Price and Quantity Trajectories: Second-order Dynamics

In two previous papers the author developed a second-order price adjustment (tatonnement) process. This paper extends the approach to include both quantity and price adjustments. It demonstrates three results: a analogue to physical energy, called “activity”, arises naturally in the model and is not conserved in general; price and quantity trajectories must either end at a local minimum of a scalar potential or circulate endlessly; and disturbances into a subspace of substitutable commodities decay over time.

From this the author argues, but does not prove, that the model features global stability, combined with local instability, a characteristic of many real markets. Following these observations and a brief survey of empirical results for price-setting and consumption behavior in markets for “real” goods (as opposed to financial markets), he conjectures that Stigler and Becker’s well-known theory of consumer preference opens the possibility of substantial degeneracy in commodity space, and therefore that price and quantity trajectories could lie on a relatively low-dimensional subspace within the full commodity space.

Read the paper (external link to arXiv.org)