Macroeconomics — Effective Demand and When the Multiplier Works

Macroeconomics — The Multiplier Is a Ceiling, Not a Promise

In Chapter 5 we computed equilibrium output and the multiplier with the Keynesian cross. This chapter looks at how that equilibrium is reached, the order in which the multiplier actually builds up, and the conditions under which it shrinks or disappears. In the short run, when prices do not move at once, output is determined by effective demand — demand that is actually spent.

1. Inventories adjust output

When planned expenditure $AE$ differs from actual output $Y$ , the difference shows up as unplanned inventory change.

Planned expenditure and inventories (AE = 62 + 0.8Y, equilibrium Y = 310)
Output Y	Planned expenditure AE	Inventory change	Firms' response
350	342	+8 (unsold)	Cut production
310	310	0	Hold steady
270	278	−8 (stocks run down)	Raise production

When output exceeds equilibrium, inventories pile up and firms cut production; when output falls short, inventories run down and firms raise production. The heart of the Keynesian short-run model is that quantities, not prices, adjust. In the national accounts unplanned inventory change is counted as investment, so $Y=C+I+G+NX$ always holds after the fact. The equilibrium condition is that planned spending equals output.

2. The multiplier builds up round by round

If government spending rises by 10 trillion won, that 10 trillion becomes someone’s income; with an MPC of 0.8, 8 trillion of it is spent and becomes someone else’s income.

The multiplier process (ΔG = 10 trillion won, MPC = 0.8)
Round	Additional income	Cumulative
1	10	10
2	8	18
3	6.4	24.4
4	5.12	29.5
5	4.10	33.6
…	…	→ 50

The multiplier as a geometric series

\Delta Y = \Delta G\,(1 + c + c^2 + \cdots) = \frac{\Delta G}{1-c}

Even after five rounds, only about two-thirds of the final effect of 50 trillion won has appeared. Each round takes time, so the multiplier effect does not arrive all at once.

3. Leakages shrink the multiplier

The part of each round’s income gain that does not return as consumption is a leakage. Taxes and imports are leakages as well as saving.

The multiplier with leakages

k = \frac{1}{1 - c(1-t) + m}

With c = 0.8, a marginal tax rate t = 0.25 and a marginal propensity to import m = 0.2, k = 1/(1 − 0.6 + 0.2) ≈ 1.67 — a third of the value of 5 without leakages.

The smaller and more open the economy, the higher its propensity to import and the smaller its multiplier: part of the stimulus leaks abroad to trading partners. This is also why, when several countries stimulate at once, each one’s exports rise and each one’s effect is larger.

4. The paradox of thrift

What happens if all households try to save more at the same time? In the economy above, suppose autonomous consumption $c_0$ falls from 20 to 10 (households try to save 10 trillion won more). The new equilibrium is $Y=52/0.2=260$ trillion won, 50 trillion lower. With disposable income of 250 trillion, consumption is $10+0.8\times 250=210$ trillion, so private saving is $250-210=40$ trillion. Private saving in the original equilibrium was also $300-260=40$ trillion. Households tried to save more, but only income fell; saving stayed the same.

From the identity $S_p=I+(G-T)+NX$ , if investment and the budget are fixed, private saving cannot rise. Saving more, which is rational for an individual, only reduces income for the economy as a whole — a fallacy of composition.

5. When the multiplier works

Channels that shrink the multiplier
Channel	Mechanism	Covered in
Taxes and imports	Leakages grow in every round	This chapter
Higher interest rates	Investment falls (crowding out)	Chapters 4 and 17
Higher prices	Real balances and net exports fall	Chapters 8 and 15
Full employment	Quantities cannot rise, so only prices do	Chapter 8
Expected future taxes	Households save more	Public Finance Chapter 6

Conversely, the multiplier is larger when interest rates are stuck at their lower bound so there is no crowding out, when there is much idle capacity and unemployment, and when many households are liquidity-constrained. That is why studies after the financial crisis reported larger fiscal multipliers in recessions and at the interest-rate lower bound.

Check your understanding

In an economy with an MPC of 0.8, a marginal tax rate of 0.25 and no imports, what are the effects of 10 trillion won of government spending on output and tax revenue? The multiplier is $1/(1-0.6)=2.5$ , so output rises by 25 trillion won and tax revenue by $0.25\times 25=6.25$ trillion. The budget deficit rises not by 10 trillion but by 3.75 trillion. With a marginal tax rate of 0, the output effect would be 50 trillion won.

References

John Maynard Keynes, The General Theory of Employment, Interest and Money (1936), ch. 10
N. Gregory Mankiw, Macroeconomics, ch. 11
Olivier Blanchard, Macroeconomics, ch. 3