Microeconomics Preferences and Utility

These flashcards cover key concepts related to preferences and utility in microeconomics, including definitions and properties of preferences, types of indifference curves, and important economic measures.

Preferences in Microeconomics

A preference relation ranks bundles. For any x, y: x■y (at least as good), x■y (strictly preferred), x∼y (indifferent). Preferences assumed complete and transitive.

Properties of Rational Preferences

Completeness: all bundles comparable. Transitivity: consistency across comparisons. Reflexivity: x■x. Together ensure coherent choice.

Indifference Curve (IC)

Set of bundles yielding the same utility: U(x1,x2)=u0. Higher ICs = higher utility. ICs cannot cross (would violate transitivity).

Monotonicity

If x1',x2' ≥ x1,x2 (with at least one strict), then x' ■ x. 'More is better.' ICs slope downward if goods desirable.

Convexity in Preferences

Convex preferences: consumer prefers mixtures to extremes. If x■y then λx+(1−λ)y■y. ICs bowed toward origin, MRS diminishes.

Convex vs. Strictly Convex Preferences

Convex: averages at least as good. Strictly convex: averages strictly better. Perfect substitutes: linear (not convex). Perfect complements: right angles (not strictly convex).

Marginal Rate of Substitution (MRS)

MRS = −dx2/dx1|U const = MU1/MU2. Rate at which consumer trades good2 for good1 holding utility constant (slope of IC).

Diminishing MRS

As x1↑ and x2↓, MRS decreases. The more you have of one good, the less you're willing to give up of the other. Reflects convexity.

Perfect Substitutes

U=ax1+bx2. ICs straight lines, slope −a/b, constant MRS. Buy only cheaper good.

Perfect Complements

U=min(ax1,bx2). Goods used in fixed proportions (right-angle ICs). Optimum: ax1=bx2.

Cobb–Douglas Preferences

U=x1^a x2^b, MRS=(a/b)(x2/x1). Smooth, strictly convex, monotonic. Utility increases when both goods increase.

Non-Transitive Preferences

Creates cycles (A■B■C■A). Inconsistent/irrational preferences; no utility function can represent them.

Non-Monotonic Preferences

More goods may not be better (e.g., pollution). ICs can slope upward or form circles around a 'bliss point.'

Bliss Point

Most preferred bundle; moving away in any direction lowers utility. ICs are concentric circles around this point.

Testing Properties Graphically

Monotonic: ICs slope down. Convex: ICs bowed inward. Perfect substitutes: lines. Perfect complements: L-shapes. Bliss: circles.

Interior Optimum Condition

Tangency: MRS = p1/p2. The rate of willing trade equals the market trade rate.

Corner Solution

Occurs if MRS never equals price ratio (e.g., perfect substitutes). Consumer buys only one good, at a corner point.

Higher Utility Number

Yes, but utility is ordinal—only ranking matters. Any monotonic transformation (log, square) represents same preferences.

Indifference Map

Full set of ICs showing all possible utility levels. Higher curves = more preferred bundles.

Verification of Well-Behaved Preferences

✔ MU1,MU2>0 (monotonic) ✔ MRS decreasing (convex) ✔ ICs non-crossing & downward-sloping ✔ Continuous & differentiable.