Skip to content

Business Economics · Determination of National Income

Keynesian Theory of Income Determination (Two Sector Economy)

Updated 1 October 2026 · Fact-checked

Keynesian theory says income in an economy settles where aggregate demand equals aggregate supply, which is the same point where planned saving equals planned investment. In a two sector model with C = a + bY and fixed investment I, equilibrium income is Y = (a + I) ÷ (1 − b).

Understand Keynesian Theory of Income Determination

Keynes argued that the level of national income depends on total spending in the economy, not on supply alone. In the short run, prices and wages are assumed sticky, and output adjusts to demand. So if people spend more, firms produce more and income rises.

A two sector economy has only households and firms. There is no government and no foreign trade. Households consume and save. Firms invest. So aggregate demand (AD) = consumption (C) + investment (I).

Aggregate supply (AS) is the total output firms produce. In this model, all income received is either consumed or saved, so AS = C + S. Think of AS as a 45° line: every rupee of output creates a rupee of income.

Equilibrium is where planned AD equals AS, so C + I = C + S. Cancel C and you get S = I. This is the saving-investment approach. Both approaches give the same income.

If AD is more than AS, stocks fall, firms raise output and income rises. If AD is less than AS, stocks pile up, firms cut output and income falls. Income stops changing only at equilibrium. Here investment is treated as autonomous, meaning it does not depend on income.

Key formulas to remember

Aggregate demand (two sector)
AD = C + I
Consumption plus planned investment. No government or foreign trade.
Aggregate supply
AS = Y = C + S
All income is either consumed or saved.
Consumption function
C = a + bY
a = autonomous consumption, b = MPC (marginal propensity to consume), 0 < b < 1.
Saving function
S = Y − C = −a + (1 − b)Y
1 − b is MPS. Saving is negative when Y is low enough.
Equilibrium condition (AD-AS)
Y = C + I
Planned AD equals output.
Equilibrium condition (S-I)
S = I
Planned saving equals planned investment.
Equilibrium income
Y = (a + I) ÷ (1 − b)
Valid when I is autonomous. Gives the same answer from both approaches.
Break-even income
Y = a ÷ (1 − b)
Income at which C = Y and S = 0.

How to solve Keynesian Theory of Income Determination questions

Use this method for any equilibrium income question in a two sector economy. Check whether the question gives a consumption function or a saving function.

  1. 1Write down what is given: C = a + bY (or S function) and the value of I.
  2. 2If only a saving function is given, note that S = −a + (1 − b)Y. You can use S = I directly.
  3. 3Pick one approach. For AD-AS, set Y = C + I. For S-I, set S = I.
  4. 4Substitute the functions and write the equation in Y.
  5. 5Collect Y terms on one side: Y − bY = a + I, so Y(1 − b) = a + I.
  6. 6Divide to get Y = (a + I) ÷ (1 − b).
  7. 7Check: compute C and S at this Y and confirm Y = C + I and S = I.
  8. 8Read the question again. It may ask for consumption, saving or the effect of a change in I, not income itself.

Quickest way: Plug in the formula and test the options

When to use it: Use when the question gives C = a + bY (or an S function) and a fixed I. Best for MCQs where each option is a different income value.

  1. Compute (a + I) ÷ (1 − b) directly. Do this first; it takes about 20 seconds.
  2. If b is a fraction like 0.8, 1 ÷ (1 − b) = 5. Multiply (a + I) by this number.
  3. If you are unsure, test one option: find C at that Y, add I, and see if it returns Y.
  4. For the S-I form, test S = I at the option value.
  5. If a question asks for a change in income after a change in I, multiply the change in I by 1 ÷ (1 − b).
  6. Do not spend time on diagrams. If you are unsure of the function given, skip and return later because wrong answers cost 0.25.

Common mistakes in Keynesian Theory of Income Determination

  • Dividing by b instead of 1 − b.

    Students mix up MPC and MPS when moving terms across the equation.

    Fix: Always write Y − bY = a + I first. The divisor is 1 − b, which is MPS.

  • Forgetting to add autonomous consumption a to I in the numerator.

    Students treat only I as the injection.

    Fix: Numerator is a + I. Both are spending that does not depend on income.

  • Using S = Y − C with the wrong sign for a.

    Students write S = a + (1 − b)Y.

    Fix: S = Y − a − bY = −a + (1 − b)Y. Autonomous saving is negative.

  • Treating equilibrium as the point where C = I.

    Mixing up AD = AS with S = I.

    Fix: Equilibrium is C + I = Y, or equivalently S = I. Never C = I.

  • Saying S = I holds at every income level.

    Students confuse ex-ante (planned) with ex-post (actual) values.

    Fix: S = I holds only at equilibrium for planned values. At other incomes planned S and planned I differ.

  • Ignoring units or mixing figures in ₹ crore with ₹ lakh.

    Rushing through the data in the question.

    Fix: Underline the unit in the question and keep it in your answer.

Worked examples

Example 1

In a two sector economy, C = 100 + 0.8Y and planned investment I = 60 (₹ crore). Equilibrium income is: (a) ₹800 crore (b) ₹900 crore (c) ₹1,000 crore (d) ₹1,200 crore

Show the solution
  1. Set Y = C + I = 100 + 0.8Y + 60.
  2. Y − 0.8Y = 160, so 0.2Y = 160.
  3. Y = 160 ÷ 0.2 = 800.
  4. Check: C = 100 + 0.8 × 800 = 740. C + I = 740 + 60 = 800. Matches Y.

Answer: (a) ₹800 crore

Example 2

Saving function is S = −50 + 0.25Y and autonomous investment is ₹100 crore. Equilibrium income is: (a) ₹400 crore (b) ₹500 crore (c) ₹600 crore (d) ₹800 crore

Show the solution
  1. At equilibrium S = I, so −50 + 0.25Y = 100.
  2. 0.25Y = 150.
  3. Y = 150 ÷ 0.25 = 600.
  4. Check: C = Y − S = 600 − 100 = 500. C + I = 600. Matches Y.

Answer: (c) ₹600 crore

Example 3

With C = 200 + 0.75Y and I = 100, what is the level of saving at equilibrium? (a) ₹100 (b) ₹200 (c) ₹300 (d) ₹1,200

Show the solution
  1. Y = (a + I) ÷ (1 − b) = (200 + 100) ÷ 0.25 = 1,200.
  2. C = 200 + 0.75 × 1,200 = 200 + 900 = 1,100.
  3. S = Y − C = 1,200 − 1,100 = 100.
  4. Check: S = I = 100.

Answer: (a) ₹100. Option (d) is the equilibrium income, not saving.

Exam tips

  • Questions are mostly direct numericals: given C and I, find Y, C or S. Practise 10 of these until they take under a minute.
  • Read what is asked at the end. Many options include equilibrium Y as a trap when the question asks for saving or consumption.
  • Know the conceptual statements: equilibrium at AD = AS, S = I, and what happens when AD exceeds AS.
  • Remember that the model assumes a two sector economy with autonomous investment. If a question adds government or trade, the formula changes.
  • Verify your answer by checking S = I. It catches most arithmetic slips quickly.

Practice questions from Determination of National Income

Keynesian Theory of Income Determination: frequently asked questions

What is the equilibrium level of income in the Keynesian model?

It is the income at which planned aggregate demand equals aggregate supply. In a two sector economy this is the same as planned saving equal to planned investment. With C = a + bY and fixed I, it is Y = (a + I) ÷ (1 − b).

Why does S = I at equilibrium?

AD is C + I and AS is C + S. Setting them equal, C cancels out and leaves S = I. So the two approaches always give the same equilibrium income.

What happens if AD is greater than AS?

Firms find their stocks falling. They increase production and hire more, so income rises. This continues until AD equals AS.

Does this formula work with government and foreign trade?

No. It is for a two sector economy only. With a government sector or foreign trade, AD includes more items such as G and net exports, so the formula changes.