New Thoughts About Inferior Goods.

This paper presents what is apparently the first published specific utility function, together with its associated demand functions to illustrate the case of a commodity with a negatively sloping income consumption curve. This specific utility function can be subjected to a monotonic transformation by squaring it, such a transformation leaves the demand functions unchanged and will produce an illustration of the case of an inferior good based on an assumption of dependence of the marginal utilities. The analysis in the article provides an answer to the question of the type of utility function necessary to produce a case of an income consumption curve for a good which is normal at low levels of income but inferior at high levels of income, as depicted in several price theory books. If the utility index is additive, such a case must involve the existence of one commodity with decreasing marginal utility and another whose marginal utility function first decreases, next reaches a minimum and then increases.