  We present the following results pertaining to Fisher's market model:
  -We give two natural generalizations of Fisher's market model: In model M_1,
sellers can declare an upper bound on the money they wish to earn (and take
back their unsold good), and in model M_2, buyers can declare an upper bound on
the amount to utility they wish to derive (and take back the unused part of
their money).
  -We derive convex programs for the linear case of these two models by
generalizing a convex program due to Shmyrev and the Eisenberg-Gale program,
respectively.
  -We generalize the Arrow-Hurwicz theorem to the linear case of these two
models, hence deriving alternate convex programs.
  -For the special class of convex programs having convex objective functions
and linear constraints, we derive a simple set of rules for constructing the
dual program (as simple as obtaining the dual of an LP). Using these rules we
show a formal relationship between the two seemingly different convex programs
for linear Fisher markets, due to Eisenberg-Gale and Shmyrev; the duals of
these are the same, upto a change of variables.
