My guess is that Gossen (1854) must be a close runner for this. The English translation of the *Entwickelung...* (MIT Press, 1983) has this theorem [7.11]:

"Man obtains the maximum of life pleasure if he allocates all his earned money E between the various pleasures and determines the e in such a manner that the last atom of money spent for each pleasure offers the same amount [intensity] of pleasure." (pp. 108-9)

Guido Erreygers, University of Antwerp

-----Original Message-----

Does anyone know who was the first author(s)  to construct the
"consumer problem" as maximizing utility subject to an income
constraint? References to journal articles reviewing this subject
would be most appreciative.