I develop a simple Schumpeterian agent-based model where the entry and exit of firms, their productivity and markup, the birth of new industries and the social structure of the population are endogenous and use it to study the causes of rising inequality and "declining business dynamism" since the 1980s. My hybrid model combines features of i) the so-called Schumpeter Mark I (centering around the entrepreneur), ii) the Mark II model (emphasizing the innovative capacities of firms), and iii) Cournot competition, with firms using OLS learning to estimate the market environment and the behavior of their competitors. A scenario which is quantitatively calibrated to US data on growth and inequality replicates a large number of stylized facts regarding the industry life-cycle, growth, inequality and all ten stylized facts on "declining business dynamism" proposed by Akcigit and Ates (AEJ:Macro, 2021). Counterfactual simulations show that antitrust policy is highly effective at combatting inequality and increasing business dynamism and growth, but is subject to a conflict of interest between workers and firm owners, as GDP and wages grow at the expense of profits. Technological factors, on the other hand, are much less effective in combatting declining business dynamism in my model.