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Equilibrium Income and Investment Multiplier ISC Class 12

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EconomicsISC Class 12 · Theory of Income and Employment

Equilibrium Income and the Investment Multiplier: Mechanism, Diagram and Numericals

Updated 17 October 2026 · Fact-checked

In a simple economy, equilibrium income is where aggregate demand equals aggregate supply (C + I = Y), which is also where planned saving equals planned investment. The investment multiplier k = change in Y / change in I = 1/(1 - MPC) = 1/MPS tells by how many times income rises when investment rises. The extra income is passed on round after round, and the process ends when extra saving equals extra investment.

Understand Equilibrium Income and the Investment Multiplier

1. Equilibrium output (income) in a two-sector economy. Aggregate demand AD = C + I (consumption plus investment); aggregate supply AS = Y (output equals income). Equilibrium is where AD = AS, i.e. Y = C + I; since Y = C + S, the same point has S = I (planned saving equals planned investment). With C = a + bY, equilibrium income is Y = (a + I) / (1 - b).

Why equilibrium holds. If AD > AS (ex-ante demand above output), stocks are run down, firms raise output and income rises. If AD < AS, unsold stocks pile up and output falls. Equilibrium is the output where planned demand equals output, so neither force acts. (The distinction of ex-ante and ex-post demand: ex-ante is planned demand, ex-post is the realised level.)

Diagram. The AD line (C + I) lies above the C line by the amount of I and cuts the 45-degree line at E, whose income is the equilibrium Y. In the second diagram the S line and the I line (a horizontal line) intersect at the same income.

2. Investment multiplier: meaning. k = change in Y / change in I. If investment rises by one rupee, income rises by k rupees. k = 1 / (1 - MPC) = 1 / MPS. The higher the MPC, the larger the multiplier. Since MPC lies between 0 and 1, k lies between 1 and infinity.

3. Mechanism (rounds of spending). Suppose investment rises by Rs 100 crore and MPC is 0.6. The Rs 100 crore becomes income of the producers of capital goods (round 1). They consume 0.6 of it (Rs 60 crore), which becomes income of others (round 2); they spend 0.6 of Rs 60 crore (Rs 36 crore), and so on. Total change in income = 100 + 60 + 36 + 21.6 + ... = 100/(1 - 0.6) = Rs 250 crore. The process stops when extra saving (0.4 x 250 = Rs 100 crore) equals the extra investment. In the diagram, the AD line shifts upward by the change in I but the new equilibrium income rises by k times that distance.

4. Reverse working. A fall in investment lowers income by k times the fall.

5. Limits (assumptions). The multiplier works fully only if there is unused capacity and unemployment (so output can respond), MPC is constant, prices do not rise, and there are no leakages other than saving (no taxes or imports in this simple model). The same formula applies to any autonomous addition to spending.

Equilibrium Income and the Investment Multiplier: key facts

Equilibrium condition
AD = AS, i.e. Y = C + I; equivalently S = I
Equilibrium income (linear)
Y = (a + I) / (1 - b) for C = a + bY
Multiplier
k = change in Y / change in I = 1 / (1 - MPC) = 1 / MPS
Change in income
Change in Y = k x change in I
Check
Change in S = MPS x change in Y = change in I

How to answer Equilibrium Income and the Investment Multiplier questions

Equilibrium and multiplier sums are done in two steps: find k from the propensity, then apply it to the change in investment.

  1. 1For equilibrium, write Y = a + bY + I and solve for Y; confirm S = I.
  2. 2For a multiplier problem, find k = 1/(1 - MPC) = 1/MPS.
  3. 3Apply: change in Y = k x change in I (or find change in I = change in Y / k).
  4. 4Find change in C = MPC x change in Y and change in S = MPS x change in Y; change in S should equal change in I.
  5. 5For the mechanism, tabulate at least three rounds and the total.

Equilibrium Income and the Investment Multiplier in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

A new bridge in a district

Suppose a state spends Rs 100 crore on a new bridge. Workers and suppliers earn this money and, with an MPC of 0.6, spend 60 per cent in local markets, whose owners spend 60 per cent of that, and so on.

By how much does district income rise, and why is it more than Rs 100 crore?

Try it first, then show the solutionSolution
  1. k = 1/(1 - 0.6) = 2.5.
  2. Change in Y = 2.5 x 100 = Rs 250 crore.
  3. Rounds: 100, 60, 36, 21.6, ... each round of spending is the next person's income.

Answer: District income rises by Rs 250 crore, since the initial Rs 100 crore is re-spent in successive rounds until the leakage into saving equals Rs 100 crore.

Memory hook: One person's spending is another's income.

Tricks to remember Equilibrium Income and the Investment Multiplier

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • k is the inverse of the leak

    k = 1/MPS: the smaller the share that leaks into saving, the larger the multiplier.

    Use it when: Quick formulas.

  • Equilibrium: saving meets investment

    What households leak (S) must equal what firms inject (I).

    Use it when: Equilibrium condition.

  • Rounds shrink by MPC

    Each round is MPC times the last; the total is a geometric series 1/(1 - MPC).

    Use it when: Mechanism table.

Equilibrium Income and the Investment Multiplier: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Multiplier from MPC · 1 mark · MCQBoard level

For an economy in which people spend nine-tenths of every extra rupee of income, the investment multiplier is:
(a) 0.1
(b) 1.11
(c) 9
(d) 10

Try it first, then show the solutionSolution
  1. k = 1/(1 - 0.9) = 1/0.1 = 10.

Answer: (d) 10

Example 2: Effects of an increase in investment · 3 marks · Short answerBoard level

Investment rises by Rs 200 crore and MPC is 0.75. Calculate the multiplier, the rise in income, and the rises in consumption and saving. (3 marks)

Try it first, then show the solutionSolution
  1. k = 1/(1 - 0.75) = 4.
  2. Change in Y = 4 x 200 = Rs 800 crore.
  3. Change in C = 0.75 x 800 = Rs 600 crore; change in S = 0.25 x 800 = Rs 200 crore (= change in I).

Answer: k = 4; income rises by Rs 800 crore; consumption by Rs 600 crore; saving by Rs 200 crore.

Example 3: Equilibrium and a rise in investment · 4 marks · Short answerHarder board level

In an economy C = 80 + 0.75Y and planned investment I = Rs 120 crore. (a) Find equilibrium income and show S = I. (b) If investment rises to Rs 160 crore, find the new equilibrium income and verify with the multiplier. (4 marks)

Try it first, then show the solutionSolution
  1. (a) Y = C + I = 80 + 0.75Y + 120, so 0.25Y = 200 and Y = Rs 800 crore. C = 80 + 600 = 680; S = 800 - 680 = 120 = I.
  2. (b) Y = (80 + 160)/0.25 = Rs 960 crore.
  3. Multiplier check: k = 4; change in I = 40; change in Y = 4 x 40 = 160 = 960 - 800.

Answer: Equilibrium income is Rs 800 crore (S = I = 120); after investment rises to Rs 160 crore it is Rs 960 crore, a rise of Rs 160 crore = 4 x 40.

Example 4: Mechanism with a table · 4 marks · Short answerHarder board level

Investment rises by Rs 100 crore; MPC is 0.6. Show the first four rounds of income, the total change in income when the process is complete, and the leftover after four rounds. (4 marks)

Try it first, then show the solutionSolution
  1. Round 1: 100. Round 2: 0.6 x 100 = 60. Round 3: 0.6 x 60 = 36. Round 4: 0.6 x 36 = 21.6.
  2. Sum of the first four rounds = 100 + 60 + 36 + 21.6 = Rs 217.6 crore.
  3. Total change = 100 x 1/(1 - 0.6) = 100 x 2.5 = Rs 250 crore; remaining rounds add 250 - 217.6 = Rs 32.4 crore.
  4. Total saving = 0.4 x 250 = Rs 100 crore = the rise in investment: the process ends.

Answer: The rounds are 100, 60, 36, 21.6, ... totalling Rs 250 crore; after four rounds Rs 217.6 crore is generated and the process ends when saving of Rs 100 crore equals the investment.

Example 5: Reverse multiplier and policy · 4 marks · Short answerHOTS / competency

Firms cut investment by Rs 50 crore and MPC is 0.8. (a) Find the fall in income. (b) How much extra autonomous spending (for example by the government) would restore income if MPC is 0.8? What if the MPC were 0.5? Comment on the difference. (4 marks)

Try it first, then show the solutionSolution
  1. (a) k = 1/(1 - 0.8) = 5; change in Y = 5 x (-50) = -Rs 250 crore.
  2. (b) To raise Y by 250: required spending = 250/5 = Rs 50 crore at MPC 0.8.
  3. If MPC = 0.5: k = 2, required spending = 250/2 = Rs 125 crore.
  4. A lower MPC means a smaller multiplier, so more spending is needed for the same recovery.

Answer: Income falls by Rs 250 crore; Rs 50 crore of extra spending restores it at MPC 0.8, while Rs 125 crore is needed at MPC 0.5.

Where students lose marks in Equilibrium Income and the Investment Multiplier

The slips examiners see most often, and what to write instead.

  • Mistake: Using k = 1/MPC

    Mixing the two propensities.

    Wrong working

    MPC 0.75: k = 1/0.75 = 1.33.

    Right working

    k = 1/(1 - 0.75) = 4.

    Do this: The denominator is 1 minus MPC, which is MPS.

    Usually costs: 2 marks.

  • Mistake: Change in C as MPC times change in I

    Using the first-round change.

    Wrong working

    Change in C = 0.75 x 200 = 150.

    Right working

    Change in C = 0.75 x change in Y = 0.75 x 800 = 600.

    Do this: Apply the MPC to the total change in income.

    Usually costs: 1-2 marks.

  • Mistake: Forgetting investment in equilibrium

    Solving only Y = C.

    Wrong working

    Y = 80 + 0.75Y gives Y = 320.

    Right working

    Y = 80 + 0.75Y + 120 gives Y = 800.

    Do this: Add I to the right side.

    Usually costs: 2 marks.

  • Mistake: Calling any S = I point an equilibrium of realised values

    Mixing ex-ante and ex-post.

    Wrong working

    S = I always, so every output is an equilibrium.

    Right working

    Planned (ex-ante) S = I only at the equilibrium output; ex-post S = I holds after adjustment.

    Do this: Use the word 'planned'.

    Usually costs: 1 mark.

Exam tips

  • Draw both diagrams: C + I against the 45-degree line, and S against I.
  • Show the mechanism with a short rounds table (at least three rounds) and give the total using the formula.
  • State k = 1/(1 - MPC) = 1/MPS and the limits: 1 to infinity.
  • Check change in S equals change in I in every multiplier numerical.
  • Mention the assumption of unused capacity when explaining why output can rise.

Practice questions on Equilibrium Income and the Investment Multiplier

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    The multiplier process comes to an end when:
    (a) extra consumption equals extra income
    (b) extra saving equals extra investment
    (c) MPC becomes zero
    (d) investment becomes zero

    Hint

    Think about leakages.

    Answer

    (b) extra saving equals extra investment

  2. Q2 · 3 marks · Short answerBoard level

    Investment rises by Rs 150 crore and MPC is 0.8. Calculate the multiplier, the rise in income, and the rise in consumption. (3 marks)

    Hint

    k = 1/MPS.

    Answer

    k = 1/0.2 = 5; change in Y = 5 x 150 = Rs 750 crore; change in C = 0.8 x 750 = Rs 600 crore (and saving rises by Rs 150 crore).

  3. Q3 · 4 marks · Short answerHarder board level

    A rise in investment of Rs 250 crore pushes national income up by Rs 1,250 crore. Find the multiplier, MPS, MPC and the rise in consumption. (4 marks)

    Hint

    k = change in Y / change in I.

    Answer

    k = 1,250/250 = 5; MPS = 1/5 = 0.2; MPC = 0.8; change in C = 0.8 x 1,250 = Rs 1,000 crore; change in S = Rs 250 crore, equal to the rise in investment.

  4. Q4 · 4 marks · Short answerHarder board level

    In an economy C = 50 + 0.8Y and I = Rs 150 crore. Find equilibrium income and check that S = I. If investment falls to Rs 100 crore, find the new income and compare the fall with the multiplier. (4 marks)

    Hint

    Y = (a + I)/(1 - b).

    Answer

    Y = (50 + 150)/0.2 = Rs 1,000 crore; S = -50 + 0.2 x 1,000 = Rs 150 crore = I. After I = 100: Y = 150/0.2 = Rs 750 crore. Income falls by Rs 250 crore; k = 5 and the change in I is -50, so 5 x (-50) = -250: the reverse multiplier.

  5. Q5 · 3 marks · Short answerHOTS / competency

    The government wishes to raise income by Rs 600 crore. If MPC is 0.75, how much extra investment (or autonomous spending) is needed? How much more would be needed if MPC were 0.5, and what does this show about the effect of high saving on the multiplier? (3 marks)

    Hint

    Change in I = change in Y / k.

    Answer

    MPC 0.75: k = 4, change in I = 600/4 = Rs 150 crore. MPC 0.5: k = 2, change in I = 600/2 = Rs 300 crore. A higher saving rate (lower MPC) makes the multiplier smaller, so a bigger initial injection is required.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Multiplier formula?Show answer

    k = 1/(1 - MPC) = 1/MPS.

  2. 2.Equilibrium condition?Show answer

    AD = AS, or planned S = planned I.

  3. 3.Range of k?Show answer

    From 1 to infinity.

  4. 4.Multiplier when MPC is 0.5?Show answer

    2.

  5. 5.When does the multiplier process stop?Show answer

    When extra saving equals the extra investment.

Equilibrium Income and the Investment Multiplier: frequently asked questions

What is the investment multiplier?

The ratio of the change in income to the change in investment, k = 1/(1 - MPC).

How is equilibrium income determined?

At the output where aggregate demand equals aggregate supply (C + I = Y), equivalent to S = I.

Why is the increase in income more than the initial investment?

Because each rupee of spending becomes someone's income, part of which is spent again in successive rounds.

Can the multiplier work in reverse?

Yes, a fall in investment reduces income by k times the fall.