AI 中文总结
研究在 AK 生产技术下竞争性企业的污染减排均值场模型，引入监管者并通过动态拍卖机制分配许可证，在均值场控制框架内推导最优政策，结果为大型经济体最优许可证分配政策提供刻画及排放交易机制设计见解。
AI 中文摘要
我们考虑了在 AK 生产技术下运营的竞争性企业的均值场模型，产出与资本成正比且生产产生排放。在此设定下，引入一个监管者，其目标是减少累积排放，类似排放交易系统（ETS），企业须持有和交易许可证以覆盖其在监管市场中的排放。监管者作为中央规划者控制许可证供应，平衡减排与总产出。许可证通过动态拍卖机制分配，实时调整供应以实现市场效率和监管者长期目标。监管者与企业通过内生许可证价格相互作用，该价格由监管者政策决定并通过市场出清条件影响企业最优策略。监管者的最优政策在均值场控制（MFC）框架内推导得出。利用线性二次结构和共同噪声的存在，通过耦合的正倒向随机微分方程（FBSDEs）系统和相关的 Riccati 方程来刻画均衡。我们的结果为大型经济体中最优许可证分配政策提供了易于处理的刻画，并为有效排放交易机制的设计提供了见解。
英文摘要
We consider a mean-field model of competitive firms operating under an AK production technology, where output is proportional to capital and production generates emissions. In this setting, we introduce a regulator whose objective is the reduction of cumulative emissions, in the spirit of Emission Trading Systems (ETS), where firms must hold and trade permits to cover their emissions in a regulated market. The regulator acts as a central planner and controls the supply of permits, balancing emission reduction and aggregate output. Permits are allocated through a dynamic auction mechanism that adjusts supply in real time to achieve both market efficiency and the regulator's long-term goals. The regulator and the firms interact through the endogenous permit price, which is determined by the regulator's policy and affects firms' optimal strategies via the market clearing condition. The regulator's optimal policy is derived within a Mean-Field Control (MFC) framework. Exploiting the linear-quadratic structure and the presence of common noise, we characterise the equilibrium via a system of coupled FBSDEs and associated Riccati equations. Our results provide a tractable characterisation of optimal permit allocation policies in large economies and offer insights into the design of efficient emission trading mechanisms.
