Marginal and Ordinal Utility, Indifference, and Demand
Goal of the chapter (summary): understand marginal utility and how it underpins the individual demand function; define and apply ordinal utility theory via indifference curves; explain how market demand for a good aggregates individual demands; relate production to costs and explain isoquants, returns to scale, and cost structures; understand various cost concepts; derive and interpret the supply function via marginal costs; define social welfare, consumer surplus, and producer surplus; discuss price ceilings, price floors, and taxes; and illustrate demand under budget constraints with elasticity concepts.
Key Concepts and Definitions
Marginal utility (MU): additional satisfaction from consuming one more unit of a good.
Diminishing marginal utility (Gossen’s First Law): MU decreases as consumption increases.
Total utility (TU): accumulative satisfaction from all units consumed; TU rises at a decreasing rate as consumption grows.
Demand interpretation from marginal utility: a consumer buys a good up to the point where MU equals the price: MU = price (in monetary terms). The demand function x(p) maps price to quantity demanded: higher price → lower quantity demanded.
Substitutability and preferences affect demand: prices of substitutes, consumer preferences, and income affect the demand function.
Cardinal vs Ordinal Theories
Cardinal utility: utility is measured in numerical units (utils). The consumer’s total utility and marginal utility are quantifiable.
Ordinal utility: only the ranking of bundles matters, not the cardinal value of utility. Indifference curves (ICs) represent bundles yielding the same (ordinal) utility.
Assumptions underpinning ordinal theory:
Completeness: a consumer can rank any two bundles A and B (A > B, B > A, or A = B).
Transitivity: if A > B and B > C, then A > C.
Non-satiation (More is better): more of a good is never worse.
Convexity: mixtures (bundles) are preferred to extremes; indifference curves are convex to the origin.
Independence of irrelevant alternatives is a common, though nuanced, assumption in some models.
Indifference curves (ICs): graphical representation of bundles providing the same utility.
ICs are downward sloping (negative slope) because more of one good requires less of the other to keep utility constant.
ICs are convex to the origin because people prefer balanced bundles (diversity/mixtures).
Higher ICs (further from the origin) entail higher utility.
IC system: a family of ICs for different utility levels; the consumer chooses the highest affordable IC given the budget.
Indifference Curve Analysis: Details and Special Cases
Convexity: ICs are convex to the origin: preference for mixtures over extremes.
Example intuition: 10 cola + 0 pizzas is less preferred than 5 cola + 5 pizzas; 0 cola + 10 pizzas is also less preferred; the mix is best.
Difference between convex and concave (for context): convex to the origin is standard in economics; concave would imply preference for extremes, which is typically unrealistic in consumer behavior.
Indifference curves: show all bundles with equal utility; higher curves imply greater utility; ICs are negatively sloped, convex, and do not intersect.
Indifference curves for special goods:
Perfect complements: ICs are L-shaped; goods must be consumed in fixed ratios (e.g., coffee and coffee filters). Knick point indicates the fixed ratio (e.g., 1 coffee with 1 filter).
Perfect substitutes: ICs are straight lines; consumer is willing to substitute one good for the other 1:1 (e.g., butter and margarine).
Normal case: convex ICs with smooth curvature; mixtures are preferred.
Budget Constraint and Optimal Choice
Budget line (budget constraint): shows all affordable bundles given income I and prices px and py.