Crux First
Most important recall points before solving MCQs
- Keynes said equilibrium income is determined by aggregate demand.
- Equilibrium need not be at full employment.
- In two-sector model: Y = C + I and equilibrium condition is S = I.
- Consumption function: C = a + bY where a = autonomous consumption and b = MPC.
- 0 < MPC < 1; also MPS = 1 - MPC.
- APC = C/Y and APS = S/Y.
- Multiplier: k = 1 / (1 - MPC) = 1 / MPS.
- Three-sector model: Y = C + I + G.
- Four-sector model: Y = C + I + G + (X - M).
- Exports are injection; imports are leakage.
- Higher MPC → higher multiplier; higher MPS or higher imports → lower multiplier.
- Deficient demand causes deflationary gap; excess demand causes inflationary gap.
1. Introduction to Keynesian Theory
- Keynes developed his theory during the Great Depression to explain persistent unemployment and inadequate demand.
- His key focus was on determination of equilibrium aggregate income and output.
- He rejected the classical belief that economy automatically reaches full employment.
- According to Keynes, output and income depend mainly on aggregate effective demand.
In MCQs, the single biggest Keynes point is this: income is demand-determined, not automatically full-employment determined.
2. Keynesian Models Covered in the Unit
| Model |
Sectors Included |
Equilibrium Formula |
| Two-sector model |
Households + Firms |
Y = C + I |
| Three-sector model |
Households + Firms + Government |
Y = C + I + G |
| Four-sector model |
Households + Firms + Government + Foreign Sector |
Y = C + I + G + (X - M) |
MCQ Trap
- Closed economy with government = three-sector model.
- Open economy = four-sector model.
3. Circular Flow in Simple Two-Sector Model
- The two main players are households and firms.
- Households supply factor services and receive factor income.
- Firms hire factors, produce goods and services, and sell them to households.
- In the simple model, entire household income is spent on consumption.
- There are no injections and no leakages in the simplest version.
Factor Payments = Household Income = Household Expenditure = Total Receipts of Firms = Value of Output
Real flow = flow of factor services and goods.
Money flow = wages, rent, interest, profit and consumption expenditure.
4. Meaning of Equilibrium
- Equilibrium means a position where there is no tendency to change.
- Output is at equilibrium when quantity produced = quantity demanded.
- In Keynesian terms, equilibrium is where firms’ production plans match households’ expenditure plans.
Equilibrium Output: Aggregate Demand = Aggregate Output
5. Aggregate Demand Function
- Aggregate Demand means total planned expenditure.
- In the simple two-sector model, it has only two parts:
- Consumption demand (C)
- Investment demand (I)
- In the short run, investment is usually treated as autonomous and exogenous.
AD = C + I
In short-run Keynesian analysis, consumption is induced by income, but investment is usually taken as autonomous.
6. Consumption Function
- Consumption function shows the relationship between consumption expenditure and disposable income.
- Keynes gave the linear form of consumption function.
C = f(Y)
C = a + bY
- a = autonomous consumption, i.e. consumption even when income is zero.
- b = marginal propensity to consume (MPC).
MPC = ΔC / ΔY = b
Must Remember
- a is the intercept.
- b is the slope.
- Keynes assumed 0 < b < 1.
- Consumption rises with income, but by less than the rise in income.
7. MPC and APC
Marginal Propensity to Consume (MPC)
- MPC shows how much consumption rises when income rises by one unit.
MPC = ΔC / ΔY
Average Propensity to Consume (APC)
- APC is the ratio of total consumption to total income.
APC = C / Y
Usually, in the Keynesian table form, APC falls as income rises, while MPC is often assumed constant.
8. Saving Function, MPS and APS
- Whatever part of income is not consumed is saved.
- Therefore saving is also a function of income.
S = Y - C
S = f(Y)
Marginal Propensity to Save (MPS)
MPS = ΔS / ΔY = 1 - MPC
Average Propensity to Save (APS)
APS = S / Y
Golden Relations
- MPC + MPS = 1
- APC + APS = 1
- If income is zero and consumption is positive, saving will be negative i.e. dissaving.
9. Aggregate Supply in Keynesian Model
- Planned aggregate supply equals national income, which is either consumed or saved.
AS = C + S
In the simple two-sector model, equilibrium comes when planned spending equals output.
10. Two-Sector Model of Income Determination
- In the two-sector model, equilibrium occurs where aggregate demand equals aggregate supply.
- That means:
C + I = C + S
Therefore, I = S
The equality S = I is the equilibrium condition in the two-sector Keynesian model.
MCQ Trap
- In Keynesian model, equilibrium is where planned expenditure = output.
- The 45-degree line shows points where aggregate expenditure = aggregate output.
11. Keynesian Cross Logic
- If aggregate demand line lies above the 45-degree line, planned expenditure exceeds output and income tends to rise.
- If aggregate demand line lies below the 45-degree line, planned expenditure is less than output and income tends to fall.
- At the intersection point, equilibrium income is reached.
Below equilibrium income: I > S
Above equilibrium income: S > I
12. Equilibrium Need Not Be Full Employment
- Keynes strongly argued that equilibrium may occur below full employment.
- So, equality of AD and AS does not guarantee full employment.
Deflationary Gap
- When aggregate demand is less than the level required for full employment, there is deficient demand.
- This creates a deflationary gap or recessionary gap.
Inflationary Gap
- When aggregate demand exceeds the full employment output level, there is excess demand.
- This creates an inflationary gap.
Exam Trap
- Deflationary gap = deficient demand
- Inflationary gap = excess demand
- Keynesian equilibrium may be at under-employment level.
13. Numerical Shortcuts for Two-Sector Model
Case 1: Given C = a + bY and I is autonomous
Y = C + I
Y = a + bY + I
Y(1 - b) = a + I
Y = (a + I) / (1 - b)
Case 2: If saving function is given
At equilibrium, S = I
Case 3: Once Y is found
C = a + bY
S = Y - C
Fast exam flow: Find Y first → then C → then S.
14. Investment Multiplier
- Multiplier shows by how much equilibrium income changes when autonomous investment changes.
- A rise in investment causes multiple rises in income because one person’s spending becomes another person’s income.
k = ΔY / ΔI
ΔY = k × ΔI
k = 1 / (1 - MPC) = 1 / MPS
Higher MPC means people spend more out of extra income. So the multiplier becomes larger.
Must Memorise
- Multiplier is directly related to MPC.
- Multiplier is inversely related to MPS.
- If MPC = 0.75, multiplier = 4.
- If MPC = 0.8, multiplier = 5.
15. Leakages that Reduce Multiplier
- High taxes
- Idle savings / high liquidity preference
- Imports
- Purchase of old securities / existing wealth
- Undistributed profits
- Repayment of debts
- Full employment situation leading only to inflation
- Scarcity of goods and services
MCQ Trap
- The more powerful the leakages, the smaller the multiplier.
- In underdeveloped countries, even with high MPC, multiplier may remain low due to structural bottlenecks.
16. Three-Sector Model: Government Included
- Now government is added to the model.
- Aggregate demand now includes government purchases also.
Y = C + I + G
- In this model:
- Injections = I + G
- Leakages = S + T
AD = C + I + G
AS = C + S + T
Equilibrium: C + I + G = C + S + T
Therefore, in equilibrium for three-sector model: I + G = S + T.
17. Role of Government Sector
- Government imposes taxes on households and firms.
- Government gives transfer payments to households and subsidies to firms.
- Government purchases goods and services.
- Government may borrow from financial markets if expenditure exceeds tax revenue.
MCQ Trap
- Taxes are leakages.
- Government expenditure is injection.
- Transfer payments affect disposable income, not direct current production.
18. Three-Sector Income Determination with Lump Sum Tax
- When government imposes lump sum tax and there are no transfer payments:
C = a + bYd
Yd = Y - T
Y = a + b(Y - T) + I + G
Y = [a - bT + I + G] / (1 - b)
If tax is lump sum, it reduces disposable income by a fixed amount.
19. Three-Sector Income Determination with Lump Sum Tax and Transfer Payments
Yd = Y - T + TR
C = a + b(Y - T + TR)
Y = a + b(Y - T + TR) + I + G
Y = [a - bT + bTR + I + G] / (1 - b)
MCQ Trap
- Transfer payments increase disposable income.
- Taxes reduce disposable income.
20. Three-Sector Model with Tax as Function of Income
- When taxes depend on income, tax function is:
T = T̄ + tY
- T̄ = autonomous tax
- t = tax rate
C = a + b(Y - T̄ - tY)
Y = a + b(Y - T̄ - tY) + I + G
Y = [a - bT̄ + I + G] / [1 - b(1 - t)]
Proportional tax reduces the multiplier because part of additional income goes away as tax.
21. Three-Sector Model with Tax Function and Transfer Payments
C = a + b(Y - T̄ - tY + TR)
Y = [a - bT̄ + bTR + I + G] / [1 - b(1 - t)]
Numerical Shortcut
- Check denominator carefully.
- With proportional tax, denominator becomes 1 - b(1 - t).
- Do not use simple 1 - b multiplier here.
22. Four-Sector Model: Open Economy
- The foreign sector is added in the four-sector model.
- Aggregate demand now includes net exports.
Y = C + I + G + (X - M)
Exports are foreign demand for domestic goods. Imports are spending on foreign goods, so they leak out from domestic circular flow.
23. Exports, Imports and Import Function
- Exports are treated as autonomous and exogenous.
- Imports depend partly on income and partly on autonomous imports.
M = M̄ + mY
- M̄ = autonomous imports
- m = marginal propensity to import
Marginal Propensity to Import = ΔM / ΔY = m
MCQ Trap
- Exports = injection
- Imports = leakage
- If X > M, net exports positive and income rises.
- If X < M, net exports negative and income falls.
24. Four-Sector Equilibrium Income Formula
- With lump sum tax and income-dependent imports:
Y = C + I + G + (X - M)
C = a + b(Y - T)
M = M̄ + mY
Y = [a - bT + I + G + X - M̄] / (1 - b + m)
With proportional tax and transfer payments also included
C = a + b(Y - T̄ - tY + TR)
M = M̄ + mY
Y = [a - bT̄ + bTR + I + G + X - M̄] / [1 - b(1 - t) + m]
In four-sector model, the denominator becomes larger because imports create additional leakage.
25. Foreign Trade Multiplier
- Foreign trade multiplier shows how much income changes due to change in exports in an open economy.
ΔY = [1 / (1 - b + m)] × ΔX
Foreign Trade Multiplier = 1 / (1 - b + m)
Must Remember
- Open economy multiplier is smaller than closed economy multiplier.
- Higher m means lower multiplier.
- More open the economy, more leakage through imports, smaller the multiplier.
26. Closed Economy vs Open Economy Multiplier
| Case |
Multiplier |
Why? |
| Closed economy |
1 / (1 - b) |
No import leakage |
| Open economy |
1 / (1 - b + m) |
Imports create extra leakage |
| With proportional tax |
1 / [1 - b(1 - t)] |
Tax reduces induced consumption |
| Open economy with proportional tax |
1 / [1 - b(1 - t) + m] |
Both tax and imports reduce multiplier |
27. Ranker Numerical Strategy
- First identify the model:
- 2-sector → no G, no X-M
- 3-sector → G and T included
- 4-sector → X and M included
- Then identify whether tax is:
- Lump sum, or
- Income-dependent
- Then form Y = AD equation and collect Y terms on left side.
- Finally solve for Y and then calculate C, S, NX or whatever is asked.
In objective questions, many mistakes happen because students forget to replace Yd properly.
28. Top MCQ Traps from This Unit
- In Keynesian model, equilibrium income is determined by aggregate demand.
- Equilibrium may exist below full employment.
- In C = a + bY, a is autonomous consumption, b is MPC.
- MPC means change in consumption due to change in income.
- MPS = 1 - MPC.
- APC = C/Y; APS = S/Y.
- In two-sector model, equilibrium condition is S = I.
- Three-sector closed economy AD = C + I + G.
- Four-sector model AD = C + I + G + (X - M).
- Taxes and imports are leakages.
- Government spending and exports are injections.
- Multiplier is greater when MPC is higher.
- Multiplier is lower when MPS, tax rate or import propensity is higher.
- At 45-degree line, planned expenditure = output.
- Deflationary gap = deficient demand; inflationary gap = excess demand.
29. Formula Sheet – Must Memorise
C = a + bY
MPC = ΔC / ΔY = b
APC = C / Y
S = Y - C
MPS = ΔS / ΔY = 1 - b
APS = S / Y
MPC + MPS = 1
Two-sector equilibrium:
Y = C + I
S = I
Y = (a + I) / (1 - b)
Multiplier:
k = ΔY / ΔI = 1 / (1 - b) = 1 / MPS
ΔY = k × ΔI
Three-sector equilibrium:
Y = C + I + G
I + G = S + T
With lump sum tax:
Y = [a - bT + I + G] / (1 - b)
With lump sum tax and transfer payments:
Y = [a - bT + bTR + I + G] / (1 - b)
With tax function T = T̄ + tY:
Y = [a - bT̄ + I + G] / [1 - b(1 - t)]
With tax function and transfer payments:
Y = [a - bT̄ + bTR + I + G] / [1 - b(1 - t)]
Four-sector equilibrium:
Y = C + I + G + (X - M)
M = M̄ + mY
Y = [a - bT + I + G + X - M̄] / (1 - b + m)
Foreign Trade Multiplier:
1 / (1 - b + m)
Final Quick Revision
1-minute recall before MCQs or numericals
- Keynes: national income depends on aggregate effective demand.
- Equilibrium can be below full employment.
- Two-sector: Y = C + I, and S = I.
- Consumption function: C = a + bY.
- a = autonomous consumption; b = MPC.
- 0 < MPC < 1.
- MPS = 1 - MPC.
- APC = C/Y; APS = S/Y.
- Multiplier: 1 / (1 - MPC).
- Three-sector: Y = C + I + G.
- Leakages in three-sector: S + T; injections: I + G.
- Four-sector: Y = C + I + G + (X - M).
- Exports increase income; imports reduce income.
- Foreign trade multiplier: 1 / (1 - b + m).
- Deflationary gap = deficient demand; inflationary gap = excess demand.
