The earliest I have seen is in "Untersuchungen =FCber die Theorie des Preises" by Rudolf Auspitz and Richard Lieben, 1889, Leipzig: Verlag von Duncker und Humblot. The quasilinear function appears several times, on pp. 471, 474, and 477; see section 2 of appendix II. For that part of their exposition, Auspitz and Lieben spelled out formally what would ensure a constant marginal utility of money. Their use of that function is a little different from later uses because the "linear good" in their function represented end-of-period money balances, i.e. the amount of money carried forward into the next period. There is then no need to restrict the amount of the "linear good" to be nonnegative. Also, there is actually a rationale for the separate treatment of one of the "goods," and it begins to resemble the discounted utility model. But because the purchasing power in the next period of the remaining funds depends on next-period prices, they placed anticipated next-period prices into the utility function as well. In all, their quasilinear function is clearly a more complex entity than that which appears in today's textbooks. But, if one reinterprets the linear good as just one more good consumed in the present, next-period prices no longer play a role, and the Auspitz-Lieben function looks the same as the modern version. Torsten Schmidt