flat salary Y, that is Y × 40 working years.
- A flat consumption level. Spread those resources evenly across all 60 adult years: C equals lifetime income divided by total years.
- A saving hump. While working, income exceeds C, so you save, and wealth W climbs to a peak at 65. In retirement income is zero, so you run W down — you dissave — until it reaches zero at 85.
The signature prediction: consumption is flat while wealth rises, then falls. The amount you save must equal the amount you dissave, because you begin and end with nothing. That equality is the whole model in one line.
3 · Friedman’s permanent income
Friedman reached the same place by another route. His permanent income hypothesis splits income in two. Permanent income is the steady flow you can count on — roughly, what your wealth and earning power sustain indefinitely. Transitory income is the rest: this year’s bonus, a lottery win, a bad harvest.
The claim is sharp. Consumption depends on permanent income, not transitory income. So the MPC out of a one-off windfall is small — you spread a fleeting sum thinly over the years ahead. The MPC out of a permanent raise is large, because it lifts the flow you can count on every year.
Both theories deliver the same headline. What matters is not how much your income changes, but for how long. (A corollary — that such consumers see through the timing of taxes — is the Ricardian-equivalence idea, developed on a companion page.)
Worked example — a graduate who starts work at 25
Use the clean case: flat salary Y = £30,000, 40 working years, 20 retirement years, zero interest.
Step 1 — Lifetime resources. Y × 40 = £30,000 × 40 = £1,200,000. Every pound this person will earn.
Step 2 — Flat consumption. Spread over all 60 years: C = £1,200,000 ÷ 60 = £20,000 a year.
Step 3 — The saving phase. While working, income £30,000 exceeds consumption £20,000, so annual saving is £10,000. Over 40 years, wealth climbs to a peak of £10,000 × 40 = £400,000 at age 65.
Step 4 — The dissaving phase. In retirement, income is zero but consumption stays at £20,000. Each year draws £20,000 from wealth. Over 20 years that is £20,000 × 20 = £400,000 — exactly the peak. Wealth hits zero at 85 and the budget closes.
Now perturb it. At age 45 — with 20 working years and 40 years of life still ahead — two different pieces of news could arrive.
Step 5 — A one-off windfall of £20,000. Spread it over the 40 remaining years: consumption rises by £20,000 ÷ 40 = £500 a year. The MPC is £500 ÷ £20,000 = 0.025 — one divided by the years remaining.
Step 6 — Instead, an equal-sized permanent raise: £20,000 more every working year. That adds £20,000 × 20 = £400,000 to lifetime resources. Spread over 40 remaining years, consumption rises by £10,000 a year. In the year the raise arrives, your extra income is £20,000 and you consume £10,000 of it — an MPC of 0.5.
Step 7 — The contrast. Both events put an extra £20,000 in your hands this year. The transitory windfall lifts consumption by £500; the permanent raise lifts it by £10,000 — twenty times as much. That gap is the permanent income hypothesis.
Not sure why a windfall and a permanent raise move consumption so differently? That gap — a small MPC out of a one-off, a large one out of a lasting change — is the single idea examiners test most in consumption theory. A one-on-one macroeconomics tutor works the lifetime budget and the permanent–transitory split with you until both come out cleanly. Book a trial session.
Practice
Q1. A different worker earns a flat Y = £42,000 for 35 years, then retires for 15 years. Interest is zero, with no inheritance or bequest. Find (a) their flat annual consumption and (b) their peak wealth at retirement.
Q2. A worker receives a one-off windfall of £24,000 with T = 30 years of life remaining. By how much does annual consumption rise, and what is the MPC out of the windfall?
Q3. The same worker instead receives a permanent raise of £6,000 a year for their 10 remaining working years (of the 30 years of life left). By how much does annual consumption rise, and what is the MPC out of this year’s extra income?
Answers. Q1: lifetime income £42,000 × 35 = £1,470,000; over 50 years, C = £29,400. Annual saving £42,000 − £29,400 = £12,600, so peak wealth = £12,600 × 35 = £441,000 (and £29,400 × 15 = £441,000 of drawdown — the budget closes). Q2: rise = £24,000 ÷ 30 = £800 a year; MPC = £800 ÷ £24,000 = 1/30 ≈ 0.033. Q3: extra resources £6,000 × 10 = £60,000; over 30 years, rise = £2,000 a year; MPC out of this year’s £6,000 = 1/3 ≈ 0.333 — ten times the windfall’s.
Key takeaways
- Consumption is smooth; income is lumpy. Both theories start here: people plan spending over a horizon far longer than one year.
- The life-cycle hypothesis predicts flat consumption, a saving hump during work and dissaving in retirement — saving and dissaving equal, so wealth begins and ends at zero.
- The permanent income hypothesis consumes out of permanent income, not transitory income. The MPC out of a one-off windfall is about 1 divided by the years remaining — small.
- Permanence, not size, drives the response. An equal-sized change moves consumption far more when permanent than when transitory. That is the distinction examiners test most.
Why NYU students choose our macroeconomics tutoring
- Intermediate-macro focus: sessions work through consumption theory, growth, IS–LM and the rest of the core sequence in your course’s own notation.
- The distinctions that carry marks: permanent versus transitory income, the MPC out of a windfall versus a raise, life-cycle versus Keynesian consumption — drilled until they come out cleanly under pressure.
- One-on-one and online: tutors work from your problem sets and past exams over a shared screen, so each session lands on the questions your paper will ask.
FAQ
Q: What is the difference between the life-cycle and permanent income hypotheses?
A: They share a core idea — consumption depends on lifetime resources, not current income. The life-cycle model stresses the age pattern of saving and dissaving; Friedman’s stresses splitting income into permanent and transitory parts. In practice they predict very similar behaviour.
Q: Why is the MPC out of a windfall so small?
A: Because you spread a one-off sum across all your remaining years. With 40 years left, a £20,000 windfall raises annual consumption by only £500 — an MPC of about 0.025. A permanent raise lifts every future year, so its MPC is far larger.
Q: Does the life-cycle model mean everyone dies with zero wealth?
A: In the clean version, yes — no bequests, so wealth runs down to zero. Real people leave bequests, face uncertain lifespans and hold precautionary savings, so wealth at death is usually positive. The model is a benchmark, not a forecast.
Q: How does the zero interest rate simplify things?
A: With r = 0, a pound saved today is worth a pound later, so lifetime resources are just the sum of income and C is lifetime income divided by years. Positive interest makes you discount future flows, tilting the path but leaving the smoothing logic intact.
Q: How do these theories relate to the Keynesian consumption function?
A: The Keynesian function C = a + cY ties consumption to current income with a fixed MPC. The life-cycle and permanent income theories replace current income with lifetime resources — which is why they predict different responses to permanent and transitory changes.
Book a macroeconomics tutor for New York University (NYU)
Consumption theory rewards students who keep two things straight: the lifetime budget that must close, and the gap between a permanent and a transitory change. One-on-one online sessions build both, on your course’s own past papers. Tell us your module and exam date, and we’ll match you with the right macroeconomics tutor this week.
