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

These notes condense the multiplier (2.3.4 item 4, a to d) and output gaps (2.3.5 item 4, a to d) from the Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics (YEC11) specification, Issue 2, June 2018. The content is in Unit 2, one of the two International AS units, and so also forms part of the full International Advanced Level. Full explanations are in the study guide. Then test yourself with the practice questions. Other links: course hub, checklist, free diagnostics. All figures are invented.

Key definitions

Term	Meaning
Multiplier	Final change in real national income divided by the initial change in injections
Multiplier process	Each round of spending becomes income, part is re-spent, and the rounds shrink until the total reaches a limit
MPC	Share of an extra unit of income spent on consumption
MPS	Share of an extra unit of income saved
MPT	Share of an extra unit of income paid in tax
MPM	Share of an extra unit of income spent on imports
MPW	Marginal propensity to withdraw = MPS + MPT + MPM
Actual growth	Percentage change in real GDP
Trend growth	Long-term average growth of productive capacity
Output gap	Actual output minus potential output, as a percentage of potential
Positive gap	Actual output above potential
Negative gap	Actual output below potential

Formulas

Use	Formula
Simple multiplier	k = 1/(1 - MPC) = 1/MPS
Full multiplier	k = 1/MPW
Change in income	change in Y = k x change in injection
Injection needed	injection = wanted change in Y / k
Output gap (%)	(actual - potential) / potential x 100
Potential output on a trend	potential next year = potential x (1 + trend rate)

Method in steps: multiplier questions

1. List every leakage given. If MPC is given and nothing else leaks, MPS = 1 - MPC.
2. Add the leakages to get MPW.
3. Take 1/MPW.
4. Multiply by the injection, with the correct sign.
5. Add a line of meaning: what happens to AD, output and jobs.

Worked reminder

MPS = 0.1, MPT = 0.2, MPM = 0.3, so MPW = 0.6 and k = 1/0.6 = 1.667. An injection of 30 raises income by 30 x 1.667 = 50. Cut MPT to 0.1 and MPW = 0.5, so k = 2.0 and the same 30 raises income by 60.

Other quick checks: MPC = 0.9 gives k = 10, so an injection of 8 gives 80. MPC = 0.6 gives k = 2.5. A fall in investment of 12 with k = 4 reduces income by 48.

Process reminder

With MPC = 0.8 and no other leakage, an injection of 25 creates 25 in round 1, 25 x 0.8 = 20 in round 2 and 20 x 0.8 = 16 in round 3. The rounds keep shrinking towards a limit of 25 / (1 - 0.8) = 125. In an exam, show at least three rounds and then state the limit.

Chain of reasoning for a longer answer

1. State the injection and say it raises AD directly.
2. Say that recipients spend part of the new income at home, which creates more income for others.
3. Say that each round is smaller because some income leaks as saving, tax or imports.
4. Give the multiplier and the final change in income.
5. Evaluate: how much spare capacity is there, how big are the leakages, how long will it take, and could the effect be offset by crowding out or lower confidence?

The multiplier: what to say about it

• What raises it: a higher MPC (spent at home), a lower MPS, MPT or MPM.
• What lowers it: more saving, higher taxes or more spending on imports.
• Why it matters: any change in AD is magnified, so a change in confidence, exports or government spending has a larger effect on output than its own size.
• Why it works in reverse: a fall in an injection reduces income by a multiple too.
• Evaluation line to learn: the multiplier is largest with spare capacity and small leakages, so the same stimulus does more in a deep slump than near full employment.
• Limits: it is weakest when the economy is near full capacity, when households save a lot in uncertain times, when leakages are large, when the government’s borrowing crowds out private spending, and when the rounds take a long time.

Output gaps in brief

Method: (1) find potential output, (2) subtract it from actual, (3) divide by potential, (4) label the gap positive or negative.

Worked reminder: actual 950, potential 1,000. Gap = -50, or -5.0%, so a negative gap. With k = 1.667, the injection needed to close it is 50/1.667 = 30.

Growth rates against trend:

• Actual growth above trend: the gap rises (more positive or less negative).
• Actual growth below trend: the gap falls (less positive or more negative).
• Positive growth below trend still widens a negative gap.

Worked series: trend growth is 2% and potential output starts at 600, so potential is 612 in Year 1 and 624.24 in Year 2. Actual output is 600, 606 and 630. Actual growth is 1.00% in Year 1 and 3.96% in Year 2. The gaps are 0.00%, -0.98% (606 against 612) and +0.92% (630 against 624.24). Growth below trend opened a negative gap, then growth above trend more than closed it and created a positive one.

Characteristics

	Positive gap	Negative gap
Capacity	Stretched	Spare
Unemployment	Low, maybe below sustainable	Higher, cyclical
Inflation	Rising pressure	Weak or falling
Profits and investment	Strong	Weak
Budget	Tax up, welfare down	Tax down, welfare up
Imports	Strong demand	Weak demand

Difficulties of measuring

• Potential output is an estimate, not an observed figure.
• Different periods or methods give different trends. A 3% trend instead of 2.5% can turn a small gap into a much larger one.
• Supply shocks and technology can shift potential, so the old trend misleads.
• GDP data is revised later.
• Informal activity is missed.
• The trend is least reliable for the most recent years.

Must-know distinctions

• Actual growth versus trend growth: one is what happened, the other is the long-run capacity rate.
• Positive versus negative gap: above versus below potential, not rising versus falling output.
• MPC versus MPS: spent versus saved.
• MPW versus MPS: MPW includes tax and imports too.
• Gap in output versus gap in growth rates: the level of the gap versus whether it is widening or narrowing.

Quick self-test

1. MPC is 0.8 and there are no other leakages. Calculate the multiplier.
2. MPS = 0.15, MPT = 0.25, MPM = 0.10. Calculate MPW and the multiplier.
3. With k = 2.5, investment rises by 16. By how much does income change?
4. Government spending falls by 20 and k = 2. State the change in income.
5. Explain why a rise in MPM reduces the multiplier.
6. Actual output is 1,050 and potential is 1,000. Calculate the output gap.
7. Actual output is 780 and potential is 800. Calculate the output gap and say what type it is.
8. Trend growth is 3% and actual growth is 1%. What happens to a negative gap?
9. Give two characteristics of a positive output gap.
10. State two reasons why output gaps are hard to measure.
11. With k = 2 and a gap of -60, what injection would close it in the model?

Answers

1. k = 1/(1 - 0.8) = 5.
2. MPW = 0.15 + 0.25 + 0.10 = 0.50, so k = 2.
3. 16 x 2.5 = 40 increase.
4. -20 x 2 = -40.
5. A larger share of each round of extra income leaks to foreign producers, so less is passed on as domestic spending, the rounds shrink faster and the total is lower.
6. 50/1,000 x 100 = +5.0%.
7. (780 - 800)/800 x 100 = -2.5%, a negative gap.
8. It widens, because growth is below trend even though it is positive.
9. For example low unemployment and upward pressure on prices, or high capacity use and higher tax revenue.
10. For example potential output is not observed and has to be estimated, and data is revised or the trend changes with supply shocks.
11. 60/2 = 30.

Where marks are usually lost

• Using MPS in the formula when tax and import leakages are also given.
• Forgetting the negative sign when an injection falls.
• Calculating a gap as a percentage of actual output.
• Calling any growth a recovery without comparing it with trend.
• Treating the multiplier as fixed with no mention of spare capacity or confidence.
• Listing characteristics with no link to the gap, such as saying only that unemployment is “high” with no reason.
• Giving a calculation with no units or interpretation.
• Writing about the difficulties of measurement in general and not about potential output.

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).