It follows from the weak axiom of revealed preference that if a consumer chooses x when he could afford y and chooses y when he could afford x, then his income must have changed between the two observations.

Weak Axiom

In economic theory, a principle stating that if a consumer prefers bundle A to bundle B, then they will not prefer B to A when prices change, keeping income constant.

Revealed Preference

A theory suggesting that consumers' preferences can be determined by observing their purchasing behavior and the choices they make among different goods.