  We study market mechanisms for allocating divisible goods to competing agents
with quasilinear utilities. For \emph{linear} pricing (i.e., the cost of a good
is proportional to the quantity purchased), the First Welfare Theorem states
that Walrasian equilibria maximize the sum of agent valuations. This ensures
efficiency, but can lead to extreme inequality across individuals. Many
real-world markets -- especially for water -- use \emph{convex} pricing
instead, often known as increasing block tariffs (IBTs). IBTs are thought to
promote equality, but there is a dearth of theoretical support for this claim.
  In this paper, we study a simple convex pricing rule and show that the
resulting equilibria are guaranteed to maximize a CES welfare function.
Furthermore, a parameter of the pricing rule directly determines which CES
welfare function is implemented; by tweaking this parameter, the social planner
can precisely control the tradeoff between equality and efficiency. Our result
holds for any valuations that are homogeneous, differentiable, and concave. We
also give an iterative algorithm for computing these pricing rules, derive a
truthful mechanism for the case of a single good, and discuss Sybil attacks.
