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 $x > z$.