Simulation of a generalized asset exchange model with investment and income mechanisms

TL;DR

The paper addresses how internal investment and guaranteed income affect wealth distribution in an economy by introducing the generalized GEDI model, which combines exchange, internal growth with multiplicative noise, a distribution mechanism, and a universal income while keeping total wealth constant. The authors show that the model yields a Boltzmann-like low-wealth tail and a Pareto high-wealth tail (Pareto index around 1.2), along with realistic Gini coefficients; the investment-driven multiplicative noise is identified as the driver of nonequilibrium behavior, whereas a nonzero guaranteed income yields ergodic steady states. By analyzing a suite of observables, the work distinguishes between equilibrium and driven-dissipative dynamics and demonstrates how parameter choices (investment fraction f_w, growth g, distribution exponent λ, and U) shape inequality and mobility. These findings offer insight into how internal wealth-growth mechanisms and public-income provisions influence wealth concentration and have potential implications for economic policy design.

Abstract

An agent-based model of the economy is generalized to incorporate investment and guaranteed income mechanisms in addition to the exchange and distribution mechanisms considered in earlier models. We find realistic wealth distributions and realistic values of the Gini coefficients and the Pareto index. We also show that although the system reaches a steady state, the system is not in thermal equilibrium. The nonequilibrium behavior is associated with the multiplicative noise generated by the investment mechanism.

Figures (12)

• Figure 1: The cumulative wealth distribution $\Pi(w)$ for the parameters $f = 0.1$, $\lambda = 0.9$, $f_w= 0.8$, $g = 0.1$, and $U = 0.01$, with $N = 10^4$ at $t=5 \times 10^4$ after an equilibration time of $2 \times 10^4$. Three regions can be identified: a low wealth region that shows Boltzmann-like behavior as shown in Fig. \ref{['fig1']}, a high $w$ region that exhibits power law behavior as shown in Fig. \ref{['fig2']}, and a transition region between these two behaviors.
• Figure 2: The cumulative wealth distribution $\Pi(w)$ for poorer agnts using the same parameters as in Fig. \ref{['fig0']}. The straight line represents an exponential fit $\Pi(w) \sim e^{-\beta w}$ with $\beta \approx 2.3$ for wealth $0.02 \leq w \leq 0.08$.
• Figure 3: The linear behavior of a log-log plot of $\Pi(w)$ for large wealth indicates a power law fit with a Pareto index of about $1.2$.
• Figure 4: The fraction of agents with wealth greater than the average wealth of 1.0 as a function of the investment fraction $f_w$ for $\lambda = 0.9$. After the initial jump at $f_w = 0$, this fraction is a decreasing function of $f_w$.
• Figure 5: The $w$-dependence of the cumulative wealth distribution $\log{\Pi(w)}$ for the GED model with the parameters $f = 0.1$, $\lambda = 0.9$, $\mu = 0.1$, and $N = 10^4$. The linear dependence for $w \lesssim 3$ indicates a Boltzmann-like distribution similar to the behavior shown in Fig. \ref{['fig1']} of the GEDI model for $w\lesssim 0.08$, but there is no indication of the power law behavior for high wealth found in the GEDI model.