Allocating Emission Permits Efficiently via Uniform Linear Mechanisms

We study how to initially allocate emission permits in an emissions trading system where firms also compete in a production market a la Cournot. We provide efficiency guarantee of simple uniform linear allocation mechanisms in the broad class of component-wise concave mechanisms in which the popular Cap-and-Trade approach is a special case. Classic economic theory states that, under standard assumptions, the equilibrium consumer surplus and social welfare are independent of the initial allocation of emission permits, and that Cap-and-Trade and Carbon Tax systems are equivalent. However, the initial allocation mechanisms previously considered in the literature were largely restricted to lump sum ones that do not take the firms’ current production quantities as input. We show that, by allowing more general allocation mechanisms that are component-wise concave in the firm’s production decision, which capture many realistic allocation rules including lump sum allocations (such as grandfathering), output-based allocations (either top-down or bottom-up), etc., the system’s equilibrium outcome will no longer be independent of the initial allocations. In particular, for N firms operating under Cournot competition that differs only in their abatement abilities, uniform linear permit allocation mechanisms achieve Pareto efficiency in consumer surplus and total pollution, which also achieve efficiency in total emission reduction. With this result, the regulator’s infinite-dimensional policy design question can be reduced to a single-dimensional one, and the original N-firm system can be equivalently represented by a monopoly so that no firm’s private information is required. Numerical experiments show that the benefit of uniform linear mechanisms compared to lump sum ones can be large. We also explain when the efficiency of uniform linear allocation mechanisms might fail, and give managerial insight into the design of allocation coefficient in practically used output-based allocation methods