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.
  • $TU = MU<em>1 + MU</em>2 + MU_3 + \dots = \sum MU$
• Marginal Utility (MU)
  • Extra utility from one additional unit.
  • $MU<em>n = TU</em>n - TU_{n-1}$

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 $P<em>X, P</em>Y$.

1. Equal Prices ($P<em>X = P</em>Y$):
   $MU<em>X = MU</em>Y$
2. Different Prices ($P<em>X \neq P</em>Y$):
   $\frac{MU<em>X}{P</em>X} = \frac{MU<em>Y}{P</em>Y}$

• 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 $(x<em>1, x</em>2)$ – 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 $P<em>1, P</em>2$.
• Budget constraint:
  $P<em>1x</em>1 + P<em>2x</em>2 \le M$

Budget Line (Price Line / Price-Income Line)

• Equation when the consumer spends the entire income:
  $P<em>1x</em>1 + P<em>2x</em>2 = M$

Key Properties

• Straight line (linear because prices are constant).
• Negative slope:
  $\text{Slope} = -\frac{P<em>1}{P</em>2}$
  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. $MRS<em>{xy} = \frac{P</em>1}{P_2}$). (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.