A multi-agent growth model based on the von Neumann-Leontief framework

This paper presents a discrete-time growth model to describe the dynamics of a multi-agent economy, and the model consists of production process, exchange process, price and technology adjustment processes etc. Technologies of agents in each period are represented by a technology matrix pair, and some properties of Perron-Frobenius eigenvalues and eigenvectors of technology matrix pairs are discussed. An exchange model is also developed to serve as the exchange part of the growth model. And equilibrium paths of the growth model are proved to be balanced growth paths sharing a unique normalized price vector. Though this paper focuses mainly on the case of n agents and n goods, the growth model can also deal with the case of m agents and n goods. A numerical example with 6 agents and 4 goods is given, which describes the dynamics of a two-country economy and has endogenous price fluctuations and business cycles.