Forward-looking investments determine the resilience of firms’ supply chains. Such investments confer externalities on other firms in the production network. We compare the equilibrium and optimal allocations in a general equilibrium model with an arbitrary number of vertical production tiers. Our model features endogenous investments in protective capabilities, endogenous formation of supply links, and sequential bargaining over quantities and payments between firms in successive tiers. We derive policies that implement the first-best allocation, allowing for subsidies to input purchases, network formation, and investments in protective capabilities. The first-best policies depend only on production function parameters of the pertinent tier. When subsidies to transactions are infeasible, the second-best subsidies for resilience depend on production function parameters throughout the network, and subsidies are larger upstream than downstream whenever the bargaining weights of buyers are non-increasing along the chain.

中文翻译：

---

多层供应链的最佳弹性


前瞻性投资决定企业供应链的弹性。这种投资给生产网络中的其他企业带来了外部性。我们将一般均衡模型中的均衡和最优分配与任意数量的垂直生产层进行比较。我们的模型的特点是保护能力的内生投资、供应链的内生形成以及连续层级企业之间对数量和付款的顺序讨价还价。我们制定实施最佳分配的政策，允许对投入品购买、网络形成和保护能力投资进行补贴。最佳策略仅取决于相关层的生产函数参数。当对交易的补贴不可行时，第二好的弹性补贴取决于整个网络的生产函数参数，并且只要买家的讨价还价权重沿着链条不增加，上游的补贴就大于下游。