Spend £1bn on a railway and national income rises by more than £1bn. Not magic — arithmetic. And running in reverse, the same arithmetic turns a downturn into a slump.
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When a household receives an extra pound, it either spends it (keeping it circulating in the domestic economy) or it leaks out. The propensities measure the split.
Whose pound matters. Low-income households have a high MPC (they must spend); rich households have a lower MPC and a higher MPS. This is why a £1bn tax cut aimed at the poorest injects far more spending than the same sum given to the richest — and why benefits and the minimum wage have large multiplier effects.
Household income rises by £500. The household spends £400 of it.
MPC = ΔC ÷ ΔY = 400 ÷ 500 = 0.8 → MPW = 1 − 0.8 = 0.2
An injection into the circular flow does not stop where it lands. The £100m paid to construction workers becomes their income; they spend a fraction of it (the MPC), which becomes someone else's income; who spends a fraction of that... Each round is smaller (because of leakages), but the total is a multiple of the original injection.
MPC = 0.8. Then k = 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5.
A government injection of £200m raises national income by 200 × 5 = £1,000m (£1bn).
Check the rounds: 200 + 160 + 128 + 102.4 + ... The infinite sum converges on exactly £1,000m. ✅
MPS = 0.1, MPT = 0.25, MPM = 0.15. Then MPW = 0.1 + 0.25 + 0.15 = 0.5.
k = 1 ÷ 0.5 = 2. A £300m injection raises national income by 300 × 2 = £600m.
The multiplier works in reverse too. A withdrawal (a spending cut, a tax rise, a collapse in exports) is multiplied downwards: this is why austerity in a slump can shrink national income by more than the cut itself, and why recessions gather momentum.
What makes the multiplier LARGE: a high MPC (low leakages), plenty of spare capacity (so extra demand raises output rather than prices), and a closed-ish economy. What makes it SMALL: high taxes, a high propensity to import (a big leakage in an open economy like the UK), high savings, an economy near full capacity, and crowding out if government borrowing raises interest rates.
The accelerator says that the level of investment depends not on the level of national income but on its RATE OF CHANGE.
The logic: firms hold a desired capital-output ratio. If demand is rising, they need more capital, so they invest. If demand is still rising but more slowly, they need less new capital than before — so investment falls even though income is still rising. That counter-intuitive result is the whole point.
A firm needs £2 of capital for every £1 of annual output (a capital-output ratio of 2).
Year 1: output rises by £50m → required net investment = 2 × 50 = £100m.
Year 2: output rises by only £20m → required net investment = 2 × 20 = £40m.
Output is still growing, but investment has collapsed by 60%. A slowdown in growth produces an absolute fall in investment — this is how booms turn to busts.
Multiplier-accelerator interaction: an injection raises income (multiplier) → rising income triggers investment (accelerator) → that investment is itself an injection, raising income further (multiplier again). The upswing feeds itself. But once growth merely slows, investment falls, which through the multiplier cuts income, which through the accelerator cuts investment further — and the boom turns into a slump. This interaction is the standard explanation of the economic cycle.
Limitations of the accelerator: it assumes a fixed capital-output ratio; it ignores spare capacity (a firm with idle machines needs no new ones however fast demand grows); investment takes time to plan and build; and it ignores expectations, credit conditions and business confidence. Real investment is lumpier and slower than the model implies.
The economic (trade) cycle is the fluctuation of actual output around the trend rate of growth. Four phases:
Causes of the cycle: the multiplier-accelerator interaction; swings in confidence and "animal spirits"; the credit cycle (banks lend freely in booms and freeze in busts); external shocks (oil, pandemics, wars); policy errors; and inventory cycles.
Consequences of a large negative output gap: lost output that can never be recovered; hysteresis — the long-term unemployed lose skills and attachment to the labour force, so LRAS itself shifts left and the damage becomes permanent; lower investment shrinks the future capital stock; falling tax revenue and rising benefit spending worsen the budget deficit.
Consequences of a positive output gap: demand-pull inflation; labour shortages and wage spirals; a widening current account deficit as imports are sucked in; unsustainable asset bubbles.
Tap a card, then tap where it belongs in the multiplier story.
Tap an item on the left, then its partner on the right.
MPC + MPW = 1. MPW = MPS + MPT + MPM. Every extra pound is spent at home or leaks out.
k = 1 / (1 − MPC) = 1 / MPW. ΔY = injection × k. Bigger leakages → smaller multiplier.
It works in reverse. A spending cut is multiplied downwards — the core case against austerity in a slump.
The accelerator. Investment depends on the RATE OF CHANGE of income. A slowdown in growth causes an absolute FALL in investment.
Multiplier × accelerator = the cycle. They feed each other on the way up and on the way down.
Hysteresis. A deep recession can shift LRAS LEFT permanently — the damage is not just cyclical.
You've now covered the multiplier and the accelerator from the OCR A-level Economics (H460) specification. Press Finish to see your score.
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