Revealed Preference Theory

1) Motivation: why “revealed preference”?

Indifference curve theory assumes preferences exist and are stable, but it still talks in terms of utility (even if only ordinal).
Revealed Preference Theory (associated strongly with Paul Samuelson) shifts the focus to observable choices:

Instead of asking “How much utility does a bundle give?”, we infer preferences from what consumers actually choose when facing budget constraints.

So preferences are revealed through market behavior.

Why it matters for CUET PG:

RPT is a core topic in modern consumer theory.
Many questions test the logic of consistency of choice, especially WARP/SARP/GARP type statements.
RPT connects strongly with demand theory and rationality axioms.

2) Core idea: choice reveals preference

Consider a consumer who faces prices $(P_x, P_y)$ and income $M$ , so their feasible set is:

P_x X + P_y Y \le M

If the consumer chooses bundle A when bundle B was also affordable, then the consumer is said to have revealed a preference for A over B.

2.1 Direct revealed preference

Bundle $A$ is directly revealed preferred to $B$ (write $A \succeq^R B$ ) if:

$A$ is chosen, and
$B$ was affordable when $A$ was chosen.

Formally, if in some budget situation $t$ :

chosen bundle is $x^t$ ,
any other bundle $x$ is affordable if $p^t \cdot x \le p^t \cdot x^t$

Then:

x^t \succeq^R x \quad \text{whenever } p^t \cdot x \le p^t \cdot x^t

Interpretation: “Given the opportunity to buy B, you bought A, so you (weakly) prefer A.”

3) Weak Axiom of Revealed Preference (WARP)

3.1 Statement (most testable form)

WARP: If bundle A is directly revealed preferred to bundle B, then B cannot be directly revealed preferred to A.

In plain words:

If you choose A when B is affordable, you should not later choose B when A is affordable (unless the two bundles are identical).

3.2 Formal intuition

Suppose:

In situation 1, consumer chooses A when B affordable ⇒ $A \succeq^R B$
In situation 2, consumer chooses B when A affordable ⇒ $B \succeq^R A$

This would mean the consumer’s choices are inconsistent with stable rational preferences.

3.3 Why “weak”?

Because it focuses on direct revealed preference (one-step affordability comparisons). It does not fully handle multi-step chains.