标题： 碳价冲击在价值链中的传播：违约的均场博弈 显示英文标题

标题： Propagation of carbon price shocks through the value chain: the mean-field game of defaults

摘要： 我们引入了一个新的均值场博弈框架，以分析碳定价在具有违约企业的多部门经济中的影响。每个部门生产一种同质商品，其价格通过市场出清内生确定。企业作为价格接受者，通过选择投入品（包括劳动力、排放物和来自其他部门的中间商品）的最优分配来最大化利润，同时通过内生的部门价格进行互动。企业还选择违约时机以最大化股东价值。形式上，我们将经济建模为每个部门内的最优停止均值场博弈。由此产生的耦合均值场博弈系统可以表述为线性规划形式，该形式通过人口测度流来表征纳什均衡。我们证明了线性规划纳什均衡的存在性，并建立了相关价格体系的唯一性。对于具有常替代弹性（CES）生产函数的企业，给出了数值示例。在一个简化的单部门经济中，碳价格冲击会引发排放与劳动力之间的替代效应。在一个三部门经济中，制造业部门面临消费者需求，并需要来自棕色部门的投入品，随着碳价格的上升，这些投入品可以逐渐被绿色部门的商品所替代。这些实验表明，碳价格冲击可以在价值链上产生显著的溢出效应，突显了部门间相互依赖性在塑造有效脱碳路径中的重要性。 显示英文摘要

摘要： We introduce a new mean-field game framework to analyze the impact of carbon pricing in a multi-sector economy with defaultable firms. Each sector produces a homogeneous good, with its price endogenously determined through market clearing. Firms act as price takers and maximize profits by choosing an optimal allocation of inputs-including labor, emissions, and intermediate goods from other sectors-while interacting through the endogenous sectoral price. Firms also choose their default timing to maximize shareholder value. Formally, we model the economy as an optimal stopping mean-field game within each sector. The resulting system of coupled mean-field games admits a linear programming formulation that characterizes Nash equilibria in terms of population measure flows. We prove the existence of a linear programming Nash equilibrium and establish uniqueness of the associated price system. Numerical illustrations are presented for firms with constant elasticity of substitution (CES) production functions. In a stylized single-sector economy, carbon price shocks induce substitution between emissions and labor. In a three-sector economy, the manufacturing sector faces consumer demand and requires inputs from a brown sector, which can be increasingly replaced by green-sector goods as carbon prices rise. These experiments reveal that carbon price shocks can generate substantial spillover effects along the value chain, underscoring the importance of sectoral interdependencies in shaping effective decarbonization pathways.