flowchart LR C[Cardinal Utility<br/>Marshall, Jevons,<br/>Walras, Menger] --> O[Ordinal Utility<br/>Edgeworth, Pareto,<br/>Hicks and Allen] O --> R[Revealed Preference<br/>Samuelson] style C fill:#FFEBEE,stroke:#C62828 style O fill:#FFF8E1,stroke:#F9A825 style R fill:#E8F5E9,stroke:#2E7D32
22 Consumer Behaviour: Utility and Indifference Curve
22.1 The Question
Microeconomics begins with a simple question: given limited income and given prices, how does a rational consumer choose what to buy? The answer has been built up over a century in three successive theoretical traditions (varian2019?; ahuja2020?):
- Cardinal utility approach — Alfred Marshall, Jevons, Walras, Menger (late 1800s).
- Ordinal utility / indifference-curve approach — Edgeworth, Pareto, Hicks and Allen (1934).
- Revealed preference theory — Paul Samuelson (1938 and 1947).
Each succeeding tradition relaxed an assumption of the previous one and produced the same downward-sloping demand curve through a more parsimonious route.
22.2 Cardinal Utility Approach
22.2.1 Total and marginal utility
Utility is the satisfaction a consumer derives from consuming a good. Marshall assumed it was measurable — like distance or weight — in subjective units called utils.
TipTotal and Marginal Utility
| Term | Definition | Symbol |
|---|---|---|
| Total Utility (TU) | Sum of utility from all units consumed | \(TU = \sum MU\) |
| Marginal Utility (MU) | Addition to TU from one extra unit | \(MU_n = TU_n - TU_{n-1}\) |
22.2.2 Law of diminishing marginal utility
H.H. Gossen’s First Law (1854), restated by Marshall: as a consumer consumes more units of a good, holding consumption of other goods constant, the marginal utility from each additional unit eventually falls (marshall1890?).
The consequences are that MU falls, becomes zero (saturation point), and then turns negative. TU rises until MU is zero, then falls.
22.2.3 Law of equi-marginal utility — consumer equilibrium
Gossen’s Second Law, also restated by Marshall: a rational consumer maximises total utility by allocating expenditure across goods so that the marginal utility per rupee is equal across all goods purchased.
\[ \frac{MU_x}{P_x} = \frac{MU_y}{P_y} = \frac{MU_z}{P_z} = \dots = \lambda \]
where \(\lambda\) is the marginal utility of money. The condition is also known as the law of substitution or the law of maximum satisfaction.
22.2.4 Derivation of the demand curve
If \(P_x\) falls, \(\frac{MU_x}{P_x}\) rises above the equi-marginal level; the consumer buys more of \(x\) until diminishing \(MU_x\) restores equilibrium. Quantity demanded therefore rises as price falls — the law of demand.
22.2.5 Consumer surplus
Marshall introduced consumer surplus — the difference between what a consumer is willing to pay (her marginal-utility-based valuation) and what she actually pays (the market price):
\[ \text{Consumer Surplus} = \text{Total Utility (in money)} - \text{Total Expenditure} \]
Graphically, it is the area below the demand curve and above the price line.
22.2.6 Limitations
- Utility is not measurable in any objective unit; the cardinal claim is heroic.
- The marginal utility of money does not stay constant once expenditure on a good is large.
- Indivisible and lumpy goods (a refrigerator) violate the smooth-MU assumption.
22.3 Ordinal Utility — Indifference Curve Approach
Hicks and Allen’s “A Reconsideration of the Theory of Value” (1934) — and Hicks’s Value and Capital (1939) — replaced cardinal measurement with mere ordering. The consumer can rank combinations of goods (more preferred, less preferred, indifferent) but need not assign numerical utilities.
22.3.1 The indifference curve
An indifference curve is the locus of all combinations of two goods that yield the same level of satisfaction; the consumer is indifferent between any two points on the curve.
TipProperties of Indifference Curves
| Property | Justification |
|---|---|
| Slope downward to the right | More of one good must be compensated by less of the other to keep utility constant |
| Convex to the origin | Diminishing Marginal Rate of Substitution |
| Higher curves represent higher utility | Consumer prefers more to less |
| Two indifference curves never intersect | If they did, transitivity of preferences would be violated |
| Do not touch the axes | Both goods are wanted |
22.3.2 Marginal Rate of Substitution (MRS)
The Marginal Rate of Substitution of X for Y (\(MRS_{xy}\)) is the amount of Y the consumer is willing to give up for one more unit of X while keeping utility constant. It is the (absolute value of the) slope of the indifference curve.
\[ MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y} \]
The law of diminishing MRS — as the consumer has more of X and less of Y, she becomes less willing to give up Y for further X. This produces the convex shape.
22.3.3 The budget line (price line)
Given income \(M\) and prices \(P_x\) and \(P_y\), the consumer’s affordable combinations satisfy:
\[ M = P_x \cdot X + P_y \cdot Y \]
The budget line slopes downward; its slope is \(-P_x / P_y\). A change in income shifts the budget line parallel; a change in one price rotates it.
22.3.4 Consumer equilibrium
The consumer maximises utility by reaching the highest indifference curve her budget can buy. This happens at the point of tangency between the budget line and an indifference curve, where:
\[ MRS_{xy} = \frac{P_x}{P_y} \quad \text{equivalently} \quad \frac{MU_x}{P_x} = \frac{MU_y}{P_y} \]
Two conditions are required: the necessary condition (tangency) and the sufficient condition (the indifference curve must be convex at that point).
flowchart LR IC[Highest reachable<br/>Indifference Curve] --- T[Tangency point<br/>Slope of IC = Slope of Budget Line] T --- BL[Budget Line<br/>Slope = − Px / Py] T --> EQ[Consumer<br/>Equilibrium] style EQ fill:#E8F5E9,stroke:#2E7D32
22.3.5 Income, substitution and price effects
A change in the price of \(X\) has two simultaneous effects on quantity demanded.
TipThree Effects of a Price Change
| Effect | Working content | Direction (price fall) |
|---|---|---|
| Substitution effect | \(X\) is now relatively cheaper; consumer substitutes into \(X\) | Always positive |
| Income effect | Real income has risen; demand for \(X\) rises (normal) or falls (inferior) | Positive for normal; negative for inferior |
| Price effect | Sum of substitution and income effects | Positive for normal; ambiguous for inferior; possibly negative for Giffen goods |
The Hicksian decomposition holds utility constant when isolating the substitution effect; the Slutsky decomposition holds purchasing power constant. Both yield the same qualitative conclusion.
22.3.6 Income-Consumption Curve and Price-Consumption Curve
- Income-consumption curve (ICC) — locus of equilibrium points as income changes, prices constant.
- Price-consumption curve (PCC) — locus of equilibrium points as the price of one good changes, the other price and income held constant.
The PCC underlies the demand curve: each price-quantity pair on the PCC produces one point on the demand curve.
22.3.7 Engel curve
An Engel curve (Ernst Engel, 1857) plots quantity demanded against income. Its slope reveals income elasticity — upward for normal goods, downward for inferior goods.
22.4 Revealed Preference Theory — Samuelson (1938, 1947)
Paul Samuelson’s revealed preference theory dispenses with utility altogether — even ordinal utility. The theory observes only what a consumer actually buys at given prices and income and derives demand-theoretic conclusions from internal consistency conditions on observed choices (samuelson1947?).
22.4.1 The basic axioms
TipAxioms of Revealed Preference
| Axiom | Statement |
|---|---|
| Weak Axiom (WARP) | If bundle A is revealed preferred to bundle B (chosen when B was affordable), then B can never be revealed preferred to A in any other choice |
| Strong Axiom (SARP) | If A is preferred to B, B to C, then A is preferred to C — transitivity holds across chains |
The theory shows that consistent choices imply a downward-sloping demand curve without assuming utility, indifference curves or any subjective construct — only observable behaviour.
22.5 Comparing the Three Approaches
TipThree Approaches to Consumer Behaviour
| Dimension | Cardinal (Marshall) | Ordinal (Hicks-Allen) | Revealed Preference (Samuelson) |
|---|---|---|---|
| Measure of utility | Cardinal (utils) | Ordinal (rank) | None — observed choice only |
| Constancy of marginal utility of money | Assumed | Not needed | Not needed |
| Independence of utilities | Assumed | Not needed | Not needed |
| Tools | TU, MU, equi-marginal | Indifference curves, MRS, budget line | Axioms of consistency |
| Decomposition of price effect | No | Yes (income + substitution) | Yes (Slutsky / Hicks) |
| Year of formal development | 1890 onward | 1934 onward | 1938 / 1947 |
22.6 Some Special Cases
TipIndifference-Curve Special Cases
| Goods | Shape of IC |
|---|---|
| Perfect substitutes (Coke vs Pepsi for some) | Straight line; constant MRS |
| Perfect complements (left and right shoes) | L-shaped; MRS = 0 or ∞ |
| Bads (pollution paired with income) | Slope upward |
| Neutral goods (one valued, one ignored) | Vertical or horizontal |
22.7 Worked Example — Equi-Marginal Allocation
A consumer has ₹10 to spend on two goods, \(X\) at ₹2 per unit and \(Y\) at ₹1 per unit. Marginal utility schedules:
TipMU Schedule
| Unit | \(MU_x\) | \(MU_y\) |
|---|---|---|
| 1 | 20 | 10 |
| 2 | 16 | 8 |
| 3 | 12 | 6 |
| 4 | 8 | 4 |
| 5 | 4 | 2 |
Compute \(MU/P\) ratios. For \(X\): 10, 8, 6, 4, 2. For \(Y\): 10, 8, 6, 4, 2. The consumer purchases units in descending order of \(MU/P\). With income ₹10 and prices ₹2 and ₹1, the consumer buys 3 units of \(X\) (cost ₹6) and 4 units of \(Y\) (cost ₹4). Equi-marginal condition is satisfied at \(MU_x/P_x = 6 = MU_y/P_y\). Total expenditure = ₹10. Total utility = (20 + 16 + 12) + (10 + 8 + 6 + 4) = 76 utils.
22.8 Exam-Pattern MCQs
Q 01
Which of the following is not an assumption of the cardinal-utility approach?
View solution
Correct Option: D
Ranking (without measurement) is the ordinal-utility assumption; the cardinal approach assumes utility is measurable.
Q 02
Match each economist with the contribution to consumer theory:
| Economist | Contribution | ||
| (i) | Alfred Marshall | (a) | Indifference-curve formalism (1934) |
| (ii) | Hicks and Allen | (b) | Cardinal utility and consumer surplus |
| (iii) | Paul Samuelson | (c) | Two laws of utility — diminishing MU and equi-marginal |
| (iv) | H.H. Gossen | (d) | Revealed-preference theory |
View solution
Correct Option: A
Q 03
A consumer is in equilibrium under the cardinal-utility approach when:
View solution
Correct Option: B
The equi-marginal-utility condition: marginal utility per rupee is equal across all goods consumed.
Q 04
Match each property of indifference curves with its justification:
| Property | Justification | ||
| (i) | Slope downward | (a) | Diminishing Marginal Rate of Substitution |
| (ii) | Convex to origin | (b) | More of one good requires giving up some of the other to keep utility constant |
| (iii) | Higher curves preferred | (c) | Transitivity of preferences |
| (iv) | Two ICs never intersect | (d) | Consumer prefers more to less |
View solution
Correct Option: A
Q 05
At the consumer's equilibrium under the indifference-curve approach:
View solution
Correct Option: C
Tangency condition: $MRS_{xy} = P_x / P_y$, equivalently $MU_x/P_x = MU_y/P_y$.
Q 06
A fall in the price of an inferior good produces:
View solution
Correct Option: B
Substitution effect is always positive (consumer substitutes into the cheaper good). For an inferior good, the income effect is negative (rising real income reduces demand for the inferior good).
Q 07
Arrange the following in chronological order of formal development: (i) Indifference-curve approach (Hicks and Allen) (ii) Marshallian cardinal-utility theory (iii) Revealed-preference theory (Samuelson) (iv) Engel curve (Engel)
View solution
Correct Option: A
Engel (1857) → Marshall (1890) → Hicks and Allen (1934) → Samuelson (1938 / 1947).
Q 08
Match each indifference-curve special case with the shape of the curve:
| Goods | Shape of IC | ||
| (i) | Perfect substitutes | (a) | L-shaped |
| (ii) | Perfect complements | (b) | Slopes upward |
| (iii) | One good and one bad | (c) | Straight line |
| (iv) | One good and one neutral | (d) | Vertical or horizontal |
View solution
Correct Option: A
ImportantQuick recall
- Three theoretical traditions: Cardinal (Marshall) → Ordinal (Hicks-Allen) → Revealed Preference (Samuelson).
- Gossen’s two laws: diminishing MU; equi-marginal MU/P equal across goods.
- Cardinal equilibrium: \(MU_x/P_x = MU_y/P_y = \lambda\).
- Consumer surplus = area below demand curve and above price (Marshall).
- Ordinal equilibrium: budget line tangent to highest indifference curve; MRS = \(P_x/P_y\).
- IC properties: downward-sloping, convex, non-intersecting, higher = better, do not touch axes.
- MRS = ΔY/ΔX = MU_x / MU_y, diminishing.
- Price effect = Substitution effect + Income effect.
- Substitution effect: always positive (Hicks holds utility constant; Slutsky holds purchasing power constant).
- Income effect: positive for normal, negative for inferior; if income effect dominates substitution → Giffen good.
- ICC (income changes), PCC (one price changes), Engel curve (income vs quantity, Engel 1857).
- Revealed Preference axioms: WARP and SARP (Samuelson).
- Special-case ICs: perfect substitutes — straight line; perfect complements — L-shaped; bads — upward-sloping; neutral — vertical/horizontal.