Ecole Normale Superieure de Cachan1
Water infrastrucutre 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. There is a tendency of neglecting water loss issues as potable water is heavily underpriced. The consequence of water loss is vast; namely, economic, financial and health problems. 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 due to energy production and consumption.
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 due to increased costs today with benefits that would appear in the long run. We show in this paper that theoretically, pipe replacement is cost efficient for the utility.
Our paper takes the first step in formalizing the significance of water loss and the need for pipe replacement in a theoretical model. 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.
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 of water input minus the amount of water lost through leakage. The amount of water loss is defined by a function that is denoted by () which depends on the quantity of replaced pipes. The greater the investment in pipe replacement the closer () is to zero ( takes values between 0 and 1).
The model is solved numerically. We estimate functions for quantity demanded, price of water charged to customers and the water loss function in order to conduct a numerical simulation. 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 (0), price elasticity of demand (), cost of pipe replacement (r), price of water (p-bar), unconstrained quantity demanded (q0), water input cost (), the total distance of pipes (K), and the cost-recovery parameter () which takes values between 0 and 1.
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 two distinct water agencies and comparing the optimal theoretical rate of replacement.
In Table 1, the simulation results show that the theoretical optimal rate of pipe replacement in France is around 4.8 percent while currently it is only 0.6 percent per year. This is a significant result as it shows that in theory water agencies should invest five times more than its current level of pipe replacement. On the other hand, the rate for the U.S. is a mere 0.92 percent while its current level is 0.5 percent. The underlying cause behind the difference lies in the forces that drive down the rate of replacement. The cost of pipe replacement (r) is almost three times greater in the U.S. than in France while the cost of water input () in France is more than ten times greater than in the U.S. Moreover the price of water charged to customers in the U.S. is less than half of France. The fact that r is highly elevated and that and p-bar are significantly lower than in France, helps explain the low rate of pipe replacement in the United States. A low price charged to customers leads to minimal cost recovery for the water utility and a low cost of water input implies little incentive to minimize water loss by replacing pipes.
The results in Table 2 of the within-country simulation in France revealed additional challenges that water utilities face. Whether the region is a highly rural or urban area plays an important role in the agencies' capability to finance their cost of investment. Pipe replacement in urban areas are in general four times more expensive than in rural areas. About 90 percent of Seine et Normandie is rural; hence the cost of replacement is less pronounced than in the region of Adour Garonne where 76 percent of the region is rural. In the table we can see that the cost of pipe replacement is about 1.3 times greater in Adour Garonne than in Seine et Normandie. Moreover, in Seine et Normandie the population is more than twice of Adour Garonne implying that the cost of investment per capita is much lower in Seine et Normandie. The agency is constrained to service high quantity demanded, leading to higher pressure on water loss; hence greater rate of replacement.
Our paper will add a new dimension to the issue of water loss in the literature of water economics. 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 initiaive. Moreover, reducing water loss does not only have positive externalities to the environment and public health, it is indeed beneficial to the water utilities.