  In this paper, we bring consumer theory to bear in the analysis of Fisher
markets whose buyers have arbitrary continuous, concave, homogeneous (CCH)
utility functions representing locally non-satiated preferences. The main tools
we use are the dual concepts of expenditure minimization and indirect utility
maximization. First, we use expenditure functions to construct a new convex
program whose dual, like the dual of the Eisenberg-Gale program, characterizes
the equilibrium prices of CCH Fisher markets. We then prove that the
subdifferential of the dual of our convex program is equal to the negative
excess demand in the associated market, which makes generalized gradient
descent equivalent to computing equilibrium prices via t\^atonnement. Finally,
we run a series of experiments which suggest that t\^atonnement may converge at
a rate of $O\left(\frac{(1+E)}{t^2}\right)$ in CCH Fisher markets that comprise
buyers with elasticity of demand bounded by $E$. Our novel characterization of
equilibrium prices may provide a path to proving the convergence of
t\^atonnement in Fisher markets beyond those in which buyers utilities exhibit
constant elasticity of substitution.
