An analytical heterogeneous agent macro model of concentration, markups, and falling labour shares

This paper presents a small-scale analytical heterogeneous agent model (HAM) to explore firm concentration dynamics and the aggregate effects on distribution and growth. It contributes to recent work on tractable macroeconomic agent-based models (ABMs) by comparing two versions of the model: an ABM with bilateral firm-customer matching, and a simplified HAM without direct agent interaction. The HAM replicates key ABM results while allowing for analytical solutions. The model captures how pricing, investment, and market concentration evolve at the micro level and affect macro-level outcomes. Firms differ in capital size and market share. Larger firms benefit from lower unit costs due to economies of scale, gain larger market shares, and charge higher markups. At the same time, customers seek lower prices, creating competitive pressure. These mechanisms drive endogenous changes in the firm size distribution. More profitable firms temporarily grow faster, leading to concentration of capital, market shares, and markups. These dynamics lead to right-skewed distributions, producing a divergence between the average profit share across firms and the aggregate profit share, which is driven up by the biggest firms. The fall in the labour share reduces consumption and slows down growth. Despite its simplicity, the model captures key empirical patterns related to superstar firms and declining labour shares.