Inheritance

We consider a population of reproducing individuals who inherit, earn, consume, and bequeath wealth. A model is constructed to describe the wealth of an individual selected from the nth generation by following a random line of descent from the initial individual. It is shown that bequests are commonly a convex function of wealth. Considering a linear approximation to the bequest function enables us to obtain estimates of the limiting distribution of wealth as the number of generations increases, when earnings of parent and offspring are independent. More generally when earnings of parent and offspring are not independent we obtain upper bounds for the tail of the wealth distribution using a martingale inequality.

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Some remarks on probability inequalities for sums of bounded convex random variables

Journal of Applied Probability ◽

10.2307/3212418 ◽

1975 ◽

Vol 12 (1) ◽

pp. 155-158 ◽

Cited By ~ 1

Author(s):

M. Goldstein

Keyword(s):

Convex Function ◽

Exponential Convergence ◽

Random Variables ◽

Upper Bounds ◽

Independent Random Variables ◽

Probability Inequalities ◽

Continuous Convex Function ◽

Bounded Convex

Let X1, X2, · ··, Xn be independent random variables such that ai ≦ Xi ≦ bi, i = 1,2,…n. A class of upper bounds on the probability P(S−ES ≧ nδ) is derived where S = Σf(Xi), δ > 0 and f is a continuous convex function. Conditions for the exponential convergence of the bounds are discussed.

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Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202520400023 ◽

2020 ◽

Vol 30 (04) ◽

pp. 685-725 ◽

Cited By ~ 5

Author(s):

Giulia Furioli ◽

Ada Pulvirenti ◽

Elide Terraneo ◽

Giuseppe Toscani

Keyword(s):

Steady State ◽

Wealth Distribution ◽

Kinetic Equations ◽

Planck Equation ◽

Logarithmic Sobolev Inequality ◽

One Dimensional ◽

Distribution Of Wealth ◽

Multi Agent ◽

Fokker Planck Equations ◽

Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

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Egalitarianism, Inequality, and Age: The Rural North in 1860

The Journal of Economic History ◽

10.1017/s0022050700042807 ◽

1981 ◽

Vol 41 (1) ◽

pp. 85-93 ◽

Cited By ~ 23

Author(s):

Jeremy Atack ◽

Fred Bateman

Keyword(s):

Life Cycle ◽

Civil War ◽

Age Structure ◽

Wealth Distribution ◽

Distribution Of Wealth ◽

Egalitarian Society ◽

Heads Of Household ◽

Life Cycle Pattern

Little is known about the distribution of wealth in the allegedly egalitarian society of the rural North on the eve of the Civil War. This paper investigates the role of the age structure of the heads of household and a life-cycle pattern of accumulation in determining the wealth distribution within that society and among the various groups that comprised it. The results suggest a need for caution in making cross-group or inter-temporal comparisons in wealth distributions without taking account of such factors.

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Brotherhood dalam Dimensi Sistem Ekonomi Islam

ISLAMICA Jurnal Studi Keislaman ◽

10.15642/islamica.2017.11.2.499-521 ◽

2017 ◽

Vol 11 (2) ◽

pp. 499

Author(s):

Fahrur Ulum

Keyword(s):

Economic System ◽

Wealth Distribution ◽

Economic Activities ◽

Distribution Of Wealth ◽

Economic Man ◽

Market Economic ◽

Islamic Economic ◽

Set Up

This article discusses the issue of brotherhood in Islamic economic system. The goal of Islamic economics is to create advantages (falâh}) for all economic man. To achieve this goal, Muslim economists have agreed to set up the philosophical pillars of Islamic economic system which consists of tawhîd, ‘ibâdah, khilâfah, and ukhuwwah. One of the important challenges to deal with is how to place the idea of brotherhood as a pillar of Islamic economic system that is applicable in economic activities which then lead to equal advantages. Muslim economists argue that Islamic economic system has led economic man to possess altruistic personality. This is not only related to the problem of consumption but also to that of production. In addition, the distribution of wealth specific in Islamic economic system has resulted in brotherhood. The spirit of brotherhood has inspired the effort of distributing wealth economically and non-economically towards shared advantages. Specific wealth distribution in Islamic economics is by placing human as economic being and social being alike. Therefore, brotherhood is implemented in market and non-market economic activities. The implementation of brotherhood is not only in the form of cooperative but more than that is to be oriented to efforts of empowering economic man.

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Distribution of Wealth for Sustainable Happiness

10.4018/978-1-7998-8258-9.ch013 ◽

2022 ◽

pp. 206-212

Author(s):

Sheakh Reyad Muhammad Noor ◽

Zobaida Afroz ◽

Ayesha Akter Mousumi

Keyword(s):

Wealth Distribution ◽

Sustainable Growth ◽

Entire Population ◽

Impossibility Theorem ◽

Wealth Maximization ◽

Distribution Of Wealth ◽

The World ◽

Physical Assets ◽

Sustainable Happiness

The richest one percent of the entire population of the world now owns more than half of the global wealth which shows global wealth is unequally distributed. Moreover, this is assumed that sustainable growth is impossible based on impossibility theorem. Considering the above, the study has been conducted and critically overviewed the wealth distribution of an ancient period based on Islamic rules and practice. Upon study, it has been found that people are very much self-centered and unaware of the broader perspective like searching happiness instead of immediate wealth maximization. The finding has also shown that right of inheritances, relatives, neighbors, society, and state should be defined clearly and need distribution of wealth based on definition. If we become more self-centered, we will find ourselves helpless. Here, wealth means knowledge and physical assets.

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ARE SOCIAL STRUCTURES DETERMINED BY THE ECONOMY?

International Journal of Modern Physics C ◽

10.1142/s0129183103004218 ◽

2003 ◽

Vol 14 (01) ◽

pp. 73-80 ◽

Cited By ~ 1

Author(s):

G. CORSO ◽

L. S. LUCENA ◽

Z. D. THOMÉ

Keyword(s):

Wealth Distribution ◽

Modern Society ◽

Social Structures ◽

Equal Opportunities ◽

Distribution Of Wealth ◽

Financial Activity ◽

Socioeconomic Structures

We simulate the interplay between productive and financial activity using a model that considers equal opportunities among individuals of a society. As the simulation evolves in time, three qualitative wealth distribution profiles are generated according to the flux of productive capital. We relate these curves to different socioeconomic structures: a primitive equalitarian society; a medieval society having a distribution of wealth with castes and discontinuities; and a modern society where this distribution is roughly exponential.

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The Distribution of Wealth and the MPC: Implications of New European Data

The American Economic Review ◽

10.1257/aer.104.5.107 ◽

2014 ◽

Vol 104 (5) ◽

pp. 107-111 ◽

Cited By ~ 30

Author(s):

Christopher D. Carroll ◽

Jiri Slacalek ◽

Kiichi Tokuoka

Keyword(s):

Wealth Distribution ◽

Wealth Inequality ◽

Income Shocks ◽

Income Dynamics ◽

Aggregate Consumption ◽

Distribution Of Wealth ◽

Marginal Propensity To Consume ◽

Transitory Shocks ◽

Transitory Income ◽

Marginal Propensity

Using a standard, realistically calibrated model of buffer-stock saving with transitory and permanent income shocks, we study how cross-country differences in the wealth distribution and household income dynamics affect the marginal propensity to consume out of transitory shocks (MPC). Across the 15 countries in our sample, we find that the aggregate consumption response ranges between 0.1 and 0.4 and is stronger (i) in economies with large wealth inequality, where a larger proportion of households has little wealth, (ii) under larger transitory income shocks, and (iii) when we consider households only use liquid assets (rather than net wealth) to smooth consumption.

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Professor Blumin on Age and Inequality

Social Science History ◽

10.1017/s0145553200019519 ◽

1982 ◽

Vol 6 (3) ◽

pp. 381-384

Author(s):

Robert E. Gallman

Keyword(s):

United States ◽

Census Data ◽

Wealth Distribution ◽

The United States ◽

Actual Distribution ◽

Distribution Of Wealth ◽

Structure Of Population ◽

Age Structure Of Population ◽

The Common ◽

Comparison Of The Results

In his essay in this issue, Stuart Blumin attempts to sort out the debate between Edward Pessen and me. Professor Blumin begins: “Gallman advances the view that inequality between generations—the association between age and wealth—does explain nearly all of the very striking differences in personal fortune that Pessen and others have discovered.” This is not the view I had intended to advance and is certainly not a view I hold. Many factors bore on the wealth distribution of the United States in the “age of the common man.” The age structure of population surely did not account for “nearly all” of the observed wealth differences. (See, for example, my treatment of this subject— based on manuscript census data for 1860—in Davis et al., 1972: 31-32. This discussion treats the influences on wealth holding of age, sex, nativity, color, occupation, and inheritance.) How Professor Blumin came to misunderstand me so badly I cannot say, but I suspect he was misled by my ill-advised comparison of the results drawn from my model with the actual distribution of wealth in 1860 (Gallman, 1978:198).

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Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Entropy ◽

10.3390/e22040386 ◽

2020 ◽

Vol 22 (4) ◽

pp. 386 ◽

Cited By ~ 2

Author(s):

Gyuchang Lim ◽

Seungsik Min

Keyword(s):

Wealth Distribution ◽

Lower Class ◽

Bimodal Distribution ◽

Rational Approach ◽

Entropy Measure ◽

Gini Coefficients ◽

Distribution Of Wealth ◽

Class Society ◽

Pareto Exponent ◽

The Rich

It is well known that two different underlying dynamics lead to different patterns of income/wealth distribution such as the Boltzmann–Gibbs form for the lower end and the Pareto-like power-law form for the higher-end. The Boltzmann–Gibbs distribution is naturally derived from maximizing the entropy of random interactions among agents, whereas the Pareto distribution requires a rational approach of economics dependent on the wealth level. More interestingly, the Pareto regime is very dynamic, whereas the Boltzmann–Gibbs regime is stable over time. Also, there are some cases in which the distributions of income/wealth are bimodal or polymodal. In order to incorporate the dynamic aspects of the Pareto regime and the polymodal forms of income/wealth distribution into one stochastic model, we present a modified agent-based model based on classical kinetic wealth exchange models. First, we adopt a simple two-class society consisting of the rich and the poor where the agents in the same class engage in random exchanges while the agents in the different classes perform a wealth-dependent winner-takes-all trading. This modification leads the system to an extreme polarized society with preserving the Pareto exponent. Second, we incorporate a solidarity formation among agents belonging to the lower class in our model, in order to confront a super-rich agent. This modification leads the system to a drastic bimodal distribution of wealth with a varying Pareto exponent over varying the solidarity parameter, that is, the Pareto-regime becomes narrower and the Pareto exponent gets larger as the solidarity parameter increases. We argue that the solidarity formation is the key ingredient in the varying Pareto exponent and the polymodal distribution. Lastly, we take two approaches to evaluate the level of inequality of wealth such as Gini coefficients and the entropy measure. According to the numerical results, the increasing solidarity parameter leads to a decreasing Gini coefficient not linearly but nonlinearly, whereas the entropy measure is robust over varying solidarity parameters, implying that there is a trade-off between the intermediate party and the high end.

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