Quadratic optimization subject to linear constraints is a fundamental building-block in many other branches of applied mathematics. However, for large-scale systems, where a common global objective function is neither naturally defined nor easily computable, it is natural to view economic equilibrium theory as an alternative approach to design and analysis. Stability and robustness of equilibria can then be studied using the concept of monotonicity. In this paper we prove fundamental monotonicity properties for price dynamics with quadratic utilities. In particular, the main theorem gives quantitative bounds on the size of the monotone cone. Simple examples illustrate the ideas.