EconomicsISC Class 12 · Demand

Ordinal Utility Analysis: Indifference Curves, MRS, Budget Line and Consumer's Equilibrium

Updated 17 October 2026 · Fact-checked

An indifference curve joins all combinations of two goods that give the consumer equal satisfaction. It slopes downward and is convex to the origin because the marginal rate of substitution (MRS) diminishes. The budget line shows what income can buy. The consumer is in equilibrium where the budget line is tangent to the highest attainable indifference curve, so MRSxy = Px/Py.

Understand Indifference Curves, Budget Line and Consumer's Equilibrium

1. The ordinal idea. Instead of measuring satisfaction in utils, the ordinal approach only ranks bundles as preferred, less preferred or equally preferred. This is the basis of indifference curve (IC) analysis.

2. Indifference curve and schedule. An indifference schedule lists different combinations of two goods (x, y) that give the consumer the same satisfaction; plotting it gives an indifference curve. Every point on one curve means the same satisfaction, so the consumer is indifferent between them.

3. Marginal rate of substitution (MRS). MRSxy is the amount of good y the consumer is willing to give up to gain one more unit of x, keeping satisfaction unchanged: MRSxy = (change in y) / (change in x), taken without the sign. It also equals the ratio of marginal utilities MUx/MUy. Diminishing MRS (DMRS): as the consumer has more x and less y, he is willing to give up fewer units of y for each additional x, because y becomes scarcer and x less valuable at the margin. DMRS is the reason ICs are convex to the origin.

4. Properties of indifference curves.

Downward sloping from left to right: to keep satisfaction the same, more of x must be matched by less of y.
Convex to the origin: because MRS diminishes.
A higher IC shows greater satisfaction: it holds more of at least one good.
Two ICs never intersect: an intersection would give one bundle two different satisfaction levels and break the ranking.
ICs do not touch either axis (for two goods both are consumed in positive amounts).
ICs need not be parallel; their slopes differ at different points.

5. Indifference map. A set of ICs for the same consumer, each higher curve showing a higher level of satisfaction (IC1 < IC2 < IC3).

6. Budget line. It shows all bundles the consumer can buy with the whole income M at given prices: Px.x + Py.y = M. Intercepts: M/Px on the x-axis and M/Py on the y-axis. Slope = Px/Py (the price ratio). A rise in income shifts the line outward and parallel; a rise in the price of x makes it steeper (the x-intercept shrinks); points inside the line are affordable but leave income unused, points outside are unaffordable.

7. Consumer's equilibrium. The consumer wants the highest IC he can reach. Conditions:
1. Budget line is tangent to an IC, so MRSxy = Px/Py (the rate at which he is willing to swap equals the rate at which the market allows).
2. The IC is convex to the origin at the point (MRS is falling), so the tangency is a maximum.
In the diagram, ICs above the tangent one lie beyond the budget; ICs below give lower satisfaction; where the budget line cuts a lower IC at two points, moving along the line to the middle reaches a higher IC. If MRS > Px/Py he gives up y to buy more x; if MRS < Px/Py he gives up x for y; either way MRS moves towards the price ratio.

Note on the two approaches. The cardinal condition MUx/Px = MUy/Py can be rearranged to MUx/MUy = Px/Py, the same as the ordinal condition.

Indifference Curves, Budget Line and Consumer's Equilibrium: key facts

MRS: MRSxy = change in y / change in x (without sign) = MUx / MUy
Budget line: Px.x + Py.y = M
Intercepts and slope: x-intercept = M/Px; y-intercept = M/Py; slope = Px/Py
Equilibrium: MRSxy = Px/Py (budget line tangent to the highest attainable IC)

How to answer Indifference Curves, Budget Line and Consumer's Equilibrium questions

Ordinal numericals ask for MRS from a schedule, the budget line from prices and income, or the direction in which a consumer will move.

1For MRS, divide the loss of y by the gain of x between neighbouring rows of the schedule.
2Check that the MRS values fall to confirm DMRS.
3For the budget line, compute M/Px, M/Py and Px/Py; test any bundle by calculating Px.x + Py.y against M.
4Compare MRS with Px/Py: if MRS is greater, buy more x; if smaller, buy less x.
5State the equilibrium condition and the second condition (convexity) in the final line.

Indifference Curves, Budget Line and Consumer's 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.

Choosing between snacks and travel

Suppose Arjun has Rs 120 a week to spend on samosas at Rs 10 each and bus rides at Rs 5 each. He is happy with 6 samosas and 12 rides, but is equally happy with 4 samosas and 16 rides.

What do these two bundles tell us, and is either of them affordable?

Try it first, then show the solutionSolution

Equal satisfaction means both bundles lie on one indifference curve.
Cost of (6, 12) = 6 x 10 + 12 x 5 = Rs 120; cost of (4, 16) = 4 x 10 + 16 x 5 = Rs 120.
Both lie exactly on the budget line.

Answer: Both bundles are on the same indifference curve and are just affordable; the equilibrium bundle is where the curve touches (is tangent to) the budget line.

Memory hook: Same happiness, same hole in the pocket: tangent point.

Tricks to remember Indifference Curves, Budget Line and Consumer's Equilibrium

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

DNC-N
Downward sloping, Never intersect, Convex to origin, Never touch the axes (and Higher means more).
Use it when: Listing properties quickly.
MRS versus price ratio
MRS is what I am willing to pay in y; Px/Py is what the market demands. Trade while willingness exceeds the price.
Use it when: Direction of movement questions.
Budget line slope
Slope = price of the good on the x-axis divided by the price of the good on the y-axis.
Use it when: Avoid inverting the ratio.

Indifference Curves, Budget Line and Consumer's Equilibrium: solved examples

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

Example 1: Equilibrium condition · 1 mark · MCQBoard level

At the point where the budget line just touches the highest attainable indifference curve, the MRSxy equals:
(a) Py/Px
(b) Px/Py
(c) MUx x MUy
(d) zero

Try it first, then show the solutionSolution

The budget line is tangent to the highest IC, so the slopes match: MRSxy = Px/Py.

Answer: (b) MRSxy = Px/Py

Example 2: MRS from a schedule · 3 marks · Short answerBoard level

A consumer is indifferent between the combinations (x, y): (1, 10), (2, 6), (3, 3), (4, 1). Calculate MRSxy between successive combinations and show that it diminishes. (3 marks)

Try it first, then show the solutionSolution

From (1, 10) to (2, 6): gives up 4 of y for 1 of x, MRS = 4/1 = 4.
From (2, 6) to (3, 3): gives up 3 for 1, MRS = 3.
From (3, 3) to (4, 1): gives up 2 for 1, MRS = 2.
The values 4, 3, 2 fall: DMRS, which makes the IC convex to the origin.

Answer: MRS = 4, 3, 2, a diminishing series; hence the indifference curve is convex to the origin.

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

A consumer has an income of Rs 240; Px = Rs 20 and Py = Rs 10. (a) Find the intercepts and slope of the budget line. (b) What happens if income rises to Rs 360? (c) What happens if Px rises to Rs 30 at the original income? (4 marks)

Try it first, then show the solutionSolution

(a) x-intercept = 240/20 = 12; y-intercept = 240/10 = 24; slope = 20/10 = 2.
(b) Intercepts become 360/20 = 18 and 360/10 = 36; slope is still 2: a parallel outward shift.
(c) x-intercept = 240/30 = 8; y-intercept stays 24; slope = 30/10 = 3: the line pivots inwards on the y-axis and becomes steeper.

Answer: (a) 12 and 24, slope 2. (b) Parallel shift to 18 and 36. (c) x-intercept falls to 8, y-intercept unchanged at 24, slope 3.

Example 4: Direction of adjustment · 4 marks · Short answerHarder board level

Income is Rs 120, Px = Rs 10 and Py = Rs 5. The consumer is at the bundle 4x + 16y with MRSxy = 3. Is he in equilibrium? If not, how will he move, and where is the equilibrium if it is at 6x + 12y? (4 marks)

Try it first, then show the solutionSolution

Cost of 4x + 16y = 4 x 10 + 16 x 5 = 40 + 80 = Rs 120: on the budget line.
Price ratio Px/Py = 10/5 = 2. MRS = 3 > 2: he would give up 3 y for one more x but the market asks only 2 y.
So he gains by buying more x and less y.
As x rises and y falls, MRS diminishes until it equals 2: bundle 6x + 12y costs 60 + 60 = Rs 120 and MRS = 2 = Px/Py.

Answer: He is not in equilibrium (MRS 3 > 2). He buys more x and less y until MRS = Px/Py = 2, reaching 6x + 12y.

Example 5: A straight indifference curve · 4 marks · Short answerHOTS / competency

A consumer treats 1 unit of x as exactly equal to 2 units of y (constant MRS = 2). Px = Rs 6, Py = Rs 4 and income is Rs 60. Does the tangency rule apply? What will he buy? (4 marks)

Try it first, then show the solutionSolution

Price ratio = 6/4 = 1.5, while MRS is constantly 2 > 1.5 at every point: x is always worth more to him than it costs in terms of y.
So he keeps swapping y for x until y is zero; there is no tangency point because the IC is a straight line (not convex).
All income on x: 60/6 = 10 units, worth 10 x 2 = 20 units of y. All on y: 60/4 = 15 units.
20 > 15 so he buys 10 units of x and none of y (a corner solution).

Answer: No tangency: with constant MRS the consumer spends everything on x (10 units). This shows why the convexity condition (diminishing MRS) is needed for an interior equilibrium.

Where students lose marks in Indifference Curves, Budget Line and Consumer's Equilibrium

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

Mistake: Writing MRS = Py/Px or inverting the slope
Mixing which price goes on top.
Wrong working
Slope of budget line = Py/Px = 10/20 = 0.5.
Right working
With x on the horizontal axis, slope = Px/Py = 20/10 = 2.
Do this: Slope = price of the good on the horizontal axis over the other price.
Usually costs: 1-2 marks.
Mistake: Two indifference curves intersecting in the diagram
Drawing curves carelessly.
Wrong working
IC1 and IC2 cross near the axes.
Right working
ICs are drawn nested, never crossing.
Do this: Draw the map from the origin outwards, in order.
Usually costs: 1 mark.
Mistake: Equilibrium without the second condition
Stating only the slope equality.
Wrong working
Equilibrium when MRS = Px/Py.
Right working
MRS = Px/Py and the IC is convex to the origin at that point (MRS diminishing).
Do this: Write both conditions.
Usually costs: 1 mark.
Mistake: Tangency with a lower indifference curve
Not seeing the highest attainable curve.
Wrong working
The budget line cuts IC1 at two points; both are equilibrium points.
Right working
A budget line that cuts an IC leaves a higher IC reachable; equilibrium is the single tangency point on the highest attainable IC.
Do this: Label the equilibrium point E on the tangent curve only.
Usually costs: 1-2 marks.

Exam tips

Draw the indifference map and budget line with both axes labelled (good x and good y), and mark E, the intercepts and the IC numbers.
Write the properties of ICs as short bullet lines, each with its reason.
In MRS numericals show the series and the word 'diminishing'.
Explain the equilibrium with the condition, the diagram and the movement if MRS is above or below the price ratio.
Remember the syllabus names MRS and DMRS together with the properties of the IC.

Practice questions on Indifference Curves, Budget Line and Consumer's Equilibrium

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
A higher indifference curve represents:
(a) lower satisfaction
(b) the same satisfaction
(c) a higher level of satisfaction
(d) a lower price level
Hint
More of at least one good.
Answer
(c) a higher level of satisfaction
Q2 · 3 marks · Short answerBoard level
A consumer gets equal satisfaction from the combinations (x, y): (1, 15), (2, 10), (3, 6), (4, 3), (5, 1). Calculate MRSxy at each step and state whether DMRS holds. (3 marks)
Hint
Loss of y divided by gain of x.
Answer
MRS = 5, 4, 3, 2 (losses of 5, 4, 3, 2 units of y for one more x). The values fall, so DMRS holds.
Q3 · 4 marks · Short answerHarder board level
A consumer has Rs 600; Px = Rs 30 and Py = Rs 20. Find the intercepts and slope of the budget line. Which of the bundles (10, 15), (8, 20), (12, 12), (15, 10) lie on the line and which are beyond the budget? (4 marks)
Hint
Cost of each bundle against Rs 600.
Answer
Intercepts 600/30 = 20 (x-axis) and 600/20 = 30 (y-axis); slope = 30/20 = 1.5. Costs: (10, 15) = 300 + 300 = 600 on the line; (12, 12) = 360 + 240 = 600 on the line; (8, 20) = 240 + 400 = 640 beyond the budget; (15, 10) = 450 + 200 = 650 beyond the budget.
Q4 · 4 marks · Short answerHarder board level
Income is Rs 100, Px = Rs 5 and Py = Rs 10. A consumer is at 4x + 8y with MRSxy = 2. Show that the bundle is affordable, explain why he is not in equilibrium, and describe how he will adjust. (4 marks)
Hint
Price ratio is 0.5.
Answer
Cost = 4 x 5 + 8 x 10 = 20 + 80 = Rs 100, on the budget line. Px/Py = 5/10 = 0.5 while MRS = 2 > 0.5. He is willing to give up 2 units of y for one x, but the market asks only half a unit of y; so he buys more x and fewer y. As he does so MRS falls (DMRS) until it equals 0.5, for example at 10x + 5y (cost 50 + 50 = Rs 100).
Q5 · 3 marks · Short answerHOTS / competency
Explain why a budget line that cuts an indifference curve at two points cannot show the consumer's equilibrium, and why the tangent curve is the best the consumer can do. (3 marks)
Hint
Think of a higher curve between the two points.
Answer
Because the IC is convex, the bundles on the budget line between the two cutting points lie above the cutting curve, on higher indifference curves, and they are still affordable; so the consumer can gain by moving there. A still higher IC lies wholly beyond the budget line. The curve that just touches (is tangent to) the line is therefore the highest attainable, with a single equilibrium point where MRS = Px/Py.

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.Slope of the budget line?Show answer
Px/Py.
2.What does MRSxy measure?Show answer
Units of y given up for one more unit of x at the same satisfaction.
3.Why is an IC convex to the origin?Show answer
Because MRS diminishes.
4.Can two ICs intersect?Show answer
No; it would break the ranking of bundles.
5.Equilibrium condition (ordinal)?Show answer
MRSxy = Px/Py with the IC convex to the origin.

Indifference Curves, Budget Line and Consumer's Equilibrium: frequently asked questions

What is an indifference curve?

A curve joining combinations of two goods that give the consumer the same satisfaction.

What is the difference between cardinal and ordinal approaches?

Cardinal measures satisfaction in utils; ordinal only ranks bundles by preference.

What happens to the budget line when income rises?

It shifts outward parallel to itself, since the price ratio does not change.

Why must MRS diminish for a stable equilibrium?

Because convex curves make the tangent point a maximum; with a straight or concave IC the tangent point is not the best choice.