Can Rising Consumption Deepen Inequality?

TL;DR

The paper investigates how rising consumption affects wealth inequality by extending Wright's Social Architecture of Capitalism with relaxed transaction timing, spending/revenue caps, and endogenous wages. It shows that the primary determinant of inequality is the ratio $R=\overline{w}/\overline{p}$, with qualitative $R$-dependent patterns robust to these relaxations, though detailed distributions and monopoly dynamics shift. Expenditure-driven GDP growth increases capitalists' income and inequality (reduces labor share), while market-revenue adjustments mainly redistribute within the capitalist class without changing total GDP. Endogenous wages introduce regime-dependent outcomes, where unemployment and inequality respond nontrivially to $\alpha$ and $R$, highlighting that economic growth does not automatically reduce inequality and can even intensify it under certain conditions. Overall, the study connects micro-level transaction rules to macro-level inequality outcomes, offering insights relevant to growth-inequality debates in real economies.

Abstract

The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income distributions. In a previous study, we demonstrated that the macroscopic behavior of the model is predominantly governed by a single dimensionless parameter, the ratio between average wealth per capita and mean salary, denoted by R. The shape of the wealth distribution, the emergence of a two-class structure, and the level of inequality -- summarized by the Gini index -- were found to depend mainly on R, with inequality increasing as R increases. In the present work, we examine the robustness of this result by relaxing some simplifying assumptions of the model. We first allow transactions such as purchases, salary payments, and revenue collections to occur with different frequencies, reflecting the heterogeneous temporal dynamics of real economies. We then impose limits on the maximum fractions of wealth that agents can spend or collect at each step, constraining the amplitude of individual transactions. We find that the dependence of the inequality on R remains qualitatively robust, although the detailed distribution patterns are affected by relative frequencies and transaction limits. Finally, we analyze a further variant of the model with adaptive wages emerging endogenously from the dynamics, showing that self-organized labor-market feedback can either stabilize or amplify inequality depending on macroeconomic conditions.

Figures (8)

• Figure 1: Complementary cumulative distributions of (a) wealth and (b) income for different scenarios: (1) $\overline{w}=2$; (2) starting from $\overline{w}=2$, after the system reaches a steady state, an amount $\Delta=4$ is distributed equally among the richest 20% of the agents; (3) as in scenario (2), but with the amount distributed equally among the poorest 20% of the agents; (4) $\overline{w}=2.8$ from the start. Monetary quantities are rescaled by $\overline{w}$ to facilitate comparisons. The insets show the Gini index for each scenario.
• Figure 2: Effects of expenditure frequency: Complementary cumulative (a) wealth and (b) income distributions for different values of $\Omega_E$. The insets show the average annual Gini. In the current and subsequent figures, each distribution was built with values recorded at the end of each year, accumulated over ($10^3$) years of a single realization. For the inequality indices, we present the average of the annual values (symbols) and their standard deviation (bars).
• Figure 3: Impact of changes in (a) $\Omega_E$ and (b) $\Phi_E$ over labor share (LS), Gini of income, normalized HHI, and rescaled GDP. The maximum measured value of GDP is $\approx 6\times10^4$ for $\Omega_E=5$ and $\approx 1.2\times10^4$ for $\Phi_E=1$.
• Figure 4: Effects of expenditure fraction $\Phi_E$: Complementary cumulative distributions of (a) wealth and (b) income for different values of $\Phi_E$ indicated in the legend. The inset shows the average annual Gini coefficient.
• Figure 5: Effects of market revenue frequency $\Omega_M$: Complementary cumulative (a) wealth and (b) income distributions for different values of $\Omega_M$. The inset shows the average annual Gini.