Consumer Behaviour: Marginal Utility & Indifference Curve – Core Points

Law of Demand & Aim of Chapter

• Law of demand: ↑Price ⇒ ↓Quantity demanded (known); chapter asks why this happens.
• Answer: study consumer behaviour through two frameworks:
  • Cardinal (Marginal-Utility) Analysis
  • Ordinal (Indifference-Curve) Analysis

Cardinal Utility Analysis (Marginal Utility)

• Utility = want-satisfying power; assumed measurable in utils (cardinal).
• Consumer is rational; seeks to maximise total utility (TU) given income.

Total & Marginal Utility

• $TU<em>n = MU</em>1+MU<em>2+\ldots+MU</em>n$
• $MU<em>n = TU</em>n - TU_{n-1}$ (change in TU from 1 more unit).
• Empirical pattern: TU rises at decreasing rate, reaches maximum, then falls; MU diminishes, hits zero, may become negative (disutility).

Relationship TU–MU

1. MU>0 \Rightarrow TU rising (at decreasing rate).
2. $MU=0 \Rightarrow TU$ maximum (point of satiety).
3. MU<0 \Rightarrow TU declining.

Law of Diminishing Marginal Utility

• Statement: Ceteris paribus, as consumption of a good increases, MU of each additional unit falls.
• Key assumptions: identical & standard units, unchanged tastes, continuous consumption, constant prices of substitutes, measurable utility, rational consumer, constant MU of money.

Consumer Equilibrium (Single Good)

• Buy quantity where $MU<em>X = P</em>X$.
  • If $MU<em>X>P</em>X$ → buy more.
  • If $MU<em>X<P</em>X$ → buy less.

Law of Equi-Marginal Utility (Multiple Goods)

• Utility-maximising rule: allocate income so MU per last rupee equal across goods.
  $\frac{MU<em>X}{P</em>X}=\frac{MU<em>Y}{P</em>Y}=\cdots =MU_{\text{money}}$
• Subject to budget constraint $P<em>X Q</em>X + P<em>Y Q</em>Y = Y$ (income).
• Reallocation continues until above equality holds; then TU is maximal.
• Practical limits: utility not observable, indivisible/expensive goods, ignorance, habits, non-constant MU of money.

Ordinal Utility Analysis (Indifference Curves)

• Rejects measurable utility; consumer can rank bundles (ordinal).
• Tool: Indifference Curve (IC) = locus of bundles giving equal satisfaction (iso-utility).

Indifference Schedule & Curve

• Example bundles of Food (F) & Clothing (C) that yield same utility plot as downward-sloping, convex IC.

Indifference Map

• Family of ICs; higher (farther from origin) ⇒ higher utility.

Marginal Rate of Substitution (MRS)

• $MRS_{xy}= -\frac{dY}{dX}$ along an IC; amount of Y consumer gives up for 1 more X, keeping utility constant.
• Diminishing MRS → convex IC.

Assumptions of IC Analysis

1. Rationality (utility maximisation).
2. Ordinal measurability.
3. Non-satiety (more is preferred).
4. Transitivity & consistency of choices.
5. Diminishing MRS (convex preferences).

Properties of Indifference Curves

• Downward sloping (negative).
• Convex to origin (diminishing MRS).
• Higher IC ⇒ higher satisfaction.
• ICs never intersect.

Budget Line

• Shows affordable bundles: $P<em>X X + P</em>Y Y = M$.
• Slope $=-\frac{P<em>X}{P</em>Y}$ (negative inverse price ratio).
• Shift factors:
  • Parallel shift with income change (prices constant).
  • Rotation with price change (income constant).

Consumer Equilibrium via Indifference Curves

Conditions for optimal bundle (point of tangency):

1. Tangency: $MRS<em>{xy}=\frac{P</em>X}{P_Y}$ (slope of IC = slope of budget line).
2. Convexity: IC convex at tangency (ensures maximum, not minimum).

• At tangency, consumer attains highest attainable IC given budget; any other feasible bundle gives lower utility (inside) or is unaffordable (outside).

Summary of Key Equations

• $MU<em>n = TU</em>n - TU_{n-1}$
• $TU<em>n = \sum MU</em>i$
• One-good equilibrium: $MU<em>X = P</em>X$
• Multi-good rule: $\frac{MU<em>X}{P</em>X}=\frac{MU<em>Y}{P</em>Y}=\cdots$
• Budget line: $P<em>X X + P</em>Y Y = M$
• Tangency equilibrium: $MRS<em>{xy}=\frac{P</em>X}{P_Y}$