Cap‐and‐Trade and Carbon Tax Meet Arrow–Debreu

We propose two general equilibrium models, quota equilibrium, and emission tax equilibrium. Government specifies quotas or taxes on emissions, and then refrains from further action. All results remain valid regardless of how government chooses its emissions target. Quota equilibrium exists; the allocation of emission property rights impacts the distribution of welfare. If the only externality arises from total net emissions, quota equilibrium is Pareto optimal among all feasible outcomes with the same total net emissions. For certain tax rates, emission tax equilibrium may not exist. Every quota equilibrium can be realized as an emission tax equilibrium and vice versa. However, different quota prices may arise in equilibrium from a single quota, and different emission levels may arise in equilibrium from a single tax rate. This leads to inequivalence between quota and emission tax equilibria.