Trophic Analysis and Supply Networks

This talk is about potential relations between economic dynamics of firms and structure of the supply network. In the first half, a new version of trophic analysis is presented. Traditional trophic analysis was developed for ecological food webs to define recursively a notion of trophic level for each species as 1 plus the average of the trophic levels of the species it eats, starting from 1 for the basal species. In the context of supply networks, trophic level is called “tier”. Then a notion of trophic incoherence was defined as the standard deviation of the differences of trophic level over edges in the web. Trophic incoherence has been related to instability of the population dynamics. Traditional trophic analysis suffers from three defects, however. Firstly, it is over-sensitive to what is included as basal species and cannot be implemented if there are none. Secondly, the results are not equivariant with respect to reversing all the edges. Thirdly, it does not allow a natural way to do local trophic analysis. We propose a new version of trophic analysis that remedies all three defects. We developed this specifically to study supply networks, with a view to seeing whether local trophic incoherence is related to variability in a firm’s economic dynamics. In the second half, we will report on our provisional results and potential extensions to financial networks. This is joint work with Bazil Sansom and Sam Johnson, supported by a grant from the UK Economic and Social Research Council via the Instability hub of the National Institute for Economic and Social Research.