9.1 The circular flow of income
- Syllabus
- 9708–2026–2027
- Topic
- 9.1
- Level
- A2
Learning objectives
9.1.1Multiplier process• The multiplier process:- definition of the multiplier- formulae for and calculation of multiplier in a closed and open economy, with and without a government sector- calculation of:- average and marginal propensities to save (aps and mps)- average and marginal propensities to consume (apc and mpc)- average and marginal propensities to import (apm and mpm)- average and marginal rates of tax (art and mrt)- national income determination using AD and income approach with the multiplier process- calculation of effect of changing AD on national income using the multiplier9.1.2AD components and determinants• Components of Aggregate Demand (AD) and their determinants:- consumption function: autonomous and induced consumer expenditure- savings function: autonomous and induced savings- autonomous and induced investment; the accelerator- government spending- net exports (exports minus imports)9.1.3National income gaps• Full employment level of national income and equilibrium level of national income:- inflationary and deflationary gaps
The multiplier converts an autonomous spending change into a larger equilibrium-income change
The national income multiplier (k) is the ratio of the final change in equilibrium national income to the initial change in autonomous aggregate demand. One person's extra spending becomes another person's income; each later round is smaller because saving, tax and imports leak out of domestic spending.
k = ΔY / ΔAD_a; ΔY = k × ΔAD_a
| Average ratio: share of the current total | Marginal ratio: share of an income change |
|---|---|
| APC=C/Y | MPC=ΔC/ΔY |
| APS=S/Y | MPS=ΔS/ΔY |
| APM=M/Y | MPM=ΔM/ΔY |
| ART=T/Y | MRT=ΔT/ΔY |
Use disposable income where consumption/saving are defined from income after direct tax. Marginal propensities determine the multiplier; average propensities describe the current level.
| Economy | Marginal leakages | Multiplier |
|---|---|---|
| Closed, no government | saving | k=1/MPS=1/(1−MPC) |
| Closed, government | saving + tax | k=1/(MPS+MRT) |
| Open, no government | saving + imports | k=1/(MPS+MPM) |
| Open, government | saving + tax + imports | k=1/(MPS+MRT+MPM) |
These textbook forms assume the marginal leakage rates are constant and do not overlap.
In an open economy with government, MPS = 0.20, MRT = 0.30 and MPM = 0.30. Total marginal leakage is 0.80, so k = 1/0.80 = 1.25. A 100millionautonomousexportrisethereforeincreasesequilibriumincomeby125 million. Of the 125millionincomerise,importsriseby37.5 million and tax by $37.5 million.
Y = AD = C + I + G + (X - M); I + G + X = S + T + M
If C = 40 + 0.5Y, I = 80, X = 100 and M = 100, equilibrium requires Y = 40 + 0.5Y + 80 + 100 - 100. Hence 0.5Y = 120 and Y = 240. The same answer follows from autonomous spending of 120 and k = 1/(1 - 0.5) = 2.
To find the initial AD change needed for a target income change, reverse the multiplier: required autonomous change = desired ΔY ÷ k. If income must rise from 1000 to full-employment income 1200 and MPC = 0.8, k = 5, so the required initial injection is 200 ÷ 5 = 40.
The full textbook effect requires spare capacity, stable marginal propensities and no offsetting rise in interest rates, prices, taxes, imports or crowding out. High MPS, MRT or MPM makes k smaller. Do not use average propensities in a marginal multiplier or assume the calculated real-output increase survives near full capacity.
Aggregate demand combines autonomous spending with expenditure induced by income and output
AD=C+I+G+(X-M)
Aggregate demand is total planned expenditure on domestically produced final goods and services. Autonomous expenditure does not depend on current national income; induced expenditure changes because income or output changes.
| Component | Autonomous/induced structure | Main determinants |
|---|---|---|
| Consumption C | C=a+bYd: a is autonomous consumption; bYd is induced and b = MPC | Disposable income, wealth, interest rates/credit, confidence, expectations and income distribution |
| Saving S | S=Yd−C=−a+(1−b)Yd in the simple model | The same income/function conditions; autonomous consumption can mean dissaving at low income |
| Investment I | Autonomous replacement, innovation or policy/confidence-led spending; induced investment responds to changing demand/output | Interest rate versus expected return/MEC, confidence, profits, credit, technology, taxes and spare capacity |
| Government G | Usually treated as autonomous in the simple model | Fiscal objectives, revenue/borrowing, cycle and political priorities |
| Net exports X-M | Exports are largely autonomous with respect to domestic income; imports contain an induced part as domestic income rises | Foreign/domestic income, relative prices, exchange rate, competitiveness, trade barriers and tastes |
A rise in disposable income moves upward along an unchanged consumption function and increases induced consumption. Greater confidence or wealth raises autonomous consumption and shifts the whole function upward. An increase in autonomous consumption can coincide with a lower MPC if the intercept rises while the slope falls; inspect both intercept and gradient.
I_{induced} = v × ΔY
The accelerator says induced net investment depends on the change in demand or output, because firms need extra capital to produce a persistently higher flow of output. If v = 3 and desired output rises by 20, induced investment is 60. If output still rises but by less than before, induced investment can fall. Temporary demand growth or large spare capacity weakens the response.
| Process | Initial change | Result |
|---|---|---|
| Multiplier | Autonomous investment/other AD changes | A larger change in equilibrium income |
| Accelerator | Income, output or consumer-demand growth changes | Induced investment changes |
Lower interest rates can raise C and I; higher government education spending raises G; stronger foreign growth raises X; higher domestic income raises induced M. The final change in AD depends on all components, so a fall in net exports and private investment may be offset by government spending.
Imports are subtracted because they are spending on foreign output, not because imports are inherently harmful. A lower interest rate is an investment determinant but is not the accelerator itself; the accelerator specifically links induced investment to the rate of change of demand/output.
Equilibrium national income need not equal full-employment national income
| Concept | Meaning |
|---|---|
| Equilibrium national income Ye | Planned aggregate expenditure equals output/income, or injections equal withdrawals; there is no tendency for income to change |
| Full-employment national income Yf | The output/income produced when available labour and other resources are used at their sustainable full-employment level; it does not require zero unemployment |
If planned spending exceeds current output, unplanned inventories fall and firms raise output, income and employment. If planned spending is below output, inventories accumulate and firms cut production. This adjustment can stop at an equilibrium below full employment because weak spending can persist.
| Position at full-employment income | Gap | Likely pressure | Closing direction |
|---|---|---|---|
| Planned expenditure is below the amount needed to support Yf | Deflationary gap: the vertical spending shortfall at Yf | Below-capacity output and cyclical unemployment; weak price pressure | Increase autonomous AD |
| Planned expenditure is above the amount compatible with Yf | Inflationary gap: the vertical excess spending at Yf | Demand exceeds sustainable real capacity, mainly raising prices | Decrease autonomous AD or expand capacity |
ΔAD_a = (Y_f - Y_e) / k
If equilibrium income is 1000, full-employment income is 1200 and k = 5, the horizontal output gap is 200, but the deflationary expenditure gap is only 200 ÷ 5 = 40. A 40 autonomous-spending rise is multiplied into a 200 income rise in the model.
If equilibrium income is 1000, full-employment income is 800 and k = 5, the economy has an inflationary position. The excess autonomous spending at full employment is (1000 − 800) ÷ 5 = 40, so a 40 reduction would return planned spending to the full-employment equilibrium in the stylised model.
On a Keynesian-cross/aggregate-expenditure diagram, read the gap vertically at Yf between planned expenditure and the 45-degree/output line. On an injections-withdrawals diagram, compare injections and withdrawals at Yf. The horizontal distance Yf−Ye is the income/output gap, not the initial expenditure gap.
Equilibrium is not proof of full employment or welfare. A deflationary gap means insufficient planned spending relative to full-employment output; it is not the same as a falling general price level. The textbook calculation also depends on a stable multiplier and available supply response.