ECON1002 · Introductory Macroeconomics
The Keynesian Short-Run Model
The Keynesian short-run model explains output when prices are sticky: firms produce to meet planned aggregate expenditure PAE = C + IP + G + NX, with consumption following C = C̄ + c(Y − T). Short-run equilibrium is where Y = PAE — the 45° 'Keynesian cross' — and any gap between output and planned spending is closed by unplanned inventory changes.
It is examined as a flagship calculation: build PAE, find the slope, compute the multiplier (1/(1−c) in two-sector, 1/(1−[c(1−t)−m]) in four-sector), solve for equilibrium Y, and find the change in autonomous spending needed to close an output gap.
What this chapter covers
- 011. Planned aggregate expenditure PAE = C + IP + G + NX (planned vs realised investment)
- 022. Inventory adjustment drives Y to equilibrium: Y > PAE ⇒ inventories rise ⇒ Y falls (and vice versa)
- 033. Keynesian consumption function C = C̄ + c(Y − T); c = MPC (0 < c < 1)
- 044. Short-run equilibrium Y = PAE on the 45° diagram
- 055. 2-sector model: withdrawals S = injections IP; multiplier = 1/(1 − c)
- 066. 4-sector model: tax T = T̄ + tY, imports M = mY; PAE slope = c(1−t) − m
- 077. 4-sector multiplier = 1 / (1 − [c(1−t) − m])
- 088. Equilibrium Y = autonomous expenditure × multiplier; higher c ⇒ bigger multiplier
Four-sector Keynesian equilibrium, the multiplier and closing a gap
- 1 markBuild PAE: PAE = 40 + 0.8(Y − 50) + 250 + 350 + (60 − 0.1Y) = (40 − 40 + 250 + 350 + 60) + (0.8 − 0.1)Y = 660 + 0.7Y. The slope is 0.7, so the multiplier = 1/(1 − 0.7) = 3.33.
- 1 mark(b) Autonomous expenditure is the PAE intercept = 660.
- 1 mark(c) Equilibrium sets Y = PAE: Y = 660 + 0.7Y ⇒ 0.3Y = 660 ⇒ Y = 660 × 3.33 = 2200.
- 1 mark(d) To raise Y by 40, the needed change in autonomous spending is ΔY / multiplier = 40 / 3.33 = 12, so ΔG = 12.
Key terms
- Planned aggregate expenditure (PAE)
- Total planned spending on domestic output: PAE = C + IP + G + NX, where IP is planned investment. It differs from actual spending when investment turns out unplanned (inventories pile up or run down).
- Consumption function
- C = C̄ + c(Y − T): consumption equals autonomous consumption C̄ plus the marginal propensity to consume c times disposable income (Y − T). The slope c (0 < c < 1) drives the size of the multiplier.
- Short-run equilibrium (Y = PAE)
- The output level at which planned spending exactly absorbs production, shown as the intersection of the PAE line with the 45° line where Y = PAE. Away from it, unplanned inventory changes push output back toward equilibrium.
- Inventory adjustment
- The mechanism that clears the goods market: if Y > PAE, firms accumulate unwanted inventories and cut production (Y falls); if Y < PAE, inventories run down and firms raise production (Y rises) until Y = PAE.
- Income-expenditure multiplier
- The factor by which equilibrium output rises per unit of autonomous spending: 1/(1 − c) in the two-sector model, or 1/(1 − [c(1−t) − m]) with a proportional tax t and import rate m. A higher MPC, lower tax rate or lower import rate all raise it.
- Marginal propensity to import (m)
- The fraction of an extra dollar of income spent on imports, M = mY. Because imports leak out of domestic spending, a higher m flattens the PAE line and shrinks the multiplier.
The Keynesian Short-Run Model FAQ
How is the Keynesian model examined in ECON1002?
It is a flagship. In MCQ you build PAE, find the slope and multiplier, and solve for equilibrium Y; in Section B you draw the 45° Keynesian cross, show a shift (e.g. G↑ or a negative shock), and explain how the multiplier magnifies it. Expect at least one full 'find the multiplier, find Y, close the gap' calculation in the IST or final.
Why is the multiplier greater than one?
Because spending circulates. A dollar of autonomous spending becomes someone's income, of which a fraction (the slope c(1−t) − m) is re-spent, becoming further income, and so on. The geometric sum of these rounds is 1/(1 − slope) > 1. The leakages — saving, taxes and imports — determine how much escapes each round and therefore how big the multiplier is.
What is the difference between the two-sector and four-sector multipliers?
The two-sector multiplier is 1/(1 − c), using only the consumption slope. The four-sector multiplier is 1/(1 − [c(1−t) − m]), adding a proportional tax t (which reduces disposable income out of each dollar) and an import rate m (which leaks spending abroad). Both leakages flatten the PAE line, so the four-sector multiplier is smaller than the two-sector one for the same c.
How does the economy return to equilibrium if output is too high?
Through unplanned inventories. If Y > PAE, planned spending falls short of production, so unsold goods accumulate as unplanned inventory investment; firms respond by cutting output, and Y falls toward PAE. If Y < PAE, inventories run down below desired levels and firms raise output. The process stops exactly where Y = PAE on the 45° line.
Exam move
Build the calculation into a fixed routine: (1) substitute T and the import/tax functions into PAE and collect the intercept (autonomous) and the slope; (2) read the slope as c(1−t) − m and form the multiplier 1/(1 − slope); (3) solve Y = PAE for equilibrium output; (4) to close a gap, divide the target ΔY by the multiplier to get the required change in autonomous spending. Practise this end-to-end until it is automatic, because the IST gives little time. For Section B, rehearse the 45° Keynesian cross: where the PAE line cuts the 45° line, how a shift moves equilibrium, and the one-line rule 'ΔY = multiplier × Δautonomous'. The single most-tested trap is forgetting the import leakage m when forming the slope.
