When the asset market is incomplete, competitive equilibria are constrained suboptimal, which provides scope for Pareto improving interventions. Price regulation can be such a Pareto improving policy, even when the welfare effects of rationing are taken into account. An appealing aspect of price regulation is that it operates anonymously on market variables. The welfare analysis of price regulation calls for an extension of the equilibrium theory of incomplete markets to fix-price equilibria.Fix-price equilibria exist under standard assumptions. There are robust examples, however, for which at regulated prices close to competitive prices, there are no fix-price equilibria close to competitive equilibria. We provide necessary and sufficient conditions for the local uniqueness of fix-price equilibria, and show that under these conditions Pareto improving price regulation is generically possible.