x-intercept

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.

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 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.

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 line (budget constraint): shows all affordable bundles given income I and prices px and py.
- Equation: $p<em>x x + p</em>y y = I$
- Intercepts: $$x ext{-intercept} = I/p_x;\