城市水价预测的长期边际成本方法理论与案例研究

A Study on Prediction of Urban Water Prices Based on the Marginal Cost Methodology

科学制定城市供水价格是直接关系城市水资源可持续发展的重要问题。本文基于长期边际成本理论下,将城市供水价格预测模型中固定成本与可变成本进行了分离,应用超越对数生产函数方法构建了供水可变成本数学模型。引入谢泼德辅助定理,建立了城市水价预测边际成本方法的对数函数模型。以苏州市1997年至2008年制水可变成本、固定成本,用水人数与用水量结构与分布变化等基础数据为依据,结合所研究的水价预测模型,分别预测了2010年苏州市居民生活水价为4.71元/m3,第二产业水价为6.5元/m3。实例研究表明:预测结果虽然略高于当前实际水价,但与水资源稀缺性日益增强的发展趋势是一致的。同时也表明:当前实际水价可能较低,是预测水价与实际水价存在一定差距的原因。通过水价预测模型与实践研究,为我国城市制定合理的水价提供了理论依据与参考。

Reasonably formulating urban water prices is an important issue related to sustainable development of urban water resources.Water scarcity is one of the serious problems needed to be addressed urgently.Formulating water prices can be considered a promising way for coordinating water allocation and thus must be justified in a rational way.This paper aims to examine the long-run marginal cost of water price forecasting models by separating the fixed cost from the variable cost.A water variable cost mathematical model was constructed by applying the transcendental logarithmic production function（translog）.The price elasticity of water demand was estimated with household-level data and the secondary industry-level data.The Shepard lemma was introduced to establish the marginal cost of urban water price forecasting methods involved in the translog function model.The proposed method was applied to Suzhou City,Jiangsu Province,offering the marginal cost of urban water price predictions.First,the water demand was forecasted to project water usage in different periods of time.Second,the population of water use was projected and analyzed.Third,the water structure was analyzed,indicating different types of water structures.Fourth,the water unit cost was analyzed.Fifth,the parameters of the model were derived.The final step was water price forecasting.By analyzing data regarding water usage structure,water users and water consumption variations,unit variable costs of water manufacture,unit fixed costs of water manufacture in Suzhou City from 1997 to 2008,it was projected that the domestic water price is 4.71 yuan/m3 and the second industrial water price is 6.5 yuan/m3 in Suzhou City in 2010.Results indicated that first,although the forecasted prices are slightly higher than current water prices,they are basically consistent with the growing trends in water scarcity.Second,current water prices may be lower than reasonable water prices.With increasing water resources scarcity,it is suggested that the water price must be increased accordingly.Research on and applications of mathematical models are critical ways to formulate reliable water prices.It was also found that due to the possibility of the choice of endogenous utility price structure,obvious differences in the elasticity across price structures may be resulted from a behavioral response to price structure,or to underlying heterogeneity among water utility service areas in Suzhou City.The water price forecasting model could be widely applied to different cities,and provides a theoretical basis for urban water price forecasting.