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MPC, MPS, Investment Multiplier & Income Determination Numericals

Income Determination questions connect several formulas: consumption, saving, MPC, MPS, multiplier and equilibrium income. This cluster keeps those relationships together with worked numericals so students can understand the sequence instead of memorising isolated formulas.

Formula map

  • MPC: MPC = ΔC ÷ ΔY — Marginal Propensity to Consume.
  • MPS: MPS = ΔS ÷ ΔY = 1 − MPC — In the simple model, MPC + MPS = 1.
  • Multiplier: k = 1 ÷ (1 − MPC) = 1 ÷ MPS — Simple Keynesian investment multiplier.
  • Income Change: ΔY = k × ΔI — Change in income equals multiplier times change in investment.
  • Equilibrium Income: Y = (C̄ + I) ÷ (1 − MPC) — Simple two-sector model with autonomous investment.

8 solved numericals with steps

These are original learning problems prepared for practice and are not labelled as official CBSE previous-year questions.

Q2. Multiplier from MPC — Basic

MPC = 0.8. Find MPS and the investment multiplier.

  1. MPS = 1 − 0.8 = 0.2
  2. k = 1 ÷ 0.2

Answer: MPS = 0.2; k = 5

Q3. Multiplier from MPS — Basic

MPS = 0.25. Find MPC and the multiplier.

  1. MPC = 1 − 0.25 = 0.75
  2. k = 1 ÷ 0.25

Answer: MPC = 0.75; k = 4

Q4. Change in Income — Board-style

MPC = 0.75 and investment rises by ₹100 crore. Find the multiplier and change in income.

  1. k = 1 ÷ (1 − 0.75) = 4
  2. ΔY = 4 × 100

Answer: k = 4; ΔY = ₹400 crore

Q5. Fall in Investment — Mixed sign

MPC = 0.75 and investment falls by ₹50 crore. Find the change in income.

  1. k = 4
  2. ΔI = −50
  3. ΔY = 4 × (−50)

Answer: Income falls by ₹200 crore

Q6. Consumption and Saving — Function

C = 100 + 0.8Y. Find consumption and saving when Y = ₹1,000.

  1. C = 100 + 0.8(1,000) = 900
  2. S = Y − C = 1,000 − 900

Answer: C = ₹900; S = ₹100

Q7. Two-sector Equilibrium Income — Equilibrium

Autonomous consumption is ₹100, autonomous investment is ₹200 and MPC = 0.8. Find equilibrium income.

  1. Y = (C̄ + I) ÷ (1 − MPC)
  2. = (100 + 200) ÷ 0.2
  3. = 300 ÷ 0.2

Answer: ₹1,500

Q8. Find MPC from Multiplier — Reverse question

The investment multiplier is 5. Find MPS and MPC.

  1. MPS = 1 ÷ k = 1 ÷ 5 = 0.2
  2. MPC = 1 − 0.2

Answer: MPS = 0.2; MPC = 0.8

Quick self-test

  1. ΔY = 600 and ΔC = 450. Find MPC. Answer: 0.75
  2. MPC = 0.6. Find MPS. Answer: 0.4
  3. MPS = 0.2. Find multiplier. Answer: 5
  4. Multiplier = 4 and ΔI = ₹75. Find ΔY. Answer: ₹300
  5. Multiplier = 2.5. Find MPS. Answer: 0.4

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Topics covered

  • MPC and MPS
  • APC and APS
  • Consumption function
  • Saving function
  • Investment multiplier
  • Equilibrium income
  • Change in income due to change in investment
  • Reverse multiplier questions

Calculators in this toolkit

Frequently asked questions

What is the relation between MPC and MPS?

In the simple consumption-saving model, MPC + MPS = 1. If one is known, the other can be calculated immediately.

How is the investment multiplier calculated?

The simple multiplier is k = 1/(1 − MPC), which is also equal to 1/MPS.

How do I calculate equilibrium income?

In a simple two-sector model with C = C̄ + MPC×Y and autonomous investment I, equilibrium income is Y = (C̄ + I)/(1 − MPC).

Are the worked questions official CBSE questions?

No. They are original practice numericals unless an official source is explicitly identified.

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