Comments are most welcome!!!
I am aware of a huge literature on GE theory with linear utility functions, beginning with the seminal work of David Gale (Gale, D. (1957): “Price equilibrium for linear
models of exchange”, Rand Corporation Technical Report P-56, August 15.)
The following is a Wikipedia page on Linear Utility.
However, I haven't come across any document on demand analysis for budget constrained linear utility maximization.
Thanks.
Somdeb.