Consumer Preferences

What Consumers Want

Microeconomics begins with the consumer — and the consumer begins with preferences.

Three axioms of rational preference:

1. Completeness: for any two bundles $A$ and $B$, the consumer can rank them — prefers $A$, prefers $B$, or is indifferent.
2. Transitivity: if $A \succsim B$ and $B \succsim C$, then $A \succsim C$. No preference cycles.
3. Non-satiation ("more is better"): a bundle with more of at least one good (and no less of any other) is strictly preferred.

Indifference curves connect all bundles the consumer considers equally good. Properties:

• They slope downward (giving up one good requires compensation with the other).
• They never cross (crossing would violate transitivity).
• Higher curves are preferred (non-satiation pushes the consumer northeast).

The marginal rate of substitution (MRS) is the slope of the indifference curve — the rate at which the consumer willingly trades one good for another:

$$MRS = -\frac{\Delta y}{\Delta x} = \frac{MU_x}{MU_y}$$

The MRS typically diminishes: the more $x$ you have (relative to $y$), the less $y$ you're willing to give up for another unit of $x$. This gives indifference curves their characteristic convex shape — bowed toward the origin.

Special cases: perfect substitutes (straight-line indifference curves, constant MRS), perfect complements (L-shaped curves, consumed in fixed proportions), and Cobb-Douglas (smooth, convex, the workhorse case).

The three axioms

Tip: Each indifference-curve property is an axiom made visible: downward slope comes from non-satiation, non-crossing from transitivity. If a drawn map violates one, an axiom has been broken somewhere.