Carbon offset market and cap-and-trade: Firm behavior, market dynamics, and policy design

The carbon offset market is a voluntary market where firms trade carbon offsets to compensate for their emissions and comply with cap-and-trade regulations. In contrast to the emission trading market, which involves government-allocated emission quotas, the carbon offset market trades offsets generated from certified emission reduction projects by independent suppliers. While both markets operate concurrently, they are governed by distinct pricing mechanisms and regulatory structures. We develop a game-theoretic model that incorporates the supply side of the offset market, often neglected in previous literature, and analyze how offsets influence firm behavior and emissions trading dynamics. We also examine how offset usage should be regulated under different governmental policy objectives.We show that introducing a carbon offset market reduces firms' direct emission abatement efforts, lowers product prices, and increases demand, while also decreasing emission allowance prices and total social abatement costs. Importantly, the allocation of emission caps among firms does not affect their behavior, provided the total cap remains constant, but it redistributes profits in a non-monotonic manner, with profit first increasing and then decreasing in a firm's own cap and exhibiting the opposite pattern with respect to other firms' caps. However, tightening the total emissions cap still affects emission prices, abatement levels, and product pricing. These effects are moderated when offset usage is supply-constrained, as firms can flexibly substitute offsets for direct reductions. To maximize total production and emissions reduction, the government should avoid imposing binding regulatory offset limits. In contrast, to minimize total abatement costs, binding regulatory limits are necessary and should be coordinated with the cap level to jointly achieve cost efficiency and market stability. We further extend the analysis to incorporate product market competition and show that our main results remain robust.