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An Economic Model For Water Utilities Facing Water Loss: A Cost Minimization Approach

Congress: 2015
Author(s): Elissa Cousin, Emmanuelle Taugourdeau
Ecole Normale Superieure de Cachan1, ENS-Cachan, CNRS, CES2

Keyword(s): Sub-theme 4: Infrastructure development,

Water infrastructure around the world is facing an age of replacement. In particular, leakage due to obsolete pipes are the principle cause of water loss in developed countries. In France, every year about 20% of water supplied is lost through leakage. There is a tendency of neglecting water loss issues as potable water is heavily underpriced. Water is a scarce resource; hence leakage due to poorly maintained pipes are extractions of water resources that is directly put to waste. For the water utlitiy, this translates to forgone potential revenue. Moreover, obsolete pipes increase pumping energy, treatment costs and intrusion of pollutants. The wasted energy has further consequences on the environment associated with the emission of CO2 and greenhouse gases. Since the introduction of the European Water Framework Directive, all member states are urged to achieve several targets such as full cost recovery in the very near future. This directive incentivises water utilities to engage in pipe replacement investments. The issue is that such an obligation will appear as cost inefficient to water utilities today with benefits that would appear in the long run. Our goal is to build a theoretical model that generalizes the behavior of a water utility in the presence of water loss and see whether it is optimal for them to invest or not in water loss reduction. In the existing literature, some empirical studies support our hypothesis. French water utilities that abide by water loss regulation tend to perform better (Salvetti, 2013). Moreover, the marginal cost of "producing" water loss is greater than the marginal cost of producing supplied water (Martins, 2012). Our paper takes the first step in building a formal theoretical model in the water economics literature. We set up a static cost minimization problem with a constraint on water loss. The results show that even under a static model, pipe replacement is indeed an optimal solution. We further obtain simulation results on the optimal rate of pipe replacement for France and the U.S. Currently, replacement rates are near 0% for U.S. and France.

We set up a static cost minimization problem where the water utility minimizes the costs of supplying water to households. The utility is subject to a production constraint which is defined by the difference between water input and water lost through leakage. This quantity must satisfy the quantity demanded. Water loss is defined by a function which we call the "iceberg cost function", that is denoted by which depends on the quantity of replaced pipes. The greater the investment the closer is to zero; hence lower water loss. The model is solved numerically. We estimate functions for quantity demanded, price of water charged to customers and the iceberg cost function. We collected data from various sources such as the United States Environmental Protection Agency (EPA) for the U.S. and Observatoire national des services d'eau et d'assainissement (SISPEA) for France. We used these data to calibrate our parameters in the model; rate of water loss, price elasticity of demand, cost of pipe replacement, price of water, unconstrained quantity demanded, water extraction cost, the total distance of pipes and the cost-recovery parameter. We simulated the impact on the rate of pipe replacement by varying the values of the above mentioned parameters for France and U.S. and compared the differences. Moreover we looked into the within-country difference for France by taking three distinct water agencies and comparing the optimal theoretical rate of replacement.

The results show that pipe replacement is very sensitive to the level of water input cost. Water input cost differs greatly from one type of water resource to another and depends on geographical differences. Moreover, by varying the cost recovery parameter from 0 to 1, we observe a siginifcant impact on the level of pipe replacement. Even when the utitlity reflects all the cost of investment on the price charged to consumers =1, the increase in the price is very little; implying an incentive for utilities to implement full cost recovery. We further observed the impat of postponing investment; i.e. the impact of level of water loss on pipe replacement. In both U.S. and France, once the rate of water loss surpasses 30%, the need for replacement accelerates rapidly; implying that it is in the interest of the utility to take action before reaching a critical level of water loss. In the case of different water agencies in France, at zero cost recovery, the replacement rate we obtained was 0%. However, once the full cost recovery was applied (=1), as shown in the following table, a replacement need was reflected most heavily in the utlity that is faced with large quantity demanded and large rate of water loss (replacement need increased from 0% to 7%). Here we took the minimum cost of water input (=4). A little increase in this cost can increase drastically the necessity to replace.

The results from our model have significant policy implications on water utility management. In particular on the rate of pipe replacement and the sensitive issue of cost recovery. As the result shows, price increase due to implementation of full cost recovery is very little compared to the significant increase in pipe replacement and reduction in water loss. Hence, the question is whether subsidies should be directed towards price charged to consumers or towards water utilities that are investing in pipe replacement. Moreover, the result shows that the longer investment is postponed, the greater would be the burden of replacement on the future generation. 1. Maria Salvetti (2013) The network efficiency rate: a key performance indicator for water services asset management? 7th IWA International Conference on Efficient Use and Management of Water
2. Rita Martins et al. (2012) Water losses and hydrographical regions influence on the cost structure of the portuguese water industry. Journal of Productivity Analysis, 38(1):81-94

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