23  Consumer behavior: Utility analysis; Indifference curve analysis

23.1 The Question

Consumer behaviour theory asks: how does a consumer with a limited income allocate it across many goods so as to maximise satisfaction? Two answers have dominated. The earlier cardinal utility analysis (Marshall, 1890; building on Jevons 1871 and Walras 1874) assumes utility is measurable in units (utils). The later ordinal utility analysis (Hicks and Allen, 1934; Pareto’s earlier work) abandons measurement and assumes only that consumers can rank combinations — the indifference-curve framework.

23.2 Cardinal Utility Analysis — Marshall

23.2.1 Assumptions

TipAssumptions of Cardinal Utility
  • Utility is cardinally measurable — in units called utils.
  • Constant marginal utility of money — money is the measuring rod.
  • Rationality — the consumer maximises total utility.
  • Independent utilities — utility of one good is unaffected by quantities of others.
  • Diminishing marginal utility — additional units yield less satisfaction.

23.2.2 Law of Diminishing Marginal Utility (Gossen’s First Law)

As a consumer takes more units of a good per unit time, the marginal utility derived from each additional unit diminishes. Formalised by H.H. Gossen in 1854 — known as Gossen’s First Law.

23.2.3 Law of Equi-Marginal Utility (Gossen’s Second Law)

A consumer is in equilibrium when she allocates expenditure so that the marginal utility per rupee is equal across all goods:

\[\frac{MU_x}{P_x} = \frac{MU_y}{P_y} = \ldots = \frac{MU_n}{P_n} = MU_m\]

where MU_m is the marginal utility of money. This is Gossen’s Second Law, also called the Law of Substitution or Maximum Satisfaction.

23.2.4 Marshall’s Consumer Surplus

The consumer surplus is the difference between what the consumer is willing to pay and what she actually pays. Geometrically, it is the area between the demand curve and the price line up to the quantity purchased.

TipCritique of Cardinal Utility
  • Utility is not measurable in objective units — Hicks-Allen critique.
  • Constant MU of money is unrealistic — money’s marginal utility itself diminishes.
  • Independent utilities fail when goods are substitutes or complements.
  • Ignores psychological dimensions of preference.

23.3 Ordinal Utility Analysis — Indifference Curves

John Hicks and R.G.D. Allen in A Reconsideration of the Theory of Value (1934) used the indifference-curve framework — earlier hinted at by Edgeworth (1881) and Pareto (1906) — to derive demand theory without assuming measurable utility.

23.3.1 Assumptions

TipAssumptions of Ordinal Utility
  • Rationality — consumer maximises satisfaction.
  • Preferences are complete — consumer can rank any two bundles.
  • Transitive preferences — if A ≻ B and B ≻ C, then A ≻ C.
  • More is preferred to less (non-satiation).
  • Diminishing marginal rate of substitution (MRS).

23.3.2 Indifference Curve and Its Properties

An indifference curve shows all combinations of two goods that give the consumer the same total satisfaction. Four properties:

TipProperties of Indifference Curves
  • Downward-sloping — to maintain satisfaction, more of one good requires less of the other.
  • Convex to the origin — diminishing MRS.
  • Higher curves represent higher satisfaction.
  • Two indifference curves cannot intersect — contradicts transitivity.

23.3.3 Marginal Rate of Substitution (MRS)

The MRS of X for Y = quantity of Y the consumer is willing to give up for one extra unit of X, holding satisfaction constant:

\[MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}\]

MRS diminishes as more X is consumed — the law of diminishing MRS.

23.3.4 Budget Line / Price Line

The budget line shows combinations of two goods the consumer can buy at given prices with a fixed money income M:

\[P_x \cdot X + P_y \cdot Y = M\]

Slope = \(-P_x/P_y\). A change in money income shifts the budget line parallel; a change in a price rotates it.

23.3.5 Consumer Equilibrium

The consumer is in equilibrium where the budget line is tangent to the highest attainable indifference curve. Two conditions:

TipTwo Conditions for Consumer Equilibrium
Condition Expression
First-order (necessary) \(MRS_{xy} = \frac{P_x}{P_y}\), i.e., slope of IC = slope of budget line
Second-order (sufficient) IC is convex to origin (diminishing MRS) at the tangency 

flowchart LR
  B[Budget Line<br/>P_x·X + P_y·Y = M] --> E[Equilibrium at<br/>tangency]
  IC[Indifference Curve<br/>highest attainable] --> E
  E --> R[MRS = P_x / P_y]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

23.4 Income and Substitution Effects

A change in the price of a good can be decomposed into:

TipIncome and Substitution Effects
Effect Working content
Substitution effect Move along the same indifference curve as relative prices change
Income effect Shift to a higher (or lower) indifference curve as real income changes

23.4.1 Two Methods of Decomposition

TipHicks vs Slutsky Decomposition
Method Compensation criterion
Hicks Maintain real income measured by utility (same indifference curve)
Slutsky Maintain real income measured by purchasing power (same bundle remains affordable)

For normal goods, income and substitution effects work in the same direction. For inferior goods they conflict; for Giffen goods the (negative) income effect dominates.

23.5 Income Consumption Curve (ICC) and Price Consumption Curve (PCC)

TipICC and PCC
Curve Derived from Information
Income Consumption Curve (ICC) Parallel shifts of the budget line as income changes Engel curves derived from ICC
Price Consumption Curve (PCC) Rotations of the budget line as one price changes The demand curve derived from PCC

23.6 Special Indifference Curves

TipSpecial Cases
Case Shape of IC
Perfect substitutes Straight line — MRS constant
Perfect complements L-shaped — consumed in fixed ratio
Neutral / Bad goods Vertical / horizontal lines
Bliss point IC encircles a single point

23.7 Revealed Preference Theory — Samuelson (1938)

Paul Samuelson in 1938 introduced Revealed Preference Theory, deriving demand directly from observed purchasing behaviour without any utility assumption.

TipSamuelson’s Two Axioms
  • Weak Axiom of Revealed Preference (WARP) — if bundle A is chosen when B was affordable, B is not chosen when A is affordable.
  • Strong Axiom of Revealed Preference (SARP) — transitivity extended over chains of choice.

The framework gave operational meaning to demand without invoking utility, and underlies modern behavioural economics.

23.8 Practice Questions

Q 01 Cardinal vs Ordinal Easy

The cardinal utility approach was developed by:

  • AHicks and Allen
  • BAlfred Marshall
  • CPaul Samuelson
  • DJ.M. Keynes
View solution
Correct Option: B
Marshall — cardinal utility; Hicks-Allen — ordinal; Samuelson — revealed preference.
Q 02 Gossen Medium

Match each law with its content:

Law Content
(i) Gossen's First Law (a) Equi-marginal utility
(ii) Gossen's Second Law (b) Diminishing marginal utility
  • A(i)-(b), (ii)-(a)
  • B(i)-(a), (ii)-(b)
  • CBoth same
  • DNeither
View solution
Correct Option: A
First — diminishing MU; Second — equi-marginal utility.
Q 03 Equilibrium Medium

Under cardinal utility, a consumer is in equilibrium when:

  • AMU_x = MU_y
  • BMU_x / P_x = MU_y / P_y
  • CP_x = P_y
  • DTU_x = TU_y
View solution
Correct Option: B
Marginal utility per rupee equal across goods.
Q 04 IC Properties Medium

Two indifference curves can never intersect because:

  • AThey would violate the law of diminishing returns
  • BIt would contradict the assumption of transitivity
  • CIt would imply utility is cardinal
  • DIt would violate equimarginal utility
View solution
Correct Option: B
Intersection ⇒ inconsistent preferences (violates transitivity).
Q 05 MRS Medium

MRS_xy in equilibrium equals:

  • AMU_x − MU_y
  • BP_x − P_y
  • CP_x / P_y
  • DMU_x × MU_y
View solution
Correct Option: C
Tangency condition: MRS = price ratio P_x/P_y.
Q 06 Special Medium

For perfect complements, the indifference curve is:

  • AStraight line
  • BL-shaped
  • CConvex
  • DConcave
View solution
Correct Option: B
Perfect complements — fixed-ratio consumption (left and right shoes) — **L-shaped**.
Q 07 Special Medium

For perfect substitutes, the indifference curve is:

  • AL-shaped
  • BConvex
  • CStraight line with constant slope
  • DDiscontinuous
View solution
Correct Option: C
Constant MRS → straight-line indifference curve.
Q 08 Hicks vs Slutsky Hard

The **Hicks** method of decomposing a price change holds constant the consumer's:

  • APurchasing power — the original bundle remains affordable
  • BUtility — same indifference curve
  • CNominal income
  • DMarginal utility of money
View solution
Correct Option: B
**Hicks** — same utility; **Slutsky** — same purchasing power.
Q 09 Samuelson Medium

"Revealed preference theory" was developed by:

  • AHicks
  • BSlutsky
  • CPaul Samuelson (1938)
  • DMarshall
View solution
Correct Option: C
**Samuelson (1938)** — observable choices replace utility postulates.
Q 10 Surplus Medium

Consumer surplus is the difference between:

  • AProducer's cost and consumer's payment
  • BWhat the consumer is willing to pay and what she actually pays
  • CMarket price and equilibrium price
  • DCost price and selling price
View solution
Correct Option: B
Marshall's consumer surplus — willingness-to-pay minus actual price.
Q 11 Budget Medium

A doubling of money income with prices unchanged:

  • ARotates the budget line
  • BShifts the budget line outward, parallel
  • CHas no effect on budget line
  • DMakes the budget line vertical
View solution
Correct Option: B
Income change ⇒ **parallel shift**; price change ⇒ rotation.
Q 12 PCC Hard

The demand curve for a consumer is derived from the:

  • AIncome Consumption Curve
  • BPrice Consumption Curve
  • CEngel curve
  • DProduction possibility curve
View solution
Correct Option: B
PCC plots equilibrium points as one price changes — yields the demand curve.
Q 13 Engel Hard

An Engel curve is derived from the:

  • AIncome Consumption Curve
  • BPrice Consumption Curve
  • CBudget line
  • DProduction curve
View solution
Correct Option: A
**ICC** → Engel curve (income vs quantity).
Q 14 MU Easy

The Law of Diminishing Marginal Utility was first systematically formulated by:

  • AMarshall
  • BH.H. Gossen (1854)
  • CJevons
  • DWalras
View solution
Correct Option: B
**Gossen 1854** — Gossen's First Law.
Q 15 Critique Medium

A key reason the ordinal utility approach replaced cardinal utility is that:

  • AUtility cannot be measured in objective units
  • BCardinal analysis is mathematically harder
  • CCardinal ignores prices
  • DOrdinal allows direct measurement
View solution
Correct Option: A
Utility cannot be measured in **utils**; rank-ordering is sufficient (Hicks-Allen).
Q 16 Convex Medium

Convexity of the indifference curve reflects:

  • AConstant MRS
  • BDiminishing marginal rate of substitution
  • CConstant marginal utility
  • DNegative income elasticity
View solution
Correct Option: B
Diminishing MRS makes IC **convex** to origin.
Q 17 Inferior Medium

For an inferior (but not Giffen) good, when its price falls:

  • AIncome and substitution effects work in opposite directions; substitution effect dominates
  • BIncome and substitution effects work in same direction
  • CIncome effect dominates
  • DNo income effect
View solution
Correct Option: A
Income effect of price fall is *negative* for inferior good but substitution remains positive; net effect is positive → quantity rises.
Q 18 Authors Medium

Match each economist with the contribution:

Economist Contribution
(i) Marshall (a) Revealed preference
(ii) Hicks & Allen (b) Cardinal utility, consumer surplus
(iii) Samuelson (c) Indifference curves; ordinal utility
(iv) Gossen (d) Diminishing MU; equi-marginal
  • A(i)-(b), (ii)-(c), (iii)-(a), (iv)-(d)
  • B(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
  • C(i)-(c), (ii)-(a), (iii)-(d), (iv)-(b)
  • D(i)-(d), (ii)-(c), (iii)-(b), (iv)-(a)
View solution
Correct Option: A
Marshall — cardinal/surplus; Hicks-Allen — ordinal/IC; Samuelson — revealed; Gossen — DMU/equi-marginal.
Q 19 WARP Hard

WARP, in revealed-preference theory, stands for:

  • AWeak Axiom of Rational Preference
  • BWeak Axiom of Revealed Preference
  • CWelfare Analysis of Rational Pricing
  • DWelfare Approach to Resource Pricing
View solution
Correct Option: B
**Weak Axiom of Revealed Preference** — Samuelson's foundational axiom.
Q 20 Slope Medium

The slope of the budget line is:

  • A−MU_x/MU_y
  • B−P_x/P_y
  • CP_y/P_x
  • DP_x × P_y
View solution
Correct Option: B
From P_x X + P_y Y = M, slope = **−P_x/P_y**.

23.9 Quick Recall

ImportantQuick recall
  • Cardinal utility (Marshall 1890; Jevons; Walras) — utility in utils; assumes constant MU of money.
  • Gossen’s First Law — diminishing MU; Gossen’s Second Law — equi-marginal utility: MU_x/P_x = MU_y/P_y.
  • Ordinal utility / Indifference curves (Hicks & Allen 1934; Edgeworth; Pareto) — preferences just need to be ranked.
  • IC properties: downward sloping, convex (diminishing MRS), higher = better, non-intersecting (transitivity).
  • Consumer equilibrium: MRS_xy = P_x/P_y AND IC convex.
  • Budget line: P_x X + P_y Y = M; slope = −P_x/P_y. Income change → parallel shift; price change → rotation.
  • Special ICs: perfect substitutes — straight line; perfect complements — L-shaped.
  • Decomposition of price effect: Hicks (same utility) vs Slutsky (same purchasing power); each yields substitution + income effects.
  • ICC → Engel curve; PCC → demand curve.
  • Samuelson’s Revealed Preference (1938) — WARP and SARP.
  • Marshallian consumer surplus = willingness to pay − actual price.