Fig 1.
Evolution of the wealth distribution for a society without classes and exactly two offspring per couple.
Initially, the wealth distribution is uniform, , for 0 < w < 2μ (left-upper panel). In the first generation the wealth distribution is triangular (right-upper panel). For later generations g, the wealth distribution converges to a Gaussian distribution, with average μ and variance
, where σ0 is the initial variance. Thus, the Gini coefficient vanishes exponentially.
Fig 2.
Evolution of the wealth distribution for a society without classes and fc = {0, 1/3, 1/3, 1/3}.
Initially, the wealth distribution is a Gaussian of average μ and σ = μ/10 (left-upper panel). In the first generation (right-upper panel), the distribution is a sequence of three peaks, which correspond to individuals from families with one, two, and three offspring. In the second generation (left-bottom panel), each peak is split into three. The wealth distribution converges rapidly to a broad stationary distribution, as shown in the right-bottom panel for generation ten. In the inset is the evolution of the Gini coefficient with the generation, which in three generations goes from ≈ 0.05 to ≈ 0.35.
Fig 3.
Distribution of the wealth among three different groups: 10% richer, the middle 40%, and the 50% poorer.
Results are for generation ten in the society of Fig 2, which are a good approximation of the stationary distribution.
Fig 4.
Stationary wealth distribution for a society without classes, in a linear-linear (left) and a log-linear (right) scale.
Results are for generation ten in the society of Fig 2. The (orange) solid line corresponds to a log-normal distribution with the same average wealth and variance. In the right panel, the (black) solid line corresponds to an exponential decay with a characteristic wealth of wc ≈ 1, 6μ.
Fig 5.
Stationary wealth distributions for a society with three classes for β = 1 (left) and β = 10 (right).
For β = 1, the Gini coefficient is 0.46 and the 10% richest individuals accumulate 34% of the total wealth. For β = 10, the Gini coefficient is 0.48 and the top 10% accumulate 48% of the total wealth.
Fig 6.
Stationary wealth distributions for a society with three classes, for β = {0, 1, 2, 10} (blue, orange, green, and red) and N0 = 2 × 105.
Fig 7.
Stationary wealth distributions for a society with N0 = 2 × 105, Nc = {10, 20, 50, 100}, and β = 1 (top) or β = 10 (bottom).
The (black) solid line corresponds to a power law decay with an exponent ≈ −2/3.