<p>This paper establishes that the local quasiconvexity of aggregate demand is a sufficient condition for equilibrium uniqueness in economies with heterogeneous CES preferences. The analysis yields two constructive contributions. First, we derive computable bounds on equilibrium prices using four representative agents constructed from the extreme values of individual preference parameters. Second, we show that even non-monotonic aggregate demand can yield a unique equilibrium, provided it exhibits a single inflection point within the equilibrium price range. Notably, the uniqueness condition is governed by the fourth-order price effect of individual demand at the upper price bound. We establish this result for two-good economies with CES preferences and then extend it to two-period economies with Kreps-Porteus preferences and to multi-country trade models. These extensions provide practical tools for equilibrium computation in applied general equilibrium analysis.</p>