Question

The scarcity of apples made its price rise to 10 dollars. However, the government maintained the one apple per person policy. With new price next week , Bernard decided to buy 10 bananas. Do these choices violate the WARP ? What about SARP ?

Answer 1

Clearly, apples have become costlier than bananas. So, if Bernard decided to buy 10 bananas and not apples, then for Bernard, apples are no longer affordable.

The Weak Axiom of Revealed Preference (WARP) states that:

If (x₁, x₂) is directly revealed preferred to (y₁, y₂), and the two bundles are not the same, then it cannot happen that (y_1, y₂) is directly revealed preferred to (x₁, x₂) [Varian, Hal R. (2010), p. 124]

So according to WARP, if earlier Bernard can afford apples, then he must have chosen apples over bananas. In the present situation, when apples cost $10 apiece, Bernard could no longer afford apples, and hence, buys bananas.

The Strong Axiom of Revealed Preference (SARP) states that:

If (x₁, x₂) is revealed preferred to (y₁, y₂) (either directly or indirectly) and the two bundles are not the same, then it cannot happen that (y_1, y₂) is directly or indirectly revealed preferred to (x₁, x₂) [Varian, Hal R. (2010), p. 128]

According to SARP, The initial choice set of Bernard no longer holds in the present scenario due to lack of affordability. SARP is a stronger axiom than WARP because it talks about strictly preferred to as opposed to weakly preferred to or indifferent between two choices.