The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application

# The diffusion of value in production networks

Lawrence Blume

Bowers College of Computing and Information Science, Cornell University, USA
lb19@cornell.edu

(Received: 2023/08/17, Published online: 2023/08/28)

Recent history has focussed our attention on the consequences of complex production networks: the supply chain problem. Here we investigate the short- and long-run consequences of a single shock in constant-returns-to-scale production technologies. All such competitive models have a price turnpike, a single ray of prices to which market prices will converge even though consumption paths may be much less well-behaved. We bound worst-case rates of convergence to the ray, relate the bounds to properties of the production network topology, and demonstrate that the short-run behavior of competitive price paths can be quite wild far from the long-run steady state.