ECON5002 · Macroeconomic Theory
The Keynesian Income-Expenditure Model and Fiscal Policy
This is the engine room of short-run macro in ECON5002. With spare capacity and sticky prices, output is demand-determined: firms produce what is planned to be bought, and equilibrium income is the level where planned injections equal planned leakages (a centre of gravity, not the accounting identity). The chapter builds the consumption and saving functions from the marginal propensity to consume, derives the expenditure multiplier 1/(1−c), and turns that machinery into fiscal policy — the tax multiplier, the balanced-budget multiplier of exactly 1, and how endogenous taxes and imports act as automatic stabilisers. It is examined only in the closed-book mid-semester test (Topics 1–3).
What this chapter covers
- 011. Macroeconomic equilibrium — the output level where planned injections equal planned leakages (I + G + X = S + T + M)
- 022. Quantity adjustment — sticky prices mean unplanned inventories, not prices, clear the goods market
- 033. Consumption & saving functions — C = a + c(Y − T), with MPC c and MPS s = 1 − c
- 044. The Keynesian cross — Y* where the aggregate-expenditure schedule crosses the 45° line
- 055. The expenditure multiplier — k = 1/(1 − c): an autonomous impulse raises income by a multiple
- 066. Fiscal multipliers — spending multiplier 1/(1−c) vs the smaller, negative tax multiplier −c/(1−c)
- 077. Balanced-budget multiplier — equals 1: matched ΔG and ΔT raise income by exactly ΔG
- 088. Leakages & budget stance — endogenous taxes t and imports m shrink k; structural vs cyclical balance
Equilibrium income, the multiplier and a tax cut
- +2Build aggregate expenditure: AE = C + I + G = 100 + 0.6(Y − 150) + 250 + 200 = 460 + 0.6Y.
- +1Set output equal to planned spending: Y = 460 + 0.6Y, so 0.4Y = 460 and Y* = 460 / 0.4 = 1150.
- +2Spending multiplier = 1/(1 − c) = 1/(1 − 0.6) = 2.5; tax multiplier = −c/(1 − c) = −0.6/0.4 = −1.5 (negative and smaller in size, because a tax change works only through consumption).
- +2Tax cut: ΔT = −40, so ΔY = (tax multiplier) × ΔT = (−1.5) × (−40) = +60; equilibrium income rises to 1210.
- +1Compare: an equal $40 rise in G would add 2.5 × 40 = 100, more than the $60 from the tax cut — spending injects fully while a tax cut leaks the MPS fraction (0.4 × 40 = 16) into saving.
Key terms
- Marginal propensity to consume (MPC, c)
- The fraction of an extra dollar of disposable income that is spent, c = ΔC/ΔYd, with 0 < c < 1. It is the slope of the consumption function and the engine of the multiplier.
- Marginal propensity to save (MPS, s)
- The fraction of an extra dollar of disposable income that is saved, s = 1 − c. Every extra dollar is either consumed or saved, so the two propensities sum to one.
- Autonomous expenditure (A)
- Spending independent of current income — autonomous consumption, planned investment, government spending, exports, less the tax-induced and import terms. Equilibrium income is the multiplier times A.
- Expenditure multiplier
- The factor by which a change in autonomous spending raises equilibrium income. In the simple closed model it is 1/(1 − c); each extra leakage (proportional tax t, import propensity m) shrinks it to 1/(1 − c + ct + m).
- Tax multiplier
- The effect on income of a lump-sum tax change, −c/(1 − c). It is negative and smaller in magnitude than the spending multiplier because a tax change reaches demand only indirectly, through consumption.
- Balanced-budget multiplier
- Equal to 1 in the simple lump-sum model: a matched rise in G and T raises income by exactly ΔG, since spending adds the full amount while the tax cuts demand only by the MPC fraction.
- Automatic stabilisers
- Income-dependent taxes and imports (and transfers) that grow in a boom and shrink in a slump without any policy decision, lowering the multiplier and damping the business cycle automatically.
- Structural vs cyclical budget balance
- The structural (cyclically-adjusted) balance is what the budget would be at equilibrium output and measures the discretionary fiscal stance; the cyclical part is driven purely by where income sits in the cycle (the tY term).
The Keynesian Income-Expenditure Model and Fiscal Policy FAQ
What is macroeconomic equilibrium in this model?
It is the single output level at which spending plans are mutually consistent — where planned injections equal planned leakages (I + G + X = S + T + M), or in the simplest closed economy planned saving equals planned investment. It is a centre of gravity the economy converges toward through changes in output, not a state it literally sits in, and it is distinct from the accounting identity that actual S always equals actual I.
Why is the balanced-budget multiplier equal to 1 and not 0?
Because government spending and an equal tax rise do not cancel. The spending enters demand in full and carries the spending multiplier 1/(1 − c), while the tax cuts demand only indirectly through consumption, carrying the smaller tax multiplier −c/(1 − c). The two sum to (1 − c)/(1 − c) = 1, so a matched rise in G and T lifts income by exactly the change in G. The one-line reason markers want: the tax leaks the MPS fraction into saving while spending does not.
Why do endogenous taxes and imports make the multiplier smaller?
Both are extra leakages from each round of spending. With a proportional tax rate t and a marginal propensity to import m, part of every extra dollar of income drains into tax revenue and foreign spending instead of being re-spent at home, so the multiplier falls from 1/(1 − c) to 1/(1 − c + ct + m). Because they automatically grow in booms and shrink in slumps, these leakages are called automatic stabilisers.
What is unplanned inventory investment, and why does it matter?
It is the gap between output and planned spending. If firms produce more than is demanded, the unsold goods are booked as unplanned inventory accumulation, which signals overproduction and leads firms to cut output toward equilibrium; if demand exceeds output, inventories are run down and firms expand. This is the quantity-adjustment mechanism that drives the economy to Y* when prices are sticky.
How is this topic assessed in ECON5002?
Topic 1 is examined only in the 30% closed-book mid-semester test (Topics 1–3) — 15 MCQ plus one two-part essay marked out of 20 — and in Quiz 1. It does not appear on the final exam. Closed-book with no formula sheet means the multiplier formulas and a labelled Keynesian-cross diagram must be memorised. Always confirm weights and dates against your own current unit outline.
Is this guide official or affiliated with the University of Sydney?
No. This is an independent AskSia study resource created to help students revise. It is not produced, endorsed by, or affiliated with the University of Sydney. Always check Canvas and the official unit outline for current content, dates and rules.
Exam move
Make the Keynesian cross something you can draw and solve from memory in under a minute, because both the MCQ and the essay reward speed and labelled diagrams. Start every quantitative question the same way — write aggregate expenditure as AE = A + cY, set Y = AE, and solve — then read the multiplier straight off as 1/(1 − c) and apply it to whatever autonomous change is asked. Drill the fiscal trio until the relationships are reflexive: the spending multiplier is the full 1/(1 − c), the tax multiplier is the smaller, negative −c/(1 − c), and the balanced-budget multiplier is exactly 1, with the one-line reason that the tax leaks the MPS fraction into saving while spending does not. Practise the leakage version 1/(1 − c + ct + m) and be ready to explain endogenous taxes and imports as automatic stabilisers. Finally, rehearse two qualitative discriminators the exam keeps returning to — the difference between the ex post identity (actual S = I) and the ex ante equilibrium (planned S = I), and why the structural rather than the actual budget balance measures the fiscal stance, since austerity that cuts G can widen the deficit ratio by dragging income and tax revenue down.
