An evolutionary model of the bank size distribution is presented based on the exchange and expansion of deposit money. In agreement with empirical results the derived size distribution is lognormal with a power law tail. The key idea of the theory is to regard the creation of money as a slow process compared to exchange processes of deposit money. The exchange of deposits causes a preferential growth of banks with a fitness determined by the competitive advantage to attract permanent deposits. They generate the lognormal part of the size distribution. Sufficiently large banks, however, benefit from economies of scale leading to a Pareto tail. The model suggests that the liberalization of the banking system in the last decades is the origin of an increasing skewness of the bank size distribution.
evolutionary economics bank size money competition Gibrat's law