EconomicsCBSE Class 12 · Determination of Income and Employment

Investment Multiplier Class 12: Formula, Working Mechanism and Solved Numericals

Updated 15 October 2026 · Fact-checked

The investment multiplier (k) is the ratio of the change in income to the change in investment that caused it: k = ΔY/ΔI = 1/(1 − MPC) = 1/MPS. Each rupee spent becomes income that is partly spent again, so income rises by a multiple of the investment. The higher the MPC, the larger the multiplier.

Understand Investment Multiplier

Definition. k = ΔY ÷ ΔI. With a consumption function of constant MPC, k = 1 ÷ (1 − MPC) = 1 ÷ MPS.

Why income rises by a multiple (the mechanism). Suppose investment rises by ₹100 crore and MPC = 0.8.

Round 1: ₹100 crore is spent on capital goods and becomes income of their producers: ΔY = 100.
Round 2: they spend 80% of it: ΔC = 80, which is new income for others.
Round 3: those receivers spend 80% of 80 = 64; and so on: 100 + 80 + 64 + 51.2 + ...
The series adds up to 100 × 1/(1 − 0.8) = ₹500 crore. At each round 20% is saved; the process stops when total extra saving (0.2 × 500 = 100) equals the extra investment.

Range of the multiplier.

MPC = 0 → k = 1 (minimum): nothing is re-spent.
MPC = 1 → k = ∞ (theoretical maximum): nothing leaks into saving.
So 1 ≤ k ≤ ∞; k is directly related to MPC and inversely to MPS.

Useful results. ΔY = k × ΔI; ΔC = MPC × ΔY; ΔS = MPS × ΔY = ΔI (in equilibrium, extra saving equals extra investment).

Works in reverse. A fall in investment reduces income by a multiple too: the 'reverse multiplier', important for understanding recessions.

Assumptions. The multiplier assumes MPC is constant, there is unused capacity (so output can rise without prices rising), and in the textbook model the economy is two-sector (no government or foreign trade leakages).

Investment Multiplier: key facts

Multiplier: k = ΔY ÷ ΔI = 1 ÷ (1 − MPC) = 1 ÷ MPS
Change in income: ΔY = k × ΔI
MPC from k: MPC = 1 − 1/k
Changes in C and S: ΔC = MPC × ΔY; ΔS = MPS × ΔY (= ΔI)
Range: 1.MPC = 0
2.k = 1; MPC = 1
3.k = ∞

How to answer Investment Multiplier questions

Multiplier numericals use three interchangeable quantities: k, MPC (or MPS), and the pair ΔY and ΔI. Find whichever is missing.

1Write k = 1/(1 − MPC) = 1/MPS = ΔY/ΔI.
2If MPC or MPS is given, compute k first.
3If ΔY and ΔI are given, k = ΔY/ΔI and then MPC = 1 − 1/k.
4Compute ΔY = k × ΔI or ΔI = ΔY/k as asked.
5For the mechanism, show at least three rounds and the total.
6Check: ΔS = MPS × ΔY should equal ΔI.

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.

Multiplier in a town

Suppose a company invests ₹10 crore to build a factory in a small town. Construction workers and suppliers spend 75% of what they earn in local shops, whose owners and staff in turn spend 75% of their extra income, and so on.

By how much will the town's income finally rise, and why is it more than ₹10 crore?

Try it first, then show the solutionSolution

MPC = 0.75, so k = 1/(1 − 0.75) = 4.
ΔY = 4 × 10 = ₹40 crore.
Each round of spending becomes another person's income; 25% leaks into saving each time.

Answer: Income rises by about ₹40 crore, four times the initial investment, because the ₹10 crore circulates through successive rounds of spending until the extra saving equals the ₹10 crore invested.

Memory hook: One rupee spent becomes several rupees of income.

Tricks to remember Investment Multiplier

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

k = 1 over leak
The multiplier is 1 divided by the leakage per round (MPS).
Use it when: Formula.
0.5 → 2, 0.75 → 4, 0.8 → 5, 0.9 → 10
Memorise common MPC-to-k pairs.
Use it when: Quick MCQs.
Saving catches up with investment
The process ends when extra saving equals extra investment.
Use it when: Explaining the mechanism.

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

If MPC is 0.75, the investment multiplier is:
(a) 0.25
(b) 1.33
(c) 4
(d) 7.5

Try it first, then show the solutionSolution

k = 1/(1 − 0.75) = 1/0.25 = 4.

Answer: (c) 4

Example 2: Change in income, consumption and saving · 3 marks · Short answerBoard level

Investment increases by ₹500 crore and MPS is 0.2. Calculate the multiplier, the increase in income, and the increases in consumption and saving. (3 marks)

Try it first, then show the solutionSolution

k = 1/0.2 = 5.
ΔY = 5 × 500 = ₹2,500 crore.
ΔC = 0.8 × 2,500 = ₹2,000 crore; ΔS = 0.2 × 2,500 = ₹500 crore (= ΔI).

Answer: k = 5; ΔY ₹2,500 crore; ΔC ₹2,000 crore; ΔS ₹500 crore.

Example 3: Round-by-round mechanism · 4 marks · Short answerHarder board level

Explain the working of the multiplier when investment increases by ₹100 crore and MPC is 0.8, showing the first three rounds and the final change in income. (4 marks)

Try it first, then show the solutionSolution

Round 1: ΔI = 100 becomes income; ΔY = 100; ΔC = 80; ΔS = 20.
Round 2: ΔY = 80; ΔC = 64; ΔS = 16.
Round 3: ΔY = 64; ΔC = 51.2; ΔS = 12.8.
Total ΔY = 100/(1 − 0.8) = ₹500 crore; total ΔS = 100 = ΔI.

Answer: Income rises in diminishing rounds (100, 80, 64, ...) to a total of ₹500 crore, when extra saving equals the ₹100 crore of extra investment.

Example 4: Finding the investment needed · 3 marks · Short answerHarder board level

Income is to rise by ₹4,000 crore. MPC is 0.75. How much additional investment is needed? (3 marks)

Try it first, then show the solutionSolution

k = 1/(1 − 0.75) = 4.
ΔI = ΔY/k = 4,000/4 = ₹1,000 crore.

Answer: ₹1,000 crore.

Example 5: MPC and the size of the effect · 4 marks · Short answerHOTS / competency

Compare the effect of an increase in investment of ₹200 crore when MPC is 0.9 and when it is 0.5. Also, if k = 5 and income rises by ₹1,000 crore, find MPC and the rise in consumption. (4 marks)

Try it first, then show the solutionSolution

MPC 0.9: k = 10, ΔY = ₹2,000 crore. MPC 0.5: k = 2, ΔY = ₹400 crore.
Higher MPC → more re-spending each round → bigger multiplier.
k = 5: MPC = 1 − 1/5 = 0.8; ΔC = 0.8 × 1,000 = ₹800 crore.

Answer: ₹2,000 crore vs ₹400 crore; with k = 5, MPC = 0.8 and ΔC = ₹800 crore.

Example 6: Multiplier and MPS · 1 mark · Assertion-reasonHOTS / competency

Assertion (A): The value of the investment multiplier is inversely related to MPS.
Reason (R): k = 1/MPS.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Try it first, then show the solutionSolution

A larger MPS means more leakage each round, so a smaller k; R explains A.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Where students lose marks in Investment Multiplier

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

Mistake: Using k = 1/MPC
Mixing the propensities.
Wrong working
MPC 0.8 → k = 1.25.
Right working
k = 1/(1 − 0.8) = 5.
Do this: Divide 1 by MPS.
Usually costs: 1-2 marks.
Mistake: Saying the multiplier can be less than 1
Forgetting the range of MPC.
Wrong working
MPC 0 → k = 0.
Right working
MPC 0 → k = 1 (minimum).
Do this: k lies between 1 and infinity.
Usually costs: 1 mark.
Mistake: Explaining the mechanism without numbers
Abstract answers.
Wrong working
'Income increases many times.'
Right working
Show rounds: 100, 80, 64, ... totalling 500.
Do this: Use a round table in 4-mark answers.
Usually costs: 1-2 marks.
Mistake: Computing ΔC as MPC × ΔI
Using the initial change.
Wrong working
ΔC = 0.8 × 500 = 400.
Right working
ΔC = 0.8 × ΔY = 0.8 × 2,500 = 2,000.
Do this: ΔC depends on the total change in income.
Usually costs: 1 mark.

Exam tips

Write k = 1/(1 − MPC) = 1/MPS at the top of every multiplier answer.
Show a rounds table when the question says 'explain the working'.
Check that ΔS equals ΔI.
The multiplier is the most repeated numerical in this chapter (3-, 4- and 6-mark items).

Practice questions on Investment Multiplier

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

Q1 · 1 mark · MCQBoard level
If MPC is zero, the value of the investment multiplier is:
(a) 0
(b) 1
(c) infinity
(d) 0.5
Hint
1/(1 − 0).
Answer
(b) 1
Q2 · 1 mark · MCQBoard level
The investment multiplier is:
(a) 1/MPC
(b) 1/(1 − MPS)
(c) 1/(1 − MPC)
(d) MPC/MPS
Hint
1/MPS.
Answer
(c) 1/(1 − MPC)
Q3 · 3 marks · Short answerBoard level
Investment rises by ₹300 crore and MPC is 0.6. Calculate the multiplier and the increase in income. (3 marks)
Hint
k = 2.5.
Answer
k = 1/0.4 = 2.5; ΔY = 2.5 × 300 = ₹750 crore.
Q4 · 3 marks · Short answerHarder board level
An increase in investment of ₹400 crore raises income by ₹2,000 crore. Find the multiplier, MPC and MPS. (3 marks)
Hint
k = ΔY/ΔI.
Answer
k = 5; MPS = 1/5 = 0.2; MPC = 0.8.
Q5 · 4 marks · Short answerHarder board level
Investment increases by ₹1,000 crore and MPC is 0.5. Show the first three rounds and the total increase in income, consumption and saving. (4 marks)
Hint
Rounds halve.
Answer
Rounds of ΔY: 1,000; 500; 250; ... Total ΔY = 1,000 × 2 = ₹2,000 crore; ΔC = ₹1,000 crore; ΔS = ₹1,000 crore (= ΔI).
Q6 · 3 marks · Short answerHarder board level
Explain the relationship between MPC and the multiplier, and why the multiplier cannot be less than one. (3 marks)
Hint
Direct relation; MPC ≥ 0.
Answer
k = 1/(1 − MPC), so a higher MPC gives a higher multiplier: more of each round of income is re-spent. Since MPC ≥ 0, 1 − MPC ≤ 1, so k ≥ 1: at the very least, the initial investment itself becomes income.
Q7 · 3 marks · Short answerHarder board level
The multiplier is 4 and income rises by ₹8,000 crore. Find the increase in investment and the increase in saving, and comment on the result. (3 marks)
Hint
MPS = 0.25.
Answer
ΔI = 8,000/4 = ₹2,000 crore. ΔS = 0.25 × 8,000 = ₹2,000 crore, equal to ΔI, as required at the new equilibrium.
Q8 · 1 mark · Assertion-reasonHarder board level
Assertion (A): The value of the investment multiplier can be less than one.
Reason (R): k = 1/(1 − MPC) and MPC lies between 0 and 1.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Hint
Minimum value.
Answer
(d) A is false, but R is true.
Q9 · 3 marks · Short answerHOTS / competency
The government wants income to rise by ₹6,000 crore. If MPS is 0.25, how much additional investment (or autonomous spending) is required? What if MPS were 0.5? (3 marks)
Hint
ΔI = ΔY × MPS.
Answer
MPS 0.25: k = 4, ΔI = ₹1,500 crore. MPS 0.5: k = 2, ΔI = ₹3,000 crore. A higher saving rate means more initial spending is needed for the same rise in income.
Q10 · 3 marks · Short answerHOTS / competency
Suppose private investment falls by ₹200 crore because firms become pessimistic, and MPC is 0.8. What happens to income? What does this suggest about recessions? (3 marks)
Hint
Reverse multiplier.
Answer
Income falls by 5 × 200 = ₹1,000 crore. The multiplier works in reverse: a fall in investment cuts incomes, which cuts consumption in successive rounds, so a small shock can deepen into a larger downturn.

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.Multiplier when MPS is 0.25?Show answer
4.
2.Range of the multiplier?Show answer
From 1 to infinity.
3.ΔI ₹50 crore, k 6: ΔY?Show answer
₹300 crore.
4.When does the multiplier process stop?Show answer
When extra saving equals the extra investment.
5.MPC if k = 10?Show answer
0.9.

Investment Multiplier: frequently asked questions

What is the investment multiplier in Class 12?

The ratio of the change in income to the change in investment: k = ΔY/ΔI = 1/(1 − MPC).

Why does income rise by more than the investment?

Each rupee spent becomes someone's income; part of it is spent again, creating further income in successive rounds.

What is the relation between MPC and the multiplier?

Direct: a higher MPC means a larger multiplier, since more of each round of income is re-spent.

Can the multiplier work in reverse?

Yes. A fall in investment reduces income by a multiple of the fall.