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This paper analyzes the equilibrium distribution of wealth in an economy where firms productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistributes the collected resources to dynasties. The equilibrium distribution of wealth is explicitly calculated and its shape crucially depends on market incompleteness. In particular, a Paretian law in the top tail only arises if capital markets are incomplete. The Pareto exponent depends on the saving rate, on the net return on capital, on the growth rate of population and on portfolio diversification. On the contrary, the characteristics of the labour market mostly affects the bottom tail of the distribution of wealth. The analysis also suggests a positive relationship between growth and wealth inequality.
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In the current era of worldwide stock market interdependencies, the global financial village has become increasingly vulnerable to systemic collapse. The recent global financial crisis has highlighted the necessity of understanding and quantifying interdependencies among the worlds economies, developing new effective approaches to risk evaluation, and providing mitigating solutions. We present a methodological framework for quantifying interdependencies in the global market and for evaluating risk levels in the world-wide financial network. The resulting information will enable policy and decision makers to better measure, understand, and maintain financial stability. We use the methodology to rank the economic importance of each industry and country according to the global damage that would result from their failure. Our quantitative results shed new light on Chinas increasing economic dominance over other economies, including that of the USA, to the global economy.
We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agent could also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.
Socio-economic inequality is measured using various indices. The Gini ($g$) index, giving the overall inequality is the most commonly used, while the recently introduced Kolkata ($k$) index gives a measure of $1-k$ fraction of population who possess top $k$ fraction of wealth in the society. This article reviews the character of such inequalities, as seen from a variety of data sources, the apparent relationship between the two indices, and what toy models tell us. These socio-economic inequalities are also investigated in the context of man-made social conflicts or wars, as well as in natural disasters. Finally, we forward a proposal for an international institution with sufficient fund for visitors, where natural and social scientists from various institutions of the world can come to discuss, debate and formulate further developments.
We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.
The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter $lambda$. Our numerical results indicate that the model has a critical point at $lambda=1$ between a phase for $lambda < 1$ with economic mobility and exponentially growing wealth of all agents and a non-stationary phase for $lambda geq 1$ with wealth condensation and no mobility. We define the energy of the system and show that the system can be considered to be in thermodynamic equilibrium for $lambda < 1$. Our estimates of various critical exponents are consistent with a mean-field theory (see following paper). The exponents do not obey the usual scaling laws unless a combination of parameters that we refer to as the Ginzburg parameter is held fixed as the transition is approached. The model illustrates that both poorer and richer agents benefit from economic growth if its distribution does not favor the richer agents too strongly. This work and the accompanying theory paper contribute to understanding whether the methods of equilibrium statistical mechanics can be applied to economic systems.
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