Coase Meets Bellman: Dynamic Programming for Production Networks

TL;DR

This paper demonstrates that various models of production networks and related economic equilibria can be effectively analyzed using dynamic programming techniques, even when these programs are non-contractive, highlighting their tractability.

Contribution

It introduces a novel approach linking Coase's theory and Bellman's dynamic programming to analyze complex production network equilibria.

Findings

Dynamic programs can recover equilibria in production networks.

The methods are applicable to models with transaction costs and multiple partners.

The approach extends to spatial and organizational distribution problems.

Abstract

We show that competitive equilibria in a range of models related to production networks can be recovered as solutions to dynamic programs. Although these programs fail to be contractive, we prove that they are tractable. As an illustration, we treat Coase's theory of the firm, equilibria in production chains with transaction costs, and equilibria in production networks with multiple partners. We then show how the same techniques extend to other equilibrium and decision problems, such as the distribution of management layers within firms and the spatial distribution of cities.