# Consumer Preferences

Business I · Microeconomics · https://tryals.app/learn/business-i/consumer-preferences

## What Consumers Want

Microeconomics begins with the consumer, and the consumer begins with **preferences**.

**Three axioms of rational preference**:
1. **Completeness**: Any two bundles can be ranked; you cannot say "I can't compare them."
2. **Transitivity**: If $A \succsim B$ and $B \succsim C$, then $A \succsim C$. This rules out preference cycles.
3. **Non-satiation** ("more is better"): A bundle with more of at least one good is strictly preferred, ruling out bliss points.

| Axiom | Says | Rules out |
| --- | --- | --- |
| Completeness | Any two bundles can be ranked | "I can't compare them" |
| Transitivity | $A \succsim B$, $B \succsim C$ $\rightarrow$ $A \succsim C$ | Preference cycles |
| Non-satiation | More is better | Bliss points inside the map |

**Indifference curves** connect all bundles the consumer considers equally good.

## Curves and Trade-offs

Indifference curves slope **downward** from non-satiation, **never cross** due to transitivity, and **higher curves are preferred**.

**The marginal rate of substitution** (**MRS**) is the rate of trade:

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

The **MRS** typically **diminishes**: the more $x$ you have, the less $y$ you will trade for it, creating **convex** curves bowed to the origin.

**Special cases** include **perfect substitutes** (straight lines, constant MRS), **perfect complements** (L-shaped, fixed proportions), and **Cobb-Douglas** (smooth, convex).

> **Tip:** Each curve property is an axiom made visible. If a drawn map violates one, an axiom is broken.

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Match each preference axiom to its meaning.

**Answer:**

- Completeness → Every pair of bundles can be ranked
- Transitivity → No preference cycles: $A \succsim B \succsim C \Rightarrow A \succsim C$
- Non-satiation → More is always better
- Convexity → Mixtures are preferred to extremes

**Why:** The four pillars of rational consumer theory, they generate well-behaved indifference curves.

Page: https://tryals.app/practice/business-i/consumer-preferences/match-each-preference-axiom-to-its-meaning

### 2. The transitivity axiom says that preferring A to B and B to C forces preferring A to C. Why does violating it make a consumer exploitable?

A. Because market prices assume all consumers share the same ranking
B. Because the consumer would be unable to rank any two bundles
C. Because intransitive preferences cannot be represented graphically
D. An intransitive consumer is a money pump

**Answer:** D. An intransitive consumer is a money pump

**Why:** Three trades return the bundle and remove the fee three times, and the loop can be repeated indefinitely, so intransitivity is not merely odd but self-destructive. The axioms describe consistency rather than good taste, which is why 'rational' in economics is a much weaker claim than it sounds.

Page: https://tryals.app/practice/business-i/consumer-preferences/the-transitivity-axiom-says-that-preferring-a-to-b-and-b-to-c-forces

### 3. Sort these goods into perfect substitutes vs perfect complements.

**Answer:**

- Perfect substitutes: Coke and Pepsi (to some consumers), Blue pen and black pen, One-euro coin and two 50-cent coins
- Perfect complements: Left shoe and right shoe, Computer and monitor, Hot dog and bun

**Why:** Substitutes: one replaces the other at a fixed rate. Complements: useless without the other, consumed in fixed proportions.

Page: https://tryals.app/practice/business-i/consumer-preferences/sort-these-goods-into-perfect-substitutes-vs-perfect-complements

### 4. The marginal rate of substitution typically diminishes as you move along an indifference curve to the right.

**Answer:** True

**Why:** As you accumulate more $x$ (and less $y$), each additional unit of $x$ becomes less valuable relative to $y$, you demand less $y$ compensation. This gives indifference curves their convex shape.

Page: https://tryals.app/practice/business-i/consumer-preferences/the-marginal-rate-of-substitution-typically-diminishes-as-you-move

### 5. Convex preferences mean averages are preferred to extremes, and the indifference curves bow inward. Why is that assumed rather than derived?

A. Because it is required for the budget constraint to be a straight line
B. Because it follows logically from non-satiation
C. Because experiments show consumers always prefer variety
D. Because it delivers a unique interior optimum, not a corner

**Answer:** D. Because it delivers a unique interior optimum, not a corner

**Why:** Convexity is an assumption chosen for the behaviour it produces. Without it the tangency condition is not the answer, and the model predicts corner solutions we mostly do not observe.

Page: https://tryals.app/practice/business-i/consumer-preferences/convex-preferences-mean-averages-are-preferred-to-extremes-and-the