# 4.1 Preferences

In the previous chapters we derived the combinations of fish and coconuts that Chuck *could produce* using his available resources and technology.

In the chapters that follow we’re going to analyze Chuck’s *optimal choice*: which combination of fish and coconuts Chuck *should produce*.

But in order to know which combination he should produce, we need to know something about what Chuck’s **preferences** are: that is, how much “happiness,” or “utility,” he would get from each potential combination of goods. This will then allow us to choose the his *most preferred* bundle from his production possibilities set.

## Comparing two choices

We’ll build up our theory of preferences from a foundation of *bilateral comparison*: that is, let’s initially consider two potential choices Chuck could make, which we’ll call $A$ and $B$. There are three possibilities for how Chuck feels about $A$ and $B$:

- He might
**strictly prefer**$A$ to $B$, which we’ll write $A \succ B$ (or $B \prec A$) - He might
**strictly prefer**$B$ to $A$; that is, $B \succ A$ (or $A \prec B$) - He might be
**indifferent**between $A$ and $B$, which we’ll write $A \sim B$

We can combine these to describe *potential* relationships between choices: in particular, we can say that Chuck **weakly prefers** $A$ to $B$, which we’ll write $A \succsim B$, if $A \succ B$ or $A \sim B$. This is a little like saying $x \ge 3$ if either $x > 3$ or $x = 3$.

## Assumptions of rational choice

Our theory of rational choice will rely on two fundamental assumptions about Chuck’s preferences:

- Preferences are
**complete**: for*any possible pair of choices*$A$ and $B$, Chuck knows whether $A \succ B$, $A \sim B$, or $A \prec B$. Put another way, there is no way that we could ask him how he felt about $A$ and $B$ and he would reply, “I don’t know!” (Note that “I don’t know” is different than “I’m indifferent between the two.”) - Preferences are
**transitive**: if there are three options $A$, $B$, and $C$ such that Chuck prefers $A$ to $B$, and also prefers $B$ to $C$, then it must be the case that he prefers $A$ to $C$. Furthermore, if his preferences are strict — that is, $A \succ B$ and $B \succ C$ — then it must be the case that he strictly prefers $A$ to $C$ ($A \succ C$). Again, the first statement is a little like saying that for any three real numbers $x$, $y$, and $z$, if $x \ge y$ and $y \ge z$, then $x \ge z$; and the second statement (about strict preferences) is similar to the proposition that if $x > y$ and $y > z$, then $x > z$.