National Income and the Multiplier

The circular flow of income tracks a single fact three different ways: households supply land, labour, capital and enterprise to firms and receive income (wages, rent, interest, profit) in return; firms supply the resulting goods and services back to households, who spend their income buying them. Because every pound spent by one side is a pound received by the other, the total value of output produced, the total income earned, and the total expenditure made in a period are three measurements of the exact same flow — which is why national income statistics can be built from any of the three approaches and (in principle) arrive at the same figure.

That flow is a rate — an amount per period — which makes it fundamentally different from wealth. Income is water flowing into a bathtub each week; wealth is however much water is already sitting in the tub, built up from every past week combined, minus whatever has drained out or is owed elsewhere. A new graduate on a strong starting salary can have high income and almost no wealth; a retiree living off a paid-off house and a pension pot built over forty years can have high wealth and comparatively low current income. The two genuinely diverge, which is exactly why the spec treats them as a distinct pair rather than two words for the same thing.

In the simplest possible circular flow — just households and firms, nothing else — whatever households earn, they spend, and it all returns to firms: a closed loop, unchanging in size. Real economies add two further sets of flows. injections are spending that enters the circular flow from *outside* the household-firm loop: investment (I, spending by firms on capital goods), government spending (G), and exports (X, spending by overseas buyers on domestic output). withdrawals are income earned *inside* the loop that leaves it rather than returning as spending on domestic output: savings (S), taxation (T), and imports (M, domestic spending redirected to foreign-made output).

The equilibrium level of real output is the output level at which the circular flow has no further reason to grow or shrink — where the size of the flow, once set, would stay exactly the same period after period if nothing else changed. What condition actually pins that point down, and why it turns out to be exactly the same condition as aggregate demand equalling aggregate supply, is worth deriving properly rather than taking on trust — see the mechanism below.

A marginal propensity answers one specific question: out of the *next* extra pound of income a household receives, what fraction goes where? There are exactly four possible destinations, spec-named directly: consumed on domestic output (MPC = ΔC/ΔY), saved (MPS = ΔS/ΔY), taken in tax (MPT = ΔT/ΔY), or spent on imports (MPM = ΔM/ΔY). Because these are the only four things that can happen to an extra pound — there's no fifth destination — the four propensities must add up to exactly 1: MPC + MPS + MPT + MPM = 1. This isn't an empirical regularity to check against data; it's true by definition of what a propensity divides the same pound into.

Group the three leakages together and call the total the marginal propensity to withdraw: MPW = MPS + MPT + MPM. Since MPC plus all three withdrawal propensities sums to exactly 1, it follows immediately that MPW = 1 − MPC — not as a separate fact to check, but as the direct consequence of the identity in the previous chunk. That single line is going to matter a great deal once the multiplier formula is derived below.

Here's the concept the rest of this lesson makes precise: an injection into the circular flow doesn't just add its own value to national income once and stop there. The firm or worker who receives that spending has themselves just received new income — and part of that, the MPC fraction, gets spent again, becoming a further round of income for someone else, who spends part of *that* again, and so on. National income rises by more than the initial injection, and exactly how much more is what the multiplier measures.

The multiplier's SIZE is set by MPW — the marginal propensities to save, tax, and import — and none of those three is something a single spending announcement changes. A government can decide how much extra to spend; it cannot, by that same announcement, decide how open its economy is to trade, how much of a windfall its households habitually save, or how progressive its tax system already is. That's why comparing two countries' fiscal stimulus packages by the headline spending figure alone — "$20bn vs $30bn, so the second policy is stronger" — is comparing numbers that were never actually comparable: an identical $20bn injected into a large, relatively closed economy with a low MPM circulates through many more rounds of domestic re-spending than the same $20bn injected into a small, trade-dependent economy where much of each round leaks straight back out as import spending. The multiplier isn't a lever the policy itself pulls; it's a property of the economy the policy happens to land in.

Nothing about the geometric-series derivation above depended on the initial change being a RISE. Exactly the same reasoning runs in reverse for a FALL in an injection or a RISE in a withdrawal: a £100m fall in investment removes £100m of income from its first recipients, who now spend MPC less themselves, removing a further £100m × MPC of income from a second round of recipients, and so on — the identical convergent series, the identical 1/(1−MPC) multiplier, applied to a contraction instead of an expansion. The symmetry runs the other way too, and it's easy to state only half of it by accident: a FALL in a withdrawal is exactly as expansionary as a RISE in an injection, not a separate case needing its own derivation — the round-by-round mechanism above never cared whether the extra spending that keeps circulating came from more investment or from less leaking out as tax, saving or import spending, only that more of each round of income stayed in the domestic circular flow. This is precisely the scenario a real WEC12 mark scheme credits: when a fall in the global oil price lowers an oil-importing economy's spending on imports (M, a withdrawal, falling), the indicative content awards "Positive multiplier effects" as a Knowledge/Application/Analysis point — and, for an oil-exporting economy whose own export revenue (X, an injection) falls instead, the mirror-image Evaluation-band point is "Negative multiplier effects" (January 2021 MS, Q14, indicative content). A recession triggered by a fall in exports or a rise in the savings rate isn't a separate mechanism from the one derived above; it's that same multiplier process running in the opposite direction — which is exactly why a small MPW is a double-edged structural feature of an economy: it makes a given stimulus punch harder, but it makes a given negative shock hit harder too.

This is the move that actually separates a Level 3 evaluation from a Level 4 one on this topic. Level 3 states that the multiplier makes a policy "more effective" or "less effective" depending on MPW, and stops there. Level 4 goes one step further and treats the multiplier itself as evidence ABOUT the structure of the economy under discussion — its openness to trade, its savings culture, its tax base — rather than as a number to calculate and move on from. A closing sentence built on that structural point, applied to a specific named country, does more work than the identical calculation simply repeated with a different label attached to it.