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

  • TUn = MU1+MU2+\ldots+MUn
  • MUn = TUn - 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 MUX = PX.
    • If MUX>PX → buy more.
    • If MUX

Law of Equi-Marginal Utility (Multiple Goods)

  • Utility-maximising rule: allocate income so MU per last rupee equal across goods.
    \frac{MUX}{PX}=\frac{MUY}{PY}=\cdots =MU_{\text{money}}
  • Subject to budget constraint PX QX + PY QY = 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: PX X + PY Y = M.
  • Slope =-\frac{PX}{PY} (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{xy}=\frac{PX}{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

  • MUn = TUn - TU_{n-1}
  • TUn = \sum MUi
  • One-good equilibrium: MUX = PX
  • Multi-good rule: \frac{MUX}{PX}=\frac{MUY}{PY}=\cdots
  • Budget line: PX X + PY Y = M
  • Tangency equilibrium: MRS{xy}=\frac{PX}{P_Y}