Bouchaud-Mézard model on a random network

Ichinomiya, Takashi

doi:10.1103/physreve.86.036111

Cited by 11 publications

(24 citation statements)

References 11 publications

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“…This result is consistent with that in our previous paper [6], in which we investigated the wealth distribution when β > 3. Third, we note also that in the limit k → ∞, we obtain β = 2 + μ k from Eq.…”

Section: Theorysupporting

confidence: 93%

“…[6,7], we make "adiabatic" and "independent" assumptions. We assume that the PDF of the wealth on each node is independent, allowing the total PDF ρ(x 1 ,x 2 , .…”

Section: Theorymentioning

confidence: 99%

“…We recently obtained the wealth distribution of the BM model on the complex network analytically in the case of β > 3 [6,7]. However, these analyses cannot be applied when β < 3, because we derive the result using the central limit theorem.…”

Section: Introductionmentioning

confidence: 99%

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Power-law exponent of the Bouchaud-Mézard model on regular random networks

Ichinomiya

2013

Phys. Rev. E

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We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as x→∞. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.

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Section: Theorysupporting

confidence: 93%

“…[6,7], we make "adiabatic" and "independent" assumptions. We assume that the PDF of the wealth on each node is independent, allowing the total PDF ρ(x 1 ,x 2 , .…”

Section: Theorymentioning

confidence: 99%

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Power-law exponent of the Bouchaud-Mézard model on regular random networks

Ichinomiya

2013

Phys. Rev. E

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“…As shown in [8,11,12], Eq. (1) generically leads to a Pareto (power-law) tail for the distribution of wealth in the stationary state.…”

mentioning

confidence: 98%

“…(1) generically leads to a Pareto (power-law) tail for the distribution of wealth in the stationary state. 8 The tail exponent α can be computed explicitly in several cases [8,11,12], and be associated to a Gini coefficient G ≈ (2α − 1) −1 . The Gini coefficient is a standard measure of inequality [27]; it is equal to zero for egalitarian societies, and to unity when a finite fraction of the total wealth is in the hands of a few individuals.…”

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confidence: 99%

On growth-optimal tax rates and the issue of wealth inequalities

Bouchaud

2015

J. Stat. Mech.

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We consider a highly stylized, yet non trivial model of the economy, with a public and private sector coupled through a wealth tax and a redistribution policy. The model can be fully solved analytically, and allows one to address the question of optimal taxation and of wealth inequalities. We find that according to the assumption made on the relative performance of public and private sectors, three situations are possible. Not surprisingly, the optimal wealth tax rate is either 0% for a deeply dysfunctional government and/or highly productive private sector or 100% for a highly efficient public sector and/or debilitated/risk averse private investors. If the gap between the public/private performance is moderate, there is an optimal positive wealth tax rate maximizing economic growth, even -counter-intuitively -when the private sector generates more growth. The compromise between profitable private investments and taxation however leads to a residual level of inequalities. The mechanism leading to an optimal growth rate is related the well-known explore/exploit trade-off.One of the most disgruntling aspects of the political debate is that intelligent people can defend in good faith totally conflicting points of view. This rarely happens in hard sciences, where either pure logic (as in mathematics) or empirical/experimental data (as in natural sciences) eventually disqualify flawed arguments. While pure logic seems of little relevance when it comes to politics, identifying questions with possible empirical answers could perhaps help.As a rough caricature, the Left (or liberals) promotes big governments and correspondingly high taxes, when the Right (or conservatives) favours individual initiatives and private investments, and thus low tax rates. Both sides, one presumes, are concerned by the economic welfare of their fellow citizens. One would like to set up a modelling framework where the question of optimal taxation can be investigated theoretically, with, for instance, long-term economic growth as a primary objective. This question is of course important enough in itself; it has however received intense scrutiny in the wake of the recent debate about inequalities and their potential remedies, introducing a global wealth tax for example [1]. If such a global tax was adopted, what should the taxation rate be? Are there theoretical guidelines helping understand if there is a tax rate that, for example, maximizes economic growth? Surprisingly, most classical results in the economics literature conclude that the optimal wealth tax rate is zero, but the assumptions made are, as often, quite extreme [2-4] and, for a recent discussion, Ref. [5]. More recently, the problem of an optimal wealth tax rate has been revisited by Piketty and Saez [5]. They conclude that the wealth tax rate should be non zero, and actually quite high (at least in the form of an inheritance tax). However, their result hinges on the fact that the "social welfare function" that the government should optimize puts a strong weight on those who rece...

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Localization phase transition in stochastic dynamics on networks with hub topology

Seroussi

Sochen

2020

Physica A: Statistical Mechanics and its Applications

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Bouchaud-Mézard model on a random network

Cited by 11 publications

References 11 publications

Power-law exponent of the Bouchaud-Mézard model on regular random networks

Power-law exponent of the Bouchaud-Mézard model on regular random networks

On growth-optimal tax rates and the issue of wealth inequalities

Localization phase transition in stochastic dynamics on networks with hub topology

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