Transient fluctuation of the prosperity of firms in a network economy

TL;DR

This paper models the transient fluctuations in firm prosperity within a network economy using a stochastic approach, revealing how network topology influences bankruptcy risk and steady-state stability.

Contribution

It introduces a novel stochastic model linking network topology to transient prosperity fluctuations and bankruptcy risk in firms.

Findings

Sparse networks increase bankruptcy risk.

Transient fluctuations depend on network topology.

Steady state may not be reached in many cases.

Abstract

The transient fluctuation of the prosperity of firms in a network economy is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the fixed cost expense to the firms to produce those materials and product. The formulae for this model are parallel to those for population dynamics. The swinging changes in the fluctuation in the transient state from the initial growth to the final steady state are the consequence of a topology-dependent time trial competition between the profitable interactions and expense. The firm in a sparse random network economy is more likely to go bankrupt than expected from the value of the limit of the fluctuation in the steady state, and there is a risk of failing to reach by far the less fluctuating steady state.