Recently, Zhang introduced the Proportional Response dynamics for finding a market equilibrium in Fisher's Market with linear utilities. These dynamics are simple, distributed, and require no global communication. Zhang showed that the PR dynamics always converge to an equilibrium, but the proof uses a potential function that gives little insight into why this happens. Our work helps to explain this result. First, we introduce a new convex program that captures equilibria of the linear Fisher market. Second, we show that the Proportional Response dynamics are equivalent to a generalized gradient descent algorithm (using Bregman divergence) on this convex program. In addition to providing insight, this framework allows us to give improved bounds on the convergence rate of the proportional response dynamics. Both the new convex program for market equilibrium and the analysis of the gradient descent algorithm may be of independent interest.