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Equilibrium in Production Chains with Multiple Upstream Partners

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  • Meng Yu
  • Junnan Zhang

Abstract

In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production network.

Suggested Citation

  • Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    • Handle: RePEc:arx:papers:1908.08208
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    Cited by:

    1. Kikuchi, Tomoo & Nishimura, Kazuo & Stachurski, John & Zhang, Junnan, 2021. "Coase meets Bellman: Dynamic programming for production networks," Journal of Economic Theory, Elsevier, vol. 196(C).

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