Attilio da Empoli's Analysis of Utility

This survey deals with the concepts of the ultramarginal phenomenon of utility and its curve characterized by finite variations. Unlike Jevons’ traditional utility curve, da Empoli’s one put on the abscissa not one need at a time, but various competing needs to be satisfied. The relationship between the (increasing) number of needs to be satisfied and the (decreasing) rapidity of their satisfaction compels the utility curve to proceed by larger and larger steps, certainly not by infinitesimal variations. In searching, like Gossen, for an indivisible good to satisfy different needs, da Empoli focuses on money, not time. Da Empoli then identifies money with income, so its use depends on the amount available and its purchasing power. Comparing this view with Gossen’s, the levelling of marginal utilities, after the given time has elapses, clearly is not applicable to da Empoli’s curve where utility depends on money available. The importance attributed to money enables us to see that an increase in the amount available makes the utility curve suddenly jumping upward, subverting the law of decreasing utility and presenting a kink. A comparison with Sweezy’s kinked demand function, which is only seven years older, is unavoidable. But while Sweezy thinks in term of prices fixed by oligopolists operating on the market, da Empoli thinks in term of utility experienced by people desiring indivisible goods that can only be obtained by an increase in their income. So, while Sweezy’ demand curve slopes downwards again beyond the kink, complying with the law of decreasing utility, da Empoli’s utility curve slopes upward after the kink. It is a fragmentary, kinked curve that can be applied, for instance, to the need for contemporary art experienced by addicted people wishing to possess indivisible goods and willing to express an inelastic demand.