Universal Growth in Production Economies

We study a simple variant of the von Neumann model of an expanding economy, in which multiple producers produce goods according to their production function. The players trade their goods at the market and then use the bundles acquired as inputs for the production in the next round. We show that a simple decentralized dynamic, where players update their bids proportionally to how useful the investments were in the past round, leads to growth of the economy in the long term (whenever growth is possible) but also creates unbounded inequality, i.e. very rich and very poor players emerge. We analyze several other phenomena, such as how the relation of a player with others influences its development and the Gini index of the system.