Incentive Contract Design for Supply Chain Enterprise's Pollution Abatement with Carbon Tax

This paper applies mechanism design to the supply chain enterprise's pollution abatement problem with carbon tax. To maximize the government's expected utility, an uncertain contract model is presented in the framework of principal-agent theory, where the government's assessment of the supply chain enterprise's carbon emission level is described as an uncertain variable. Afterwards, the equivalent model is provided to obtain the optimal contract for the uncertain pollution abatement problem. The results demonstrate that the supply chain enterprise's optimal output decreases with the carbon emission level. Furthermore, the government's optimal transfer payment decreases with the carbon emission level if the carbon tax is low. In contrast, if the carbon tax is high, the optimal transfer payment increases with the carbon emission level. In addition, an increase in the carbon emission level decreases the optimal utilities of both the government and the supply chain enterprise and also leads to the supply chain enterprise's incremental marginal utility. Finally, we provide a numerical example, which illustrates the effectiveness and practicability of the proposed model.