Non ergodic properties of the dynamics of industry concentration

The long-run evolution of industry concentration has been a primary concern in industrial dynamics. In general it is difficult to analyse the final outcome of industry evolution in terms of concentration, unless a great deal of details is added to the technological and institutional description of the industry. We propose that the structural evolution of concentration can be predicted by studying the joint evolution of two vertically-related industries, i.e. a supplier and a buyer industry. In particular, a summary statistics of the structure of relations between two industries is given by the density of the network, that is the total number of relations between each individual buyer and supplier divided by the maximum number of potential relations. We build a mathematical model of the relation between the density of a network connecting two vertically-related industries, i.e. a supplier and a buyer industry, and the concentration of the supplier industry in the long run; this model is a stochastic one based on the use of finite states Markov chains.