Complex dynamical behaviour in economic production networks

A dynamical model of an economic production network is proposed as an extension of von Neumann’s static model. Sets of input commodities are jointly converted into sets of output commodities by production processes. The rate of production of a given production process is limited by the minimum quantity of its set of input commodities. It is shown that economic production is autonomously sustained, without price divergence, even without the imposition of any external constraints on price determination. This is accomplished through switching between different choices of the minimum input commodity, which leads to the appearance of complex cyclic behaviour. The mechanism and origin of this oscillation is analysed in depth. The generation of complex oscillations with multiple timescales is also shown when several processes are combined to form a chain or a network.