Abstract: Water-saving management contract (WSMC) is a water-saving mechanism that uses water rates saved to cover water-saving renovation costs and obtain benefits. It mainly involves two participants, namely, users and watersaving service companies. This paper studies the benefit allocation of WSMC in the fixed investment and return model in which users cannot observe the actions of water-saving service companies. Considering that the profit is first repaid the investment, and then shared by participants, it requires incentive mechanisms to increase water-saving income for water-saving service companies. Firstly, the incentive contract for water-saving service companies is designed by users with the renovation cost and water-saving amount as incentive factors. Simultaneously, the output function of the water-saving amount is developed. Secondly, with the goal of maximizing the user’s expected utility, the incentive model for water-saving service companies is established which is solved by using the backstepping method. Thirdly, the analysis of the equilibrium results shows that the optimal cost sharing ratio and optimal water-saving amount sharing ratio of water-saving service companies are negatively correlated with the risk aversion, effort cost coefficient, and project uncertainty. In addition, the optimal water-saving sharing ratio is positively correlated with the comprehensive capacity. Finally, we discuss the changes in the share ratio and effort level with contract parameters using numerical analysis.

Key words: water-saving management contract, fixed investment and return model, profit distribution, principalagent theory

摘要： 合同节水管理(WSMC)是一种用节约的水费支付改造成本并获取收益的节水模式,主要涉及用户与节水服务公司两个参与方。本文研究用户无法观测节水服务公司行动条件下固定投资回报型WSMC中的收益分配问题,该模式优先偿还投资,其次分享收益的特征需要激励机制诱使节水服务公司增加节水收益。首先,选取改造成本和节水量作为激励因素,设计用户对节水服务公司的激励合同,并构建节水量产出函数。其次,以用户的期望效用最大化为目标,建立用户对节水服务公司的激励模型并采用逆推法求解模型。再次,对均衡结果进行分析,结果表明:节水服务公司的最优成本分享比例和最优节水量分享比例与风险规避程度、努力成本系数和项目不确定性负相关;此外,最优节水量分享比例与综合能力正相关。最后,通过数值分析探讨分享比例和努力程度随合同参数的变化情况。

关键词: 合同节水管理, 固定投资回报型, 收益分配, 委托-代理理论