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Price and Quantity Trajectories: Second-order Dynamics

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  • Eric Kemp-Benedict

Abstract

In two previous papers the author developed a second-order price adjustment (t\^atonnement) process. This paper extends the approach to include both quantity and price adjustments. We demonstrate 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 we argue, although we do 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), we conjecture 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.

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  • Eric Kemp-Benedict, 2012. "Price and Quantity Trajectories: Second-order Dynamics," Papers 1204.3156, arXiv.org.
  • Handle: RePEc:arx:papers:1204.3156
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    References listed on IDEAS

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    Cited by:

    1. Eric Kemp-Benedict, 2012. "General Equilibrium as a Topological Field Theory," Papers 1209.1705, arXiv.org.

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