Pearson Edexcel International Advanced Level Economics: Multiplier, output gaps (YEC11)

This guide follows the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics (YEC11) specification, Issue 2, June 2018. It covers 2.3.4 item 4 (a to d, the multiplier) and 2.3.5 item 4 (a to d, output gaps). Both sit in Unit 2, Macroeconomic performance and policy. The specification calls Units 1 and 2 the International AS (IAS) units and Units 3 and 4 the additional International A2 (IA2) content for the full International Advanced Level, so this material is IAS content and also part of the full qualification. All figures below are invented for illustration.

Related pages: revision notes, practice questions, economic growth guide, exam preparation, the course hub, the checklist and the free diagnostics.

What this guide covers

Spec point	You must be able to
2.3.4 4a	Explain the multiplier and the multiplier process
2.3.4 4b	Define MPC, MPS, MPT and MPM and show how each affects the multiplier
2.3.4 4c	Calculate with 1/(1 - MPC) and 1/MPW, where MPW = MPS + MPT + MPM
2.3.4 4d	Judge the significance of the multiplier for shifts in AD and for economic activity
2.3.5 4a	Compare the actual growth rate with the long-term trend
2.3.5 4b	Distinguish positive and negative output gaps
2.3.5 4c	Describe the characteristics of each
2.3.5 4d	Explain why output gaps are hard to measure

Teaching of the circular flow, injections and withdrawals, and the causes and effects of growth sits in other guides. Here we use them only as background.

The multiplier and the multiplier process (4a)

An injection into the circular flow is spending that does not come from households’ income in the same period: investment, government spending or exports. The first round of spending becomes income for someone. They spend part of it, which becomes income for someone else, and so on. Total extra income is therefore a multiple of the first injection. This is the multiplier effect.

The multiplier is the ratio of the final change in real national income to the initial change in injections (or autonomous spending): k = change in Y / change in injection.

The process, round by round

Country A has a marginal propensity to consume of 0.75 and no other leakages. Spending by the government on a new road adds 20 (millions of units) to AD.

Round	New income created	Cumulative income
1	20.00	20.00
2	20 x 0.75 = 15.00	35.00
3	15 x 0.75 = 11.25	46.25
4	8.44	54.69
5	6.33	61.02
6	4.75	65.76

Each round is 0.75 of the one before, so the rounds shrink and the total approaches a limit: 20 / (1 - 0.75) = 80. The process stops because part of each round leaks out of the flow instead of being re-spent.

Marginal propensities (4b)

Each is a share of an extra unit of income.

• MPC: the share of extra income spent on consumption.
• MPS: the share saved.
• MPT: the share paid in tax.
• MPM: the share spent on imports.

Saving, tax and imports are withdrawals (leakages). Extra income is either spent on domestic output or leaks, so MPS + MPT + MPM + (share spent on domestic output) = 1. A larger MPS, MPT or MPM means a smaller share is passed on each round, and a smaller multiplier. A larger MPC (spent at home) means a bigger multiplier.

Watch the wording. In the simplest model, with no tax or trade, MPC is the share of extra income that goes back into the domestic circular flow, so MPC + MPS = 1. Once tax and imports exist, only the share spent at home keeps the process going. That is why the second formula uses all the leakages.

Calculating the multiplier (4c)

There are two forms of the formula.

• Simple form: k = 1/(1 - MPC) = 1/MPS when saving is the only leakage.
• Full form: k = 1/MPW, where MPW (marginal propensity to withdraw) = MPS + MPT + MPM.

Both say the same thing: the multiplier is the reciprocal of the share that leaks.

Worked example 1: full form

Country C has MPS = 0.12, MPT = 0.18 and MPM = 0.20. Exports rise by 45.

MPW = 0.12 + 0.18 + 0.20 = 0.50
k   = 1 / 0.50 = 2
change in Y = 45 x 2 = 90

Worked example 2: a change in a propensity

The government changes tax rules so that MPT falls from 0.18 to 0.10. Other propensities are unchanged.

new MPW = 0.12 + 0.10 + 0.20 = 0.42
new k   = 1 / 0.42 = 2.381
change in Y from the same 45 = 45 x 2.381 = 107.14
extra income compared with before = 107.14 - 90 = 17.14

Lower withdrawals raise the multiplier, so the same injection has a larger effect. The effect also works in reverse: a fall in an injection reduces income by the same multiple. If investment fell by 12 with k = 4, income would fall by 48.

Method in steps

1. Identify every leakage given and add them to find MPW (or find MPS from MPC).
2. Take the reciprocal.
3. Multiply by the change in injection, keeping the sign.
4. State the units and say what the figure means.

Why the multiplier matters (4d)

The multiplier means a shift in AD is larger than the initial change in spending. A rise in investment of 30 with k = 2 shifts the AD curve right by 60 at each price level (in the model). Governments and central banks care about this because small changes in confidence, investment or export demand can produce big changes in output and jobs.

Evaluate by asking how much of the AD shift becomes real output.

• Spare capacity: if the economy has unused resources, extra AD raises output and employment. Near full capacity it raises prices more than output, so the real multiplier is smaller.
• Size of leakages: an economy that imports heavily or taxes heavily gets a small multiplier, so stimulus has less effect.
• Time: rounds take time. Income may take months to work through.
• Behaviour: MPC is not constant. If households expect a recession they save more, and the multiplier falls.
• Crowding out: if the government borrows to fund spending, higher interest rates may reduce private investment, partly cancelling the gain.
• Direction: the same process magnifies a fall in exports or investment, so downturns can spread through the economy.

A sensible judgement says the multiplier is most important when there is spare capacity and low leakages, and least reliable when inflation is rising.

Output gaps (2.3.5 4a)

Actual growth is the percentage change in real GDP. Long-term trend growth is the average rate at which the economy’s productive capacity grows over time. Potential output is the level of output on that trend path. The output gap measures how far actual output lies from potential (trend) output, usually shown as a percentage of potential.

Output gap (%) = (actual - potential) / potential x 100.

You can also compare growth rates. If actual growth is above trend, the gap is getting more positive (or less negative). If it is below trend, the gap is shrinking (or becoming more negative).

Worked example 3: a gap series

Country B has trend growth of 2.5% a year. Potential output starts at 800 in Year 0. Actual output is shown below.

Year	Potential	Actual	Actual growth	Output gap
0	800.0	800	n/a	0.00%
1	820.0	822	2.75%	+0.24%
2	840.5	859	4.50%	+2.20%
3	861.5	851	-0.93%	-1.22%
4	883.1	870	2.23%	-1.48%

Year 2 growth of 4.5% is well above trend, so the gap widens to +2.20%. In Year 3 actual output falls, which swings the economy to a negative gap of 10.5 units (-1.22%). In Year 4 growth of 2.23% is positive but below the 2.5% trend, so the negative gap widens again to -1.48%. A recovery that is slower than trend does not close a gap.

Positive and negative gaps (4b and 4c)

A positive output gap means actual output is above potential. A negative output gap means it is below.

Feature	Positive gap	Negative gap
Resource use	Above normal capacity: overtime, full order books	Spare capacity, idle machines
Unemployment	Low, perhaps below its sustainable level	Higher, with cyclical unemployment
Inflation	Upward pressure on wages and prices	Weak price pressure, possibly falling inflation
Firms	High profits, high capacity use, possible shortages	Lower profits, cuts to investment
Government budget	Tax revenue high, welfare spending low: deficit tends to fall	Tax revenue low, welfare spending high: deficit tends to rise
Trade	Strong import demand may worsen the trade balance	Weak import demand

A positive gap is usually hard to sustain, because output is above what the economy can produce at normal capacity. A negative gap means resources are going unused.

Worked example 4: using the multiplier on a gap

Country D has potential output of 1,250, actual output of 1,150 and MPW = 0.4, so k = 2.5.

gap = 1,150 - 1,250 = -100
as a percentage = -100 / 1,250 x 100 = -8.0%
injection needed to close it = 100 / 2.5 = 40

If instead actual output were 1,300, the gap would be +50 (+4.0%). An extra injection of 20 would raise output by 50 to 1,350, a gap of +100 (+8.0%). In the model that widens the gap, which is why stimulus fits a negative gap and not a positive one.

Difficulties of measuring gaps (4d)

Potential output cannot be observed. It has to be estimated, and the estimate is uncertain.

• Choice of trend: a different period or method gives a different trend. In Example 3, if Country B’s trend were 3% rather than 2.5%, Year 4 potential would be 900.4 instead of 883.1, and the gap would be -3.38% instead of -1.48%.
• Shocks to supply: an energy price rise, a new technology or a financial crisis can shift potential itself, so the old trend is wrong.
• Data revisions: first estimates of GDP are revised later, so a gap seen at the time may look different afterwards.
• Hidden activity: informal output and unpaid work are not captured.
• Recent data: a trend estimated using recent years is the least reliable, at the point where policymakers most need it.
• Interpretation: a gap measured in output can differ from one measured in unemployment or capacity use.

The practical lesson is that policy based on a gap estimate carries risk. A government that thinks it faces a negative gap and stimulates may be mistaken, and cause inflation instead.

Common errors

• Dividing the injection by the multiplier, or leaving out the sign of a fall.
• Using only MPS when tax and imports are also given.
• Treating MPC + MPS = 1 as the full identity when MPT and MPM are present.
• Working out the gap as a percentage of actual output, not potential.
• Saying a gap closes whenever growth is positive, without comparing it with the trend.
• Giving a multiplier answer with no comment on spare capacity.

Official syllabus

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics (YEC11), Specification, Issue 2, June 2018, first teaching September 2018, published by Pearson Education Limited. Sections 2.3.4 (item 4) and 2.3.5 (item 4).