1. Ordinal utility, indifference curve and map
Ordinal utility: the consumer ranks bundles (preferred, less preferred, indifferent) without measuring utility.
Indifference schedule: combinations of two goods giving the same satisfaction. Indifference curve: the graph of such a schedule. Indifference map: a set of indifference curves, a higher curve showing higher satisfaction.
Assumptions: ordinal utility; consistency (transitivity); non-satiety; diminishing MRS; given tastes.
| Point | Cardinal approach | Ordinal approach |
|---|---|---|
| Measurement | Utility counted in utils | Bundles only ranked |
| Tool | Marginal utility schedule | Indifference curve and map |
| Money | MU of money constant | Not needed |
| Statement | "30 utils from grapes" | "Grapes preferred to guavas" |
Key terms
- Ordinal utility
Utility that can be ranked but not measured in numbers.
- Indifference curve
A curve joining combinations of two goods that give equal satisfaction.
- Indifference map
A set of indifference curves of one consumer, ranked by satisfaction.
2. Marginal rate of substitution
MRSxy = amount of Y the consumer gives up for one more unit of X, staying on the same indifference curve: MRSxy = ΔY ÷ ΔX (absolute slope of the curve).
Diminishing MRS: as X increases and Y decreases, X matters less and Y more, so MRS falls. This makes the indifference curve convex to the origin. A constant MRS would give a straight-line curve.
| Move | ΔApples | ΔBananas | MRS (dozen per kg) |
|---|---|---|---|
| A → B | +1 | −5 | 5 |
| B → C | +1 | −4 | 4 |
| C → D | +1 | −3 | 3 |
| D → E | +1 | −2 | 2 |
| Cups of tea | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Biscuit packets | 20 | 14 | 10 | 8 | 7 |
| MRS | — | 6 | 4 | 2 | 1 |
Key terms
- Marginal rate of substitution
The rate at which a consumer substitutes one good for another at constant satisfaction.
- Diminishing MRS
The fall in MRS as more of one good replaces the other.
3. Properties of indifference curves
- Slope downward — more X must be offset by less Y.
- Convex to the origin — diminishing MRS.
- Higher curve, higher satisfaction — more of at least one good (non-satiety).
- Never intersect — an intersection would make two satisfaction levels equal (proof with points A, B, C and transitivity).
- Need not be parallel, and usually do not touch the axes (the consumer wants some of both goods).
| Property | Reason |
|---|---|
| Slopes downward | More X must be offset by less Y |
| Convex to the origin | MRS diminishes |
| Higher curve, higher satisfaction | More of at least one good |
| Never intersect | One bundle cannot give two levels |
| Need not be parallel | Only non-intersection is required |
| Bundle (rice kg, dal kg) | Compared with P (6, 4) | Curve |
|---|---|---|
| Q (6, 5) | Same rice, more dal | Higher than P |
| T (7, 4) | More rice, same dal | Higher than P |
| U (5, 4) | Less rice, same dal | Lower than P |
| V (7, 3) | More rice, less dal | Cannot tell without the map |
Key terms
- Non-satiety
The assumption that more of a good is preferred to less.
- Transitivity
If A is preferred to B and B to C, then A is preferred to C.
4. The budget line
Budget line: all bundles that cost exactly the consumer's income: Px·X + Py·Y = M. Intercepts M ÷ Px and M ÷ Py; absolute slope Px ÷ Py (the market rate of exchange).
Budget set: all bundles costing M or less (the triangle under the line). A bundle inside leaves income unspent; one outside is unaffordable.
| Notebooks (X) | 0 | 3 | 6 | 9 | 12 |
|---|---|---|---|---|---|
| Pens (Y) on the line | 24 | 18 | 12 | 6 | 0 |
Key terms
- Budget line
The set of bundles that use up the whole income at given prices.
- Budget set
All bundles that cost no more than the income.
5. Changes in the budget line
- Income rises (falls): both intercepts rise (fall) — parallel outward (inward) shift.
- Px falls (rises): x-intercept rises (falls) — line rotates on the Y-axis, becoming flatter (steeper).
- Py rises (falls): y-intercept falls (rises) — line rotates on the X-axis, becoming flatter (steeper).
- Income and both prices change in the same proportion: no change.
| Change | x-intercept M ÷ Px | y-intercept M ÷ Py | Budget line |
|---|---|---|---|
| Income rises | Rises | Rises | Parallel outward shift |
| Income falls | Falls | Falls | Parallel inward shift |
| Px falls | Rises | Same | Rotates outward on Y-axis, flatter |
| Py rises | Same | Falls | Rotates inward on X-axis, flatter |
| M, Px, Py all double | Same | Same | No change |
Key terms
- Parallel shift
Movement of the budget line caused by a change in income, slope unchanged.
- Rotation
Movement of the budget line caused by a change in one price, pivoting on the other axis.
6. Consumer's equilibrium
Conditions: (1) MRSxy = Px ÷ Py — the budget line is tangent to an indifference curve; (2) the curve is convex at that point (MRS diminishing).
Why not elsewhere: where the line cuts a curve, MRS ≠ Px ÷ Py and a move along the line reaches a higher curve; curves above the tangency are unaffordable. If MRS > Px ÷ Py buy more X; if MRS is below Px ÷ Py buy less X.
The whole income is spent at equilibrium.
| Step | Working |
|---|---|
| Tangency | Y ÷ X = 20 ÷ 10 = 2, so Y = 2X |
| Budget | 20X + 10(2X) = 240, so X = 6 |
| Bundle | 6 notebooks, 12 pens |
| Check | Cost 240; MRS 12 ÷ 6 = 2; curve convex |
| Situation | Budget line | Equilibrium (X, Y) |
|---|---|---|
| ₹300; fare ₹30; snack ₹15 | 10 rides, 20 packets | (5, 10) |
| Fare falls to ₹20 | 15 rides, 20 packets | (7.5, 10) |
Key terms
- Consumer's equilibrium
The affordable bundle on the highest attainable indifference curve.
- Tangency
The point where the budget line just touches an indifference curve, so their slopes are equal.
Exam tips
Common mistakes
- Saying the bundles on an indifference curve cost the same — that describes a budget line.
- Writing MRS as ΔX ÷ ΔY, or forgetting "at the same satisfaction".
- Claiming indifference curves must be parallel.
- Stating only the tangency condition and leaving out convexity.
- Treating a point where the budget line cuts a curve as equilibrium.
- Shifting the budget line parallel when only one price changes (it rotates).
How marks are usually awarded
- 1-mark MCQ / assertion-reason: one correct option.
- 2 marks: a definition or condition plus a reason or step.
- 3 marks: three points, or a numerical with formula, working and answer.
- 5 marks (and the ISC paper's 4- and 8-mark parts): a labelled diagram with a full explanation of each part.