Consumer Equilibrium – Cardinal & Ordinal Utility

Consumer Equilibrium – Core Idea

  • Concerns the interaction of consumer demand and producer supply in determining the price of a commodity.
  • Central consumer objective: allocate limited income across goods/services to obtain maximum satisfaction (utility).
  • Two methodological approaches:
    • Cardinal (Utility) Analysis – utility assumed to be measurable in “utils.”
    • Ordinal (Indifference-Curve) Analysis – utility ranked, not measured.

Cardinal Utility Theory

Concept & Features of Utility

  • Quantitative measure of satisfaction ("want-satisfying power").
  • Depends on urgency/intensity of want; is subjective and varies across persons/time.
  • Utility is measurable (cardinally) but not synonymous with usefulness (e.g.
    drugs give utility to an addict).

Kinds of Utility

  • Total Utility (TU)
    • Psychological satisfaction from consuming a given quantity of a good.
    • TU = MU1 + MU2 + MU_3 + \dots = \sum MU
  • Marginal Utility (MU)
    • Extra utility from one additional unit.
    • MUn = TUn - TU_{n-1}

Law of Diminishing Marginal Utility (DMU)

  • First enunciated by German economist H. H. Gossen; called “Gossen’s First Law” / Marshall’s formulation.
  • Statement: As a consumer consumes more units of a good, MU from each successive unit falls.
Assumptions
  1. Cardinal measurability – utility expressible as 1, 2, 3 … utils.
  2. Monetary measurability – utils convertible into money.
  3. Standard unit – units consumed neither excessively large nor tiny.
  4. Continuous consumption – no time gap between units.
  5. Uniform quality – all units identical in quality.
  6. Constancy of MU of money – purchasing power of ₹1 in utils is unchanged.
  7. Fixed income & prices – consumer’s budget and prices stay constant.
TU–MU Relationship
  • MU>0 \;\Rightarrow\; TU\;\text{rises}
  • MU=0 \;\Rightarrow\; TU\;\text{is maximum/constant}
  • MU<0 \;\Rightarrow\; TU\;\text{falls}
  • MU curve is the slope of the TU curve.
Exceptions to DMU
  1. Hobbies/collectibles (e.g. stamp collecting).
  2. Drunkards (alcohol may yield rising utility initially).
  3. Misers (hoarding money may raise utility).
  4. Music & poetry (appreciation may grow with exposure).
  5. 3-D experiences (novelty may enhance utility for a while).

Consumer’s Equilibrium – Cardinal Approach

  • Equilibrium: consumer has no incentive to re-allocate expenditure; satisfaction is maximised.

Single Commodity Case

  1. Condition: MU = P
    (marginal utility of the good equals its market price).
  2. Further purchases beyond this point reduce total gain because MU < P.

Two-Commodity Case

Let goods be X and Y with prices PX, PY.

  1. Equal Prices (PX = PY):
    MUX = MUY
  2. Different Prices (PX \neq PY):
    \frac{MUX}{PX} = \frac{MUY}{PY}
  • Interpretation: the last rupee spent on each good yields the same MU.
  • If \frac{MUX}{PX} > \frac{MUY}{PY}, shift expenditure toward X (and vice-versa) until equality holds.

Ordinal Utility Theory (Indifference-Curve/Budget-Line Framework)

Consumption Bundle

  • Denoted (x1, x2) – amounts of “good 1” and “good 2”. Called a bundle.

Budget Set

  • All bundles affordable to the consumer given money income M and market prices P1, P2.
  • Budget constraint:
    P1x1 + P2x2 \le M

Budget Line (Price Line / Price-Income Line)

  • Equation when the consumer spends the entire income:
    P1x1 + P2x2 = M
Key Properties
  • Straight line (linear because prices are constant).
  • Negative slope:
    \text{Slope} = -\frac{P1}{P2}
    Indicates market rate at which one good can be substituted for the other.
  • Horizontal intercept: \frac{M}{P_1} (all income on good 1).
  • Vertical intercept: \frac{M}{P_2} (all income on good 2).
  • Downward slope embodies the trade-off: to consume more of one good, consumer must forego some of the other.
Shifts/Rotations of the Budget Line
  1. Change in Income (M) – prices fixed.
    • M \uparrow shifts line outward, parallel.
    • M \downarrow shifts line inward, parallel.
  2. Change in Price of Good 1 (P₁) – M, P_2 fixed.
    • P_1 \downarrow pivots line outward along x-axis (flatter).
    • P_1 \uparrow pivots inward along x-axis (steeper).
  3. Change in Price of Good 2 (P₂) – symmetric pivot about y-axis.

Indifference Curve Analysis & Equilibrium (brief, as transcript stops)

  • An indifference curve (IC) shows bundles yielding equal satisfaction.
  • Equilibrium occurs at the point where highest attainable IC is tangent to the budget line (i.e. MRS{xy} = \frac{P1}{P_2}). (Full discussion continues beyond current transcript.)

Practical, Philosophical & Ethical Notes

  • Recognition that utility is subjective highlights ethical issues (e.g. drugs give utility to addicts yet may harm society).
  • Budget constraint models real-world scarcity, forcing trade-offs & prioritisation (philosophy of choice under scarcity).
  • DMU underlies progressive taxation rationale: marginal utility of income falls with wealth, so richer individuals can be taxed more heavily with less utility loss.