Such situations of indifference are however made methodologically inadmissible by Samuelson in his theory. But, if the existence of indifference even between a few combinations in the vicinity of the combination actually chosen by the consumer is admitted, it would not be possible to prove demand theorem with the help of revealed preference.
(iii) According to Stonier and Hague, “The division of price effect into income and substitution effects is less fundamental. It does not allow us to separate pure income effect an pure substitution effect.” Further, Samuelson proves the demand theorem by assuming positive income elasticity of demand.
When, however, the income elasticity of demand is negative, Samuelson’s revealed preference theory is unable to establish the demand theorem. Given negative income elasticity of demand, it is not possible to know on the basis of revealed preference, the direction of change in demand as result of change in price.
Therefore, the revealed preference theory fails to enunciate the demand theorem when (a) income elasticity of demand is negative and the positive income effect is smaller than the substitution effect, and (b) the income elasticity of demand is negative and the positive income effect is stronger that the substitution effect. Therefore, Samuelson’s theory fails to explain the case of inferior goods and account for the Giffen’s paradox, in which case income elasticity of demand has to be negative.
(iv) Samuelson’s theory says nothing about the market demand curve.
(v) The theory fails to explain how the equilibrium of the consumer is arrived at. It just starts with a particular chosen position.