Inequality in a model of capitalist economy
By Jhordan Silveira Borba, Sebastian Gonçalves, Celia Anteneodo
DOI https://doi.org/10.48550/arXiv.2410.22369
Abstract
We analyze inequality aspects of the agent-based model of capitalist economy named it Social Architecture of Capitalism that has been introduced by Ian Wright. The model contemplates two main types of agents, workers and capitalists, which can also be unemployed. Starting from a state where all agents are unemployed and possess the same initial wealth, the system, governed by a few simple rules, quickly self-organizes into two classes. After a transient, the model reproduces the statistics of many relevant macroeconomic quantities of real economies worldwide, notably the two regimes of the distributions of wealth and income. We perform extensive simulations testing the role of the model parameters (number of agents, total wealth, and salary range)on the resulting distribution of wealth and income, the social distribution of agents, and other stylized facts of the dynamics. Our main finding is that,according to the model, in an economy where total wealth is conserved and with a fixed average wage, the increase in wealth per capita comes with more inequality.
Overview
This paper investigates how inequality emerges in a simplified simulation of a capitalist economy. Using an agent‐based model called the Social Architecture (SA) model—originally introduced by Ian Wright—the authors explore how simple rules governing employment and wealth exchange can naturally produce two key features observed in real-world economies:
- A dual-regime distribution of wealth and income: one part with an exponential (rapidly decaying) behavior at lower values, and another part with a power-law (slowly decaying) behavior for high values.
- The spontaneous formation of two distinct social classes: one representing workers (and the unemployed) and the other representing capitalists (firm owners).
The study also examines how changing certain parameters affects the overall inequality measured by standard indices such as the Gini and Kolkata indexes.
Key Sections
Abstract and Main Finding
Starting Conditions & Self-Organization:
The model begins with all agents having equal wealth and being unemployed. Despite this uniform start, the simple rules of the model cause the system to quickly evolve into two distinct groups: one where most agents remain workers (or unemployed) and another where a smaller group becomes capitalists.Dual-Regime Distributions:
The paper confirms that the resulting wealth and income distributions show two regimes:Exponential-like behavior for the majority (lower end of wealth/income).
Power-law behavior for the richer minority (upper end), which is often linked to Pareto’s law.
Main Conclusion:
When total wealth is conserved and the average wage is fixed, an increase in wealth per person (wealth per capita) leads to a higher level of inequality. In simple terms, even if everyone’s starting point is equal, a richer overall economy may actually worsen the wealth gap.
Introduction
Background on Economic Distributions:
The authors discuss Pareto’s observations that in real economies, a small percentage of people control a large portion of wealth. This phenomenon is evident in the two-regime structure of wealth distributions:The lower portion of the population follows an exponential decay, meaning most people have moderate to low wealth.
The top end follows a power-law, meaning a few individuals accumulate extremely high wealth.
Agent-Based Modeling:
The paper uses an agent-based model where:Agents can represent individuals or entities like firms.
Each agent has a certain amount of wealth.
Agents can switch roles (worker, employer, or remain unemployed) through processes such as hiring, firing, and receiving wages.Example: Think of a simulation game where every player starts with the same amount of money and no job. As the game progresses, some players become bosses by hiring others, and over time, a few bosses end up with much more money than the players, mirroring real-world capitalist dynamics.
Relevance to Econophysics:
The paper situates its work in the field of econophysics, which applies ideas from physics (like statistical mechanics) to understand economic systems. It builds on previous studies that used random exchanges and savings models to explain wealth concentration, highlighting how minimal rules can lead to complex, emergent patterns.
Model Description
Agents and Roles:
Workers and Employers:
Agents can be employed or become employers (capitalists) who hire workers.Unemployed Agents:
Initially, all agents are unemployed.
Key Parameters:
System size (N): Number of agents in the simulation.
Wealth per capita (w): The amount of wealth each agent starts with.
Wage range ([pa, pb]): The minimum and maximum wages that can be paid.A crucial ratio in the model is R = w/p (wealth per capita divided by the average wage), which influences how easily the system can transition from its initial state into a dynamic one with hiring and firing.
- Dynamics – How the Economy Works:
Each time step (representing a month) involves:Agent Selection: Randomly picking an agent.
Hiring: Unemployed agents can be hired by others if the prospective employer has enough wealth.
Expenditure: Random spending by an agent increases a “market value,” simulating consumer spending.
Revenue: Employers (or their workers) receive income from this market value.
Firing: Employers might fire some workers based on their wealth compared to the number of employees.
Wage Payment: Employers pay wages to their employees.These rules allow wealth to circulate and accumulate, eventually leading to the observed inequality.
Main Findings
Effect of System Size (N):
Increasing the number of agents tends to:Keep average wealth values for workers and the unemployed roughly constant.
Increase the variance in wealth among capitalists, leading to a longer tail in the wealth distribution.
This means that as the economy grows in size, a small group becomes significantly wealthier compared to everyone else.Effect of Wealth per Capita (w):
When the wealth per person is increased:The capitalist class becomes even more distinct, with the tail of the wealth distribution flattening (more individuals with extremely high wealth).
The Gini index (a common measure of inequality) rises noticeably.
Example: If every person in the simulation starts with more money, the richest get disproportionately richer, widening the wealth gap.Effect of Wage Range:
The results depend mainly on the average wage rather than the exact range. In other words, if you change the range of possible wages but keep the average the same, the overall pattern of inequality does not change significantly.Income Distribution Mirrors Wealth Distribution:
Similar trends are observed for income (earnings) distribution:Workers earn wages, and capitalists earn revenue.
Both show a two-regime structure and respond similarly to changes in system size and wealth per capita.This reinforces that the model’s dynamics consistently lead to increasing inequality, regardless of whether one looks at wealth or income.
Final Remarks and Conclusions
Self-Organization and Emergence of Inequality:
The SA model starts from an equal state but naturally evolves into a society with two distinct classes. The model robustly produces real-world-like wealth and income distributions, confirming that even without external interventions (like taxes or subsidies), inequality can arise solely from the internal dynamics of the economy.Implications for Economic Understanding:
The finding that higher wealth per capita (with a fixed average wage) leads to greater inequality suggests caution when using indicators like gross domestic product as a sole measure of economic progress. A higher total wealth might mask a growing concentration of wealth in a few hands.Robustness Across Parameters:
The behavior of the model remains consistent even when parameters such as system size and wage range are varied. The key factor driving inequality is the ratio of wealth per capita to the average wage.Broader Relevance:
While the model is simplified, it helps illustrate fundamental mechanisms that may be at play in real capitalist economies. By understanding these mechanisms, researchers can better analyze and perhaps design policies to address economic inequality.
Concluding Example
Imagine a classroom where every student begins with the same amount of candy. As the teacher allows trading based on simple rules (some students become “bosses” and start collecting more candy from others), soon a few students end up with large piles of candy while most have much less. This simulation, though simplified, reflects the real-world dynamics of wealth concentration and inequality that the SA model aims to capture.