We examine the statistical properties of a closed monetary economy with multi-aggregates interactions. Building upon Yakovenko's single-agent monetary model (Dragulescu and Yakovenko, 2000), we investigate the joint equilibrium distribution of aggregate size and wealth. By comparing theoretical and simulated data, we validate our findings and investigate the influence of both micro dynamics and macro characteristics of the system on the distribution. Additionally, we analyze the system's convergence towards equilibrium under various conditions. Our laboratory model may offer valuable insights into macroeconomic phenomena allowing to reproduce typical wealth distribution features observed in real economy.