The multiplier, aggregate demand and equilibrium income
The multiplier, aggregate demand and equilibrium income: build the core model, apply it to evidence and qualify conclusions where outcomes depend on context.
9708 section 9.1; A Level. Checked against Cambridge's 2026–2028 Version 2 (latest version published December 2025) and 2029 Version 1 (published September 2026). Cambridge states that neither version has significant changes affecting teaching. Always follow the syllabus for the candidate's examination year.
Before you begin
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
In the simple closed-economy model, what does a higher MPS do to the multiplier?
What you will learn
- Calculate multiplier values and average and marginal propensities
- Analyse Aggregate Demand components and determinants
- Use the multiplier to explain equilibrium income and output gaps
Core model and terms
The multiplier measures the final change in national income relative to an initial autonomous change in spending. In a closed economy without government, k = 1/MPS; with imports, k = 1/(MPS + MPM); with proportional tax, add MRT to the leakages. MPS, MPC, MPM and MRT use changes in saving, consumption, imports and tax divided by a change in income; average propensities divide each total by income. In two-sector accounting, APC + APS = 1. The multiplier is smaller when more income leaks into saving, tax or imports.
Apply and evaluate
AD = C + I + G + (X − M). Consumption and saving can each contain autonomous and income-induced parts; investment has autonomous and induced elements, and the accelerator links investment to changes in output. Government spending and net exports also affect AD. Equilibrium income occurs where planned expenditure equals output, equivalently where injections equal leakages under the model. If equilibrium income is below the full-employment level there is a deflationary gap; above it there is an inflationary gap. Use the model’s assumptions when applying a multiplier estimate.
Pause and explain
Which statement best applies the multiplier, aggregate demand and equilibrium income?
Worked example
In an open economy with government, MPS is 0.20, MRT is 0.10 and MPM is 0.10. Calculate the multiplier and the income effect of an $8bn rise in autonomous investment.
Show the worked solution
- k = 1 ÷ (0.20 + 0.10 + 0.10) = 2.5
- Change in national income = 2.5 × $8bn
- Income rises by $20bn in this model
Answer k = 1 ÷ (0.20 + 0.10 + 0.10) = 2.5 → Change in national income = 2.5 × $8bn → Income rises by $20bn in this model
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
In an open economy with government, MPS is 0.20, MRT is 0.10 and MPM is 0.10. Calculate the multiplier and the income effect of an $8bn rise in autonomous investment.
Give me a hint
Add marginal leakages, take the reciprocal, then multiply by the injection.
Compare my reasoning
- k = 1 ÷ (0.20 + 0.10 + 0.10) = 2.5
- Change in national income = 2.5 × $8bn
- Income rises by $20bn in this model
k = 1 ÷ (0.20 + 0.10 + 0.10) = 2.5 Change in national income = 2.5 × $8bn Income rises by $20bn in this model
Look for these in your work
- k = 1 ÷ (0.20 + 0.10 + 0.10) = 2.5
- Change in national income = 2.5 × $8bn
- Income rises by $20bn in this model
In a closed economy without government, MPC is 0.8. Calculate MPS and the simple multiplier.
Give me a hint
Use MPC + MPS = 1, then take the reciprocal of MPS.
Compare my reasoning
- MPS = 1 − 0.8 = 0.2
- k = 1 ÷ 0.2
- The multiplier is 5
MPS = 1 − 0.8 = 0.2 k = 1 ÷ 0.2 The multiplier is 5
Look for these in your work
- MPS = 1 − 0.8 = 0.2
- k = 1 ÷ 0.2
- The multiplier is 5
Income rises by $200m; consumption rises by $120m, saving by $50m and tax by $20m. Calculate MPC, MPS and MRT.
Give me a hint
Divide each change by the same $200m change in income.
Compare my reasoning
- MPC = 120 ÷ 200 = 0.60
- MPS = 50 ÷ 200 = 0.25
- MRT = 20 ÷ 200 = 0.10
MPC = 120 ÷ 200 = 0.60 MPS = 50 ÷ 200 = 0.25 MRT = 20 ÷ 200 = 0.10
Look for these in your work
- MPC = 120 ÷ 200 = 0.60
- MPS = 50 ÷ 200 = 0.25
- MRT = 20 ÷ 200 = 0.10
Equilibrium income is $900bn and full-employment income is $1,000bn. Identify the output gap and explain one likely implication.
Give me a hint
Compare equilibrium with capacity output before assigning the sign.
Compare my reasoning
- Equilibrium is $100bn below full-employment income
- This is a deflationary gap
- Spare capacity may persist unless demand or productive conditions change
Equilibrium is $100bn below full-employment income This is a deflationary gap Spare capacity may persist unless demand or productive conditions change
Look for these in your work
- Equilibrium is $100bn below full-employment income
- This is a deflationary gap
- Spare capacity may persist unless demand or productive conditions change
Common mistakes
- Applying a closed-economy multiplier to an open economy without including tax or import leakages, or treating the model estimate as a guaranteed forecast.
What can you explain now?
In the simple closed-economy model, what does a higher MPS do to the multiplier?
Compare with the explanation
It lowers the multiplier because more extra income leaks into saving
The multiplier is the reciprocal of marginal leakage in this model.
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Make it stick
Before moving on, explain the central idea in the multiplier, aggregate demand and equilibrium income and state one condition that could change its effect.
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