engleski

Are Business Cycles Phase Transitions?

In this note we interpret the well-known one- dimensional Cahn-Hilliard functional as the model for achieving the dynamic equilibrium over large periods of time in given national economy with known initial aggregate economic parameters. The economy is viewed as the dynamical system, without strict separation to exogenous and endogenous variables, but with assumed existence of business cycles (viewed as "phases" or "states"), which bring both balance and imbalance to the state of the economy. Our conclusions are based on a number of results obtained by A. Raguz outside the economic context, which are related to standard analysis of Cahn-Hilliard functionals in one dimension. Mathematical apparatus used is Gamma convergence of functionals defined on appropriately chosen space of functions, as well as the relaxation method in the variational calculus over the space of Young measures. We prove that under relatively mild assumption on double well potential function and the optimal profile function we can indeed deduce both economic interpretation of the mentioned model and the desired equilibrium state of the national economy in terms of balancing the usual economic parameters.

Convergence, dynamical system, equilibrium, minimization, Cahn-Hilliard functional

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