Is positive income elasticity of demand really associated with normal goods?: revisiting the Slutsky equation and net benefit ratio

Incorporating a household’s net sale status into a rearranged Slutsky equation with combined ordinary and endowment income effects, this paper aims to reinterpret the income elasticity of demand in the case of buying and selling and to associate it with types of goods in a novel manner. To this end, the Deaton’s (1989) net benefit ratio (NBR) approach is expressed as the difference between original and endowment budget shares, and formulated in its elasticity form as the difference between the Hicksian and Marshallian own-price elasticities at any given price, divided by the income elasticity. While the numerator in the latter expression is always positive (negative) for normal (inferior) goods, the denominator may be either positive or negative for either type of good, depending on the net sale position of the household. A positive NBR for a normal good implies that the household is a net demander of that good and that the income elasticity is positive. When the NBR is negative for such a good, it implies that the household is a net seller and that the income elasticity is negative. Again, a positive NBR for an inferior good refers to the fact that the household is a net demander and the income elasticity is negative, whereas a negative NBR reveals that the household is a net seller of that good, which has, unconventionally, a positive income elasticity.