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2022/10/17

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Capital Fund Management | Chairman and Head of research

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Dynamical systems are usually such that the stability of equilibrium points can be studied by linearizing the dynamics in their vicinity, i.e. assuming small perturbations that evolve according to a (possibly high dimensional) linear system. Stability is then decided according to the largest eigenvalue z of the corresponding matrix. If |z| < 1 then equilibrium is stable, as any perturbation decays with time t at least as fast as |z|^t. If on the other hand |z| > 1, then perturbations generically diverge with time and a full non-linear analysis is required. In our recent study of the dynamics of firm networks, we discovered a new generic scenario, with possibly interesting consequences for macroeconomics. https://lnkd.in/eBABN4fH At economic equilibrium, all markets clear. This means that supply (of goods and labour) is equal to demand. But when equilibrium is perturbed, it matters whether demand is greater than or less than supply, and in which markets. The resulting dynamics is indeed governed by phenomena that are completely different. For example, excess supply will lead to inventories, when excess demand leads to unfulfilled orders. Wage updates are not symmetric when the job market is hot or when there is unemployment. Etc. What this means is that the resulting dynamics of fluctuations around equilibrium are only “cone-wise linear”. In other words, depending on the direction of the perturbation, the dynamics of small perturbations is still linear, but the stability matrix depends on the `cone’ within which the perturbation lies. This may lead to an exquisitely complex evolution, where the system jumps between stable cones and unstable cones – resulting in relatively calm periods interrupted by instabilities, as the type of imbalances in the economy changes (see figure). The overall stability of equilibrium cannot be simply decided, as it depends on the relativ

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https://www.linkedin.com/feed/update/urn:li:activity:6987743014337060865

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https://www.linkedin.com/in/jean-philippe-bouchaud-bb08a15/

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