Cumulative probability distribution of the net wealth, composed of assets (including cash, stocks, property, and household goods) and liabilities (including mortgages and other debts) in the United Kingdom shown on log-log (main panel) and log-linear (inset) scales. Points represent the data from the Inland Revenue, and solid lines are fits to the Boltzmann-Gibbs (exponential) and Pareto (power) distributions (Ref. 15 ).
(Color online) Wealth distribution f(w) for uniformly distributed (or ) in the interval (0,1); f(w) is decomposed into partial distributions , where each is obtained by counting the statistics of those agents with parameter in a specific sub-interval (from Ref. 36 ). The left panel shows the decomposition of f(w) into ten partial distributions in the λ-subintervals (0, 0.1), (0.1, 0.2),…, (0.9, 1). The right panel decomposes the final partial distribution in the λ-interval (0.9, 1) into partial distributions obtained by counting the statistics of agents with λ-subintervals (0.9, 0.91), (0.91, 0.92),…, (0.99, 1). Note how the power law appears as a consequence of the superposition of the partial distributions.
(Color online) Example of a realistic wealth distribution, from Ref. 36 . The continuous curve (red online) shows a wealth distribution obtained by simulations of a mixed population of agents, such that 1% of the agents have uniformly distributed saving propensities and the other 99% of the agents have . The dotted curve (magenta online) shows an exponential wealth distribution ( ) with the same average wealth, plotted for comparison with the distribution in the intermediate-wealth region. The dashed curve (green online) shows a Pareto power law ( ), plotted for comparison with the large-income part of the distribution.
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