We explore the relative importance of income and household characteristics (such as family size) in explaining differences in household consumption of natural gas and LPG. In a simple model of vertically (willingness to pay) ordered households we posit that the relative importance of the income elasticity of demand (vs. the family size elasticity) depends positively on the price faced by households. Thus, very low prices tend to depress the across households income elasticity of demand relative to the characteristic-elasticity and the opposite holds for under high prices. We test this hypothesis using, for the first time in Argentina, data from the household expenditure survey on Natural gas and LPG and compare the cross-consumption equations for both fuels, which have quite different price regimes. Finally, we explore welfare implications for low-user tariff scheme reforms in natural gas.