arXiv subjects

Eric Kemp-Benedict

Publications and source records attributed to Eric Kemp-Benedict.

5 recordsLinked to original sources

arXiv2012

General Equilibrium as a Topological Field Theory

General equilibrium is the dominant theoretical framework for economic policy analysis at the level of the whole economy. In practice, general equilibrium treats economies as being always in equilibrium, albeit in a sequence of equilibria as driven by external changes in parameters. This view is sometimes defended on the grounds that internal dynamics are fast, while external changes are slow, so that the economy can be viewed as adjusting instantaneously to any changed conditions. However, the argument has not been presented in a rigorous way. In this paper we show that when conditions are such that: a) economies do respond essentially instantaneously to external influences; b) the external changes are small compared to the values that characterize the economy; and c) the economy's dynamics are continuous and first-order in time (as for Walrasian tatonnement), the resulting economic theory is equivalent to a topological field theory. Because it is a topological theory it has no dynamics in a strict sense, and so perturbatively---that is, when examining dynamics in the region of a critical point---the field theory behaves as general equilibrium posits. However, the field-theoretic form of the theory admits non-perturbative instanton solutions that link different critical points. Thus, in this theory, and in contrast to general equilibrium, the internal dynamics of the model occasionally make an appearance in the form of abrupt, noise-driven transitions between critical points.

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arXiv2012

Confronting the Kaya Identity with Investment and Capital Stocks

Scaling relations, such as the IPAT equation and the Kaya identity, are useful for quickly gauging the scale of economic, technological, and demographic changes required to reduce environmental impacts and pressures; in the case of the Kaya identity, the environmental pressure is greenhouse gas emissions. However, when considering large-scale economic transformation, as with a shift to a low-carbon economy, the IPAT and Kaya identities and their cousins fail to capture the legacy of existing capital, on the one hand, and the need for new investment, on the other. While detailed models can capture these factors, they do not allow for rapid exploration of widely different alternatives, which is the appeal of the IPAT and Kaya identities. In this paper we present an extended Kaya identity that includes investment and capital stocks. The identity we propose is a sum of terms, rather than a simple scaling relation. Nevertheless, it allows for quick analysis and rapid exploration of a variety of different possible paths toward a low-carbon economy.

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arXiv2012

Price and Quantity Trajectories: Second-order Dynamics

In two previous papers the author developed a second-order price adjustment (tâtonnement) 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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arXiv2012

Second-order Price Dynamics: Approach to Equilibrium with Perpetual Arbitrage

The notion that economies should normally be in equilibrium is by now well-established; equally well-established is that economies are almost never precisely in equilibrium. Using a very general formulation, we show that under dynamics that are second-order in time a price system can remain away from equilibrium with permanent and repeating opportunities for arbitrage, even when a damping term drives the system towards equilibrium. We also argue that second-order dynamic equations emerge naturally when there are heterogeneous economic actors, some behaving as active and knowledgeable arbitrageurs, and others using heuristics. The essential mechanism is that active arbitrageurs are able to repeatedly benefit from the suboptimal heuristics that govern most economic behavior.

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arXiv2011

Second-Order, Dissipative Tâtonnement: Economic Interpretation and 2-Point Limit Cycles

This paper proposes an alternative to the classical price-adjustment mechanism (called "tâtonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a process can result from simple behavioural rules. The discrete-time form of the model can result in two-step limit cycles, but as the distance covered by the cycle depends on the size of the damping, the proposed mechanism can lead to both highly unstable and relatively stable behaviour, as observed in real economies.

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