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Consumption and Saving Functions: APC, MPC Numericals ISC

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EconomicsISC Class 12 · Theory of Income and Employment

Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Income

Updated 17 October 2026 · Fact-checked

The consumption function C = a + bY links consumption to income, where a is autonomous consumption and b is the marginal propensity to consume (MPC). Saving is the part of income not consumed: S = Y - C. APC = C/Y, MPC = change in C / change in Y, APS = S/Y and MPS = change in S / change in Y, with APC + APS = 1 and MPC + MPS = 1. At the break-even income, C = Y and saving is zero.

Left of the break-even income, C is above the 45-degree line (dissaving); right of it, C falls below the line, so saving is positive.

Illustration drawn for QuestionBuddy.

Understand Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point

1. Consumption function. Households' consumption expenditure depends mainly on income. The simple (linear) Keynesian form is C = a + bY, where:

  • a = autonomous consumption (consumption even at zero income, financed by past savings or borrowing),
  • b = MPC, the slope, with 0 < b < 1,
  • bY = induced consumption.

2. Saving function. S = Y - C = Y - a - bY = -a + (1 - b)Y. So the saving function has an intercept -a (dissaving at zero income) and slope 1 - b = MPS.

3. Propensities (average and marginal).

  • APC = C/Y: the fraction of income consumed. It falls as income rises (when a > 0).
  • MPC = change in C / change in Y: the fraction of an additional rupee of income that is consumed; constant in the linear function.
  • APS = S/Y: the fraction of income saved.
  • MPS = change in S / change in Y.

4. Relationships.

  • APC + APS = 1 (since C + S = Y, divide by Y).
  • MPC + MPS = 1 (since change in C + change in S = change in Y).
  • MPC lies between 0 and 1; MPS lies between 0 and 1.
  • With a > 0, APC > MPC at every income; APC falls and approaches MPC as income rises.
  • Below the break-even income, APC is greater than 1 and APS is negative; above it, APC is less than 1 and APS is positive.

5. Break-even point. The income at which C = Y, so saving is zero, APC = 1 and APS = 0. Solving a + bY = Y gives Y = a / (1 - b). Below it consumption exceeds income (dissaving, S < 0, APC > 1); above it saving is positive (APC < 1). In the diagram, the consumption line meets the 45-degree line at the break-even point, and the saving line cuts the income axis at the same income.

6. Factors that shift the function. Wealth, expectations, the distribution of income and the availability of credit change a (shift the function); a change in income causes a movement along it. (Details beyond these are not required.)

Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point: key facts

Consumption function
C = a + bY (b = MPC)
Saving function
S = Y - C = -a + (1 - b)Y
Average propensities
APC = C/Y; APS = S/Y; APC + APS = 1
Marginal propensities
MPC = change in C / change in Y; MPS = change in S / change in Y; MPC + MPS = 1
Break-even income
Y = a / (1 - b), where C = Y and S = 0

How to answer Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point questions

Propensity sums work from a table of Y and C (or S), or from the equation.

  1. 1If only C and Y are given, find S = Y - C.
  2. 2MPC = change in C divided by change in Y between two rows; MPS = 1 - MPC.
  3. 3APC = C/Y and APS = S/Y at each row; check they add to 1.
  4. 4From two points, find b (MPC) first, then a = C - bY.
  5. 5Break-even Y satisfies C = Y: Y = a/(1 - b); check S = 0 and APC = 1 there.

Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point 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 family budget in a mill town

Suppose a family's monthly consumption (in rupees) follows C = 4,000 + 0.8Y. Their income is Rs 25,000 in a good month and drops to Rs 18,000 in a slack month.

Find their consumption and saving in each month and the income at which they neither save nor borrow.

Try it first, then show the solutionSolution
  1. Y = 25,000: C = 4,000 + 20,000 = 24,000; S = 1,000; APC = 0.96.
  2. Y = 18,000: C = 4,000 + 14,400 = 18,400; S = -400 (dissaving).
  3. Break-even: 4,000 + 0.8Y = Y, so Y = 4,000/0.2 = Rs 20,000.

Answer: They save Rs 1,000 in the good month and dissave Rs 400 in the slack month; the break-even income is Rs 20,000.

Memory hook: Even with no income, people must eat.

Tricks to remember Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point

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

  • Two sums to one

    Whatever is not consumed is saved, so APC + APS = 1 and MPC + MPS = 1.

    Use it when: Finding the missing propensity.

  • Break-even: C meets Y

    At break-even the 45-degree line touches the consumption line: consumption equals income, saving zero, APC = 1.

    Use it when: Diagram and numerical.

  • APC beats MPC

    With autonomous consumption, the average is above the marginal; the average slides down towards the marginal.

    Use it when: Comparison questions.

Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point: solved examples

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

Example 1: APS at break-even · 1 mark · MCQBoard level

At the break-even level of income, the average propensity to save is:
(a) one
(b) zero
(c) negative
(d) equal to MPC

Try it first, then show the solutionSolution
  1. At break-even C = Y, so S = 0 and APS = 0.

Answer: (b) zero

Example 2: Propensities from a table · 3 marks · Short answerBoard level

Consumption at incomes of Rs 100, 200, 300 and 400 crore is Rs 110, 190, 270 and 350 crore. Calculate saving, APC, APS and MPC, and find the break-even income. (3 marks)

Try it first, then show the solutionSolution
  1. S = Y - C = -10, 10, 30, 50.
  2. APC = 110/100 = 1.1; 190/200 = 0.95; 270/300 = 0.9; 350/400 = 0.875. APS = -0.1, 0.05, 0.1, 0.125 (each pair adds to 1).
  3. MPC = 80/100 = 0.8 at every step; MPS = 0.2.
  4. Consumption function C = 30 + 0.8Y; break-even: 30 + 0.8Y = Y, so Y = 30/0.2 = Rs 150 crore.

Answer: S = -10, 10, 30, 50; APC = 1.1, 0.95, 0.9, 0.875; MPC = 0.8, MPS = 0.2; break-even income = Rs 150 crore.

Example 3: Using the equation · 4 marks · Short answerHarder board level

The consumption function of an economy is C = 120 + 0.75Y (Rs crore). Find consumption, saving, APC and APS at Y = 1,000, find the saving function, and find the break-even income. What happens at Y = 300? (4 marks)

Try it first, then show the solutionSolution
  1. At Y = 1,000: C = 120 + 750 = 870; S = 1,000 - 870 = 130; APC = 0.87; APS = 0.13.
  2. Saving function: S = Y - 120 - 0.75Y = -120 + 0.25Y.
  3. Break-even: 120 + 0.75Y = Y, so Y = 120/0.25 = Rs 480 crore (S = 0, APC = 1).
  4. At Y = 300: C = 120 + 225 = 345, S = 300 - 345 = -45: dissaving of Rs 45 crore (APC = 1.15), financed by past savings or borrowing.

Answer: C = 870, S = 130, APC 0.87, APS 0.13; S = -120 + 0.25Y; break-even Y = 480; at Y = 300 there is dissaving of Rs 45 crore.

Example 4: Finding the function from two points · 4 marks · Short answerHarder board level

When income is Rs 2,000 crore saving is Rs 300 crore, and when income is Rs 2,400 crore saving is Rs 400 crore. Find MPS, MPC, the consumption function, and the break-even income. (4 marks)

Try it first, then show the solutionSolution
  1. MPS = (400 - 300)/(2,400 - 2,000) = 100/400 = 0.25; MPC = 0.75.
  2. Consumption: at 2,000, C = 2,000 - 300 = 1,700; at 2,400, C = 2,400 - 400 = 2,000. Change in C = 300 = 0.75 x 400 (consistent).
  3. a = 1,700 - 0.75 x 2,000 = 200, so C = 200 + 0.75Y; S = -200 + 0.25Y (check: S at 2,000 is 300).
  4. Break-even: 200 + 0.75Y = Y, so Y = 200/0.25 = Rs 800 crore.

Answer: MPS = 0.25, MPC = 0.75, C = 200 + 0.75Y, and break-even income is Rs 800 crore.

Example 5: APC versus MPC · 4 marks · Short answerHOTS / competency

For C = 120 + 0.75Y, find APC at Y = 480, 2,000 and 10,000, and compare with MPC. Why can APC never fall below MPC here? (4 marks)

Try it first, then show the solutionSolution
  1. Y = 480: C = 120 + 360 = 480, APC = 1.0.
  2. Y = 2,000: C = 1,620, APC = 0.81.
  3. Y = 10,000: C = 7,620, APC = 0.762.
  4. MPC = 0.75 throughout. APC = C/Y = a/Y + b, which equals MPC plus a positive term a/Y, so APC > MPC; as Y grows the term shrinks and APC approaches 0.75 from above but never reaches it.

Answer: APC = 1.0, 0.81, 0.762, always above MPC (0.75) because of autonomous consumption; the gap closes as income rises.

Where students lose marks in Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point

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

  • Mistake: Computing MPC as C/Y

    Mixing average and marginal.

    Wrong working

    MPC = 190/200 = 0.95.

    Right working

    MPC = (190 - 110)/(200 - 100) = 0.8.

    Do this: MPC uses changes, APC uses levels.

    Usually costs: 2 marks.

  • Mistake: Break-even wrongly solved

    Using S = 0 in the wrong function.

    Wrong working

    Break-even Y = a x (1 - b) = 100 x 0.2 = 20.

    Right working

    Y = a/(1 - b) = 100/0.2 = 500.

    Do this: Put C = Y and solve.

    Usually costs: 2 marks.

  • Mistake: Positive saving below break-even

    Ignoring dissaving.

    Wrong working

    At Y = 300, S = 40.

    Right working

    At Y = 300, S = 300 - 340 = -40.

    Do this: Subtract C from Y with the sign.

    Usually costs: 1 mark.

  • Mistake: Saying MPC can exceed 1

    Not recognising the limits.

    Wrong working

    MPC = 1.2.

    Right working

    0 < MPC < 1 for the normal case since part of extra income is saved.

    Do this: Check the answer lies between 0 and 1.

    Usually costs: 1 mark.

Exam tips

  • Write C = a + bY and S = -a + (1 - b)Y at the start of every function problem.
  • Present the table with columns Y, C, S, APC, APS and check each row adds to 1.
  • Show the diagram: consumption line, 45-degree line and the break-even point; the saving line below.
  • The specimen paper tests the break-even idea (APC = 1, APS = 0), so know all three statements.
  • ISC wants only simple numericals here; avoid heavy algebra.

Practice questions on Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point

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

    If the average propensity to consume is 0.9, the average propensity to save is:
    (a) 0.9
    (b) 1.9
    (c) 0.1
    (d) 0.09

    Hint

    APC + APS = 1.

    Answer

    (c) 0.1

  2. Q2 · 3 marks · Short answerBoard level

    Income rises from Rs 500 crore to Rs 600 crore and consumption from Rs 420 crore to Rs 500 crore. Find MPC, MPS and the APC and APS at Rs 500 crore. (3 marks)

    Hint

    MPC uses the changes.

    Answer

    MPC = 80/100 = 0.8; MPS = 0.2; APC at 500 = 420/500 = 0.84; APS = 1 - 0.84 = 0.16 (saving Rs 80 crore).

  3. Q3 · 4 marks · Short answerHarder board level

    The consumption function is C = 60 + 0.6Y. Derive the saving function, find the break-even income, and find C, S and APC at Y = 300. (4 marks)

    Hint

    Break-even where C = Y.

    Answer

    S = Y - 60 - 0.6Y = -60 + 0.4Y. Break-even: 60 + 0.6Y = Y, so Y = 60/0.4 = Rs 150. At Y = 300: C = 60 + 180 = 240; S = 300 - 240 = 60; APC = 240/300 = 0.8.

  4. Q4 · 4 marks · Short answerHarder board level

    Saving is Rs -50, 0, 50 and 100 crore at incomes of Rs 0, 200, 400 and 600 crore. Find consumption at each income, MPS, MPC and the consumption function. What is the break-even income? (4 marks)

    Hint

    C = Y - S.

    Answer

    C = 50, 200, 350, 500. MPS = 50/200 = 0.25, MPC = 0.75. C = 50 + 0.75Y (check at 600: 50 + 450 = 500). Break-even income = Rs 200 crore, where saving is zero.

  5. Q5 · 3 marks · Short answerHOTS / competency

    A household has the consumption function C = 4,000 + 0.8Y (rupees a month). Its income falls from Rs 25,000 to Rs 18,000. Find consumption and saving in each case, the break-even income, and explain how the family can consume more than it earns when income is Rs 18,000. (3 marks)

    Hint

    Compare C with Y at 18,000.

    Answer

    At Rs 25,000: C = 24,000, S = 1,000. At Rs 18,000: C = 4,000 + 14,400 = 18,400, S = -400. Break-even = 4,000/0.2 = Rs 20,000. At Rs 18,000 the family dissaves Rs 400 by drawing on past savings or borrowing, because part of its consumption (autonomous Rs 4,000) does not fall with income.

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.APC + APS equals?Show answer

    One.

  2. 2.MPC + MPS equals?Show answer

    One.

  3. 3.At break-even income, APC equals?Show answer

    One (consumption equals income).

  4. 4.Break-even income formula?Show answer

    Y = a / (1 - b).

  5. 5.What does 'a' in C = a + bY stand for?Show answer

    Autonomous consumption, the consumption at zero income.

Consumption and Saving Functions: APC, MPC, APS, MPS and the Break-Even Point: frequently asked questions

What is the consumption function?

The relationship between consumption and income, C = a + bY.

What is the difference between APC and MPC?

APC is total consumption divided by income; MPC is the change in consumption divided by the change in income.

What is the break-even point?

The income at which consumption equals income and saving is zero.

Why does APC fall as income rises?

Because autonomous consumption is a smaller share of larger incomes, so the average moves towards the MPC.