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Utility Budget Line Consumer Equilibrium Class 11

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EconomicsCBSE Class 11 · Theory of Consumer Behaviour

Utility, Budget Line and Consumer Equilibrium

Updated 17 October 2026 · Fact-checked

Total utility is the sum of satisfaction from all units; marginal utility is the extra satisfaction from one more unit and diminishes as consumption rises. A consumer buying one good is in equilibrium where MU = price (in money terms); for two goods where MUx/Px = MUy/Py within the budget. By indifference curves, equilibrium is where the budget line touches the highest indifference curve: MRS = Px/Py.

Understand Utility, Budget Line and Consumer Equilibrium

Utility. The want-satisfying power of a good. Total utility (TU) = sum of utility from all units. Marginal utility (MU) = change in TU from one more unit = TUₙ − TUₙ₋₁. Law of diminishing marginal utility: as consumption of a good rises, MU falls (other things constant). TU rises while MU is positive, is maximum when MU = 0 and falls when MU is negative.

Worked table (apples). Units 1 to 6: MU = 10, 8, 6, 4, 2, 0; TU = 10, 18, 24, 28, 30, 30 (maximum where MU = 0).

Cardinal approach: one good. MU measured in money. A consumer buys until MU = price (equilibrium): if MU > P, buy more; if MU < P, buy less. With MU in rupees of 10, 8, 6, 4, 2 and price Rs 4, the consumer buys 4 units (MU of 4th = 4).

Two goods. The consumer maximises total utility with a given income when MUx ÷ Px = MUy ÷ Py, and all income is spent.

  • Example: income Rs 12, Px = Rs 2, Py = Rs 3. MU of X (units 1 to 5) = 12, 10, 8, 6, 4; MU of Y = 15, 12, 9, 6, 3. MU per rupee: X: 6, 5, 4, 3, 2; Y: 5, 4, 3, 2, 1.
  • Equal MU per rupee of 4 occurs at 3 units of X and 2 units of Y; expenditure = 3 × 2 + 2 × 3 = 12 ✓. TU = (12 + 10 + 8) + (15 + 12) = 30 + 27 = 57, higher than any other affordable bundle (for example 4X + 1Y gives 36 + 15 = 51).

Budget set and budget line (ordinal approach). The budget set is all bundles the consumer can afford: P₁x₁ + P₂x₂ ≤ M. The budget line is P₁x₁ + P₂x₂ = M. Example: M = Rs 60, Px = Rs 10, Py = Rs 5: intercepts 60 ÷ 10 = 6 units of X and 60 ÷ 5 = 12 units of Y; slope = −Px/Py = −2 (to buy one more X, give up two Y). Income rise shifts the line parallel outward; a price change rotates it.

Indifference curve (IC). All bundles giving equal satisfaction. Properties: slope downward, convex to the origin, higher IC means more satisfaction, ICs never intersect. MRS = number of units of Y given up for one more X to keep satisfaction constant; diminishes along the IC (the reason for convexity); MRS = MUx ÷ MUy.

Equilibrium by IC. The consumer is at the point where the budget line touches (is tangent to) the highest attainable IC: MRS = Px/Py.

Flow chart: income and prices → budget line; preferences → IC; tangency → equilibrium bundle.

Utility, Budget Line and Consumer Equilibrium: key facts

Marginal utility
MU_n = TU_n - TU_(n-1)
Diminishes
One good
MU (in money) = Price
Equilibrium
Two goods
MUx/Px = MUy/Py | spend all income
Utility rule
Budget line
  • Px x + Py y = M
  • slope = -Px/Py
  • intercepts M/Px and M/Py
Ordinal approach

How to answer Utility, Budget Line and Consumer Equilibrium questions

Questions give utility tables or prices and incomes.

  1. 1Find MU per rupee for each good.
  2. 2Pick units where the ratios are equal while spending exactly the income.
  3. 3Compute TU to confirm it is highest.
  4. 4For budget lines, find the intercepts and slope.
  5. 5For IC equilibrium state the tangency condition.

Utility, Budget Line and Consumer Equilibrium 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.

Samosa and tea

Suppose a student with Rs 12 buys samosas at Rs 2 each and cups of tea at Rs 3 each, and the extra pleasure of each unit falls as she has more.

What bundle gives the greatest satisfaction by the tables in this page?

Try it first, then show the solutionSolution
  1. Compute MU per rupee for each unit.
  2. Equal values (4) arise at the third samosa and the second tea.
  3. Spending: 3 x 2 + 2 x 3 = 12, TU = 57.

Answer: 3 samosas and 2 teas.

Memory hook: Equalise utility per rupee.

Tricks to remember Utility, Budget Line and Consumer Equilibrium

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

  • MU falls, TU rises

    TU rises with positive MU and peaks when MU = 0.

    Use it when: Relation

  • Equal per rupee

    MUx/Px = MUy/Py.

    Use it when: Equilibrium

  • Slope = Px over Py

    Budget line slope magnitude is the price ratio.

    Use it when: Budget line

Utility, Budget Line and Consumer Equilibrium: solved examples

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

Example 1: MU and TU · 3 marks · Short answerBoard level

Given MU of apples 10, 8, 6, 4, 2, 0, find TU for each unit and state when TU is maximum.

Try it first, then show the solutionSolution
  1. TU = 10, 18, 24, 28, 30, 30 (1 mark).
  2. TU is maximum (30) when MU = 0 at the 5th and 6th units (1 mark).
  3. MU falls with each unit, showing diminishing marginal utility (1 mark).

Answer: TU 10, 18, 24, 28, 30, 30.

Example 2: One-good equilibrium · 3 marks · Short answerBoard level

A consumer values apples as 10, 8, 6, 4, 2 rupees for successive units and the price is Rs 4. How many units does she buy and why?

Try it first, then show the solutionSolution
  1. Buy as long as MU is at least the price (1 mark).
  2. Fourth unit has MU = 4 = price, fifth has MU = 2 < price (1 mark).
  3. So she buys 4 units; here MU = price (1 mark).

Answer: 4 units.

Example 3: Two-good equilibrium · 5 marks · Long answerHarder board level

Income Rs 12, Px = 2, Py = 3. MU of X: 12, 10, 8, 6, 4; MU of Y: 15, 12, 9, 6, 3. Find the equilibrium bundle and TU.

Try it first, then show the solutionSolution
  1. MU per rupee of X: 6, 5, 4, 3, 2; of Y: 5, 4, 3, 2, 1 (1 mark).
  2. Equality at 4: 3rd unit of X and 2nd of Y (1 mark).
  3. Spending = 3 x 2 + 2 x 3 = 12 = income (1 mark).
  4. TU = (12+10+8) + (15+12) = 57 (1 mark).
  5. Check: 4X + 1Y costs 11 and gives only 36 + 15 = 51 (1 mark).

Answer: 3 X and 2 Y; TU 57.

Example 4: Budget line · 3 marks · Short answerHarder board level

Income Rs 60, Px = Rs 10, Py = Rs 5. Find the intercepts and slope of the budget line, and say whether 3 X and 6 Y is affordable.

Try it first, then show the solutionSolution
  1. X-intercept = 60/10 = 6; Y-intercept = 60/5 = 12 (1 mark).
  2. Slope = -Px/Py = -2 (1 mark).
  3. Cost of 3X + 6Y = 30 + 30 = 60, so it lies on the line and is affordable (1 mark).

Answer: 6; 12; slope -2; affordable.

Example 5: IC equilibrium · 5 marks · Long answerHOTS / competency

At a bundle the MRS of X for Y is 3 while Px/Py = 2. Is the consumer in equilibrium? Which good should she buy more of and what happens to the MRS?

Try it first, then show the solutionSolution
  1. MRS (3) > Px/Py (2), so she is not in equilibrium (1 mark).
  2. She values X more than the market asks she give up Y for it (1 mark).
  3. She should buy more X and less Y (1 mark).
  4. As she buys more X, MRS falls due to diminishing MRS (1 mark).
  5. Equilibrium is reached when MRS = Px/Py = 2 (1 mark).

Answer: Buy more X until MRS = 2.

Where students lose marks in Utility, Budget Line and Consumer Equilibrium

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

  • Mistake: MU = TU

    Terms confused.

    Wrong working

    MU is the sum of utilities.

    Right working

    TU is the sum; MU is extra utility.

    Do this: Add for TU.

    Usually costs: 1 mark.

  • Mistake: Using prices unequal

    Ratio ignored.

    Wrong working

    Buy where MUx = MUy.

    Right working

    MUx/Px = MUy/Py.

    Do this: Per rupee.

    Usually costs: 1 mark.

  • Mistake: Slope = Py/Px

    Inversion.

    Wrong working

    Budget line slope is Py/Px.

    Right working

    Slope magnitude is Px/Py.

    Do this: X price over Y price.

    Usually costs: 1 mark.

Exam tips

  • Make MU per rupee columns.
  • Check that spending equals income.
  • Confirm TU against alternatives.
  • State the IC condition MRS = Px/Py.

Practice questions on Utility, Budget Line and Consumer Equilibrium

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

    When marginal utility of a good becomes zero, total utility is
    (a) zero (b) at its maximum (c) negative (d) still rising

    Hint

    Peak of TU.

    Answer

    (b).

  2. Q2 · 1 mark · Assertion-reasonHarder board level

    Assertion (A): The budget line shifts outward when income rises.
    Reason (R): Income increases the quantity of both goods that can be bought.
    (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

    Parallel shift.

    Answer

    (a).

  3. Q3 · 2 marks · Very short answerBoard level

    If M = Rs 100, Px = Rs 5 and Py = Rs 20, find both intercepts and the slope of the budget line.

    Hint

    Divide M by prices.

    Answer

    X-intercept = 20; Y-intercept = 5; slope = -5/20 = -0.25.

  4. Q4 · 4 marks · Case-basedHarder board level

    Read and answer.
    Suppose MUx = 24 with Px = 6, and MUy = 20 with Py = 5.
    (a) Find MU per rupee for each. (1)
    (b) Is the consumer in equilibrium? (1)
    (c) Which good should she buy more of? (2)

    Hint

    24/6 and 20/5.

    Answer

    (a) X: 4; Y: 4. (b) Yes, if the whole income is spent, since MUx/Px = MUy/Py. (c) Neither: any shift would lower total utility.

  5. Q5 · 3 marks · Short answerHOTS / competency

    Suppose income doubles and prices stay the same. Describe the new budget line, and explain why the consumer's old equilibrium is no longer the best.

    Hint

    Parallel shift.

    Answer

    The budget line shifts outward in parallel with twice the intercepts and the same slope. The consumer can reach a higher IC, so the old bundle (on a lower IC) is no longer the best.

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.Law of DMU?Show answer

    MU falls as consumption rises.

  2. 2.TU at MU = 0?Show answer

    Maximum.

  3. 3.Budget line slope?Show answer

    -Px/Py.

  4. 4.MRS?Show answer

    MUx/MUy.

  5. 5.IC shape?Show answer

    Convex to origin.

  6. 6.Equilibrium by IC?Show answer

    Tangency.

Utility, Budget Line and Consumer Equilibrium: frequently asked questions

What is marginal utility?

Extra utility from one more unit.

What is a budget set?

All affordable bundles.

What is an indifference curve?

Bundles of equal satisfaction.

Why is IC convex?

Diminishing MRS.

When is a consumer in equilibrium?

At the best affordable bundle.