Abstract

The notion of drought is most often associated with the aridity of landscapes and vegetation. But a green landscape can hide a frequent imbalance between water availability and the quantity necessary to maintain rivers in a suitable state, to satisfy different water needs. This is the case, for example, in the French region called New Aquitaine. Regularly, "drought" crisis committees are set up there to limit water use through administrative constraints, which is technically difficult and costly for many, and with an overall unsatisfactory situation from rural areas to the coast. But in summer, water consumption is mainly due to irrigation. Some water resource managers have consequently set up an original non-linear water pricing system for irrigation to achieve several objectives: above all, to limit water consumption in order to respect a minimum flow rate in rivers, to anticipate water supply-demand imbalances before agricultural plantations are made, to allocate water to the users who value it best, to recover water supply costs, to be transparent and sufficiently simple in its application to be acceptable. In this chapter, we propose to describe one of such original pricing systems, as well as some of its main mathematical properties and its practical interests.

Keywords: drought, irrigation, nonlinear pricing, environment, mathematical economics

## 1. The problem of chronic droughts in France

Economic and trade developments and the growth of the world's population are leading to an increasing exploitation of natural resources. In addition, this global evolution is accompanied by changes in the economic, social, and environmental context (climate change and spread of species becoming invasive), making more uncertain the context in which different professions work. For example, the farmers now face a multiplicity of new climatic, market, and biotic risks. In this context, the implementation of measures to secure various resources, including water, helps to mitigate the negative effects of these developments. More generally, various tools to combat hazards have been put in place at the individual level: insurance or other risk pooling systems, diversification, etc.

But with regard to water resources, even in some areas where they were once considered abundant, the limits of their exploitation may have been reached. And because property rights over these resources are often poorly established,

the "tragedy of the commons" (see [1]) is repeated. For example, in the agricultural sector, everyone is encouraged to make the most of available water in their own interest, while well-designed coordination of the different uses would improve everyone's well-being or economic performance (see, for example, [2]).

minimum flow rates in the nearby rivers). Finally, we show that it is possible to

Can Nonlinear Water Pricing Help to Mitigate Drought Effects in Temperate Countries?

on irrigation water resource pricing (see [7] for some aspects), as well as on

In a way, by creating value not only from the water resources but also simultaneously from public and private information, this makes it easier to resolve conflicts of use, by reducing the frequency of crises. This approach combines mechanism

In the rest of this chapter, we give a very short overview of some of the literature

nonlinear pricing (see [8]). Then we develop a mathematical model to show different properties of this pricing formula and in particular why volume subscription

In France, after having built many individual or collective dams in order to increase water-storage capacity ("supply management"), efforts are currently focused on "demand management," that is, the use of less irrigation water for the same production and the search for more efficient alternatives for sharing water among the different uses while trying to find more efficient water pricing schemes (see [9]). The problem is similar in other parts of the world (see, e.g., [10] for China). The aims of water management are multiple and may sometimes be understood as contradictory ([11]): the first one is to allocate water to users who valorize it at the best (efficiency). The second is to guarantee an access to this essential good to everybody and to be acceptable in order to be applied (equity). Moreover, as mentioned in [12], it may be a tool to redistribute public investment benefits. The third is to recover costs induced by water extraction/distribution/use. The fourth is to be transparent and simple enough to be understandable, and it is clear that a two variable tariff, as the one presented here, is quite acceptable as shown by the fact that it was implemented in the CAEDS area. Another nonlinear pricing scheme is also established in the Compagnie d'Aménagement des Coteaux de Gascogne area in the southwest of France and is compared in [13] and [14] to the one presented here as regards the agricultural production, the farmers revenue, and the water quantity

modify the volumes consumed globally by varying the parameters.

by farmers makes it possible to anticipate their consumption.

2. Literature review: agricultural water economics

used for irrigation in accordance with the climatic conditions.

they do not encourage saving water.

31

Generally speaking, water pricing practices can be classified in two families: volumetric and non-volumetric methods. Volumetric methods rely on the volume and require metered water facility (see [15] or [16], for examples of the implementation of a volumetric pricing system). Non-volumetric methods are based on output/input other than water, for example, in the agricultural sector as per area pricing (see [17]). The last methods are widespread because of their simplicity, but

When using volumetric methods, water can be priced in three main ways. The price can be either constant whatever the level of consumed water or defined "per block": the cost per additional consumed unit varies when the consumption reaches some given thresholds. The marginal pricing can either increase with the level of consumption (increasing block tariff) or decrease (declining block rate). The application of such a pricing is studied for domestic water use, for example, in [18].

The increasing block tariffs (IBT) can be used to impose conservation incentives

on some target group of large users. Customers facing the higher prices at the margin will, in theory, use less water than they would under the uniform pricing; customers facing lower prices at the margin will use more. The expectation is that

and nonlinear pricing

design, game theory, and nonlinear pricing results.

DOI: http://dx.doi.org/10.5772/intechopen.86529

The problems thus created have repercussions on the agricultural activity itself, which can no longer rely on a sufficient supply of water, and on the community in general: on the environmental level (e.g., river dewatering), on the economic level (impact on downstream sectors, such as shellfish farming or tourism, as the European Coastal project shows, see [3]), or on the social level with farmers quite often being accused of many wrongdoings. This is also one of the reasons for the implementation at European Union level of the Water Framework Directive (see e.g., [4]).

Thus, a green landscape such as those frequent in the French region of New Aquitaine can hide recurrent problems of drought, with very frequent crises in areas such as the Charente "département." As a result, the public authorities regularly intervene, imposing different constraints to farmers or to their Water User Associations (WUA) in charge of the resource management (e.g., restrictions on irrigation, while crops are in place) to allocate the water shortage. The situation is then penalizing for everyone, and especially for farmers, who too often cannot adequately grow the crops in which they have invested. And it ultimately leads to a perfectible situation on each of the three pillars of a sustainable development: economic, social, and environmental.

This situation is well documented and explained in game theory, particularly in the context of the "prisoner's dilemma" (see [5]). But it gives few solutions, except to seek coordination between stakeholders. The "tragedy of the commons" can generally be resolved by privatizing the resource, but in France and in many countries, this solution cannot be applied to the water resource for legal reasons (see, for example, [6] for their developments on this subject). This is what opponents of water storage in reservoirs remind us, arguing that the resource must benefit all uses and that it cannot be used by a single sector of the economy.

On the other hand, at some short distance from this Charente département, and still in the New Aquitaine Region, an original attempt at water pricing has been made in order to try to better coordinate farmers' actions, by anticipating as well as possible the annual imbalances between water supply and demand. The objective is thus to make the best use of public information (the water level in rivers, groundwater or reservoirs, climatic conditions, market conditions, etc.) and also private information (importance for farmers of securing their water supply, linked, for example, to their product sales contracts, their debt level, or more simply their risk aversion), but without being inquisitorial (by making them reveal only what is important for the water resource management). Of course, this does not guarantee that there will be no crisis, but it does make it possible to anticipate them as well as possible and to resolve a majority of possible conflicts well before the plots are planted, that is, before the distribution of the shortage has any serious consequences. This too gives the farmers the possibility to change their culture choices in order to adapt them more precisely to the available water.

The idea, developed by the irrigators of the Compagnie d'Aménagement des Eaux des Deux-Sèvres (CAEDS), is to base the price of irrigation water paid each year on two variables: the quantity of water reserved by each farmer (before planting) and the quantity actually consumed. We show here that the pricing formula used encourages the farmer to subscribe a quantity directly related to what he expects to consume (which makes it possible to deduce very quickly what each farmer plans to consume and the total consumption, which makes it easier, as we saw, to resolve possible conflicts, as well as consequently to respect more easily the

#### Can Nonlinear Water Pricing Help to Mitigate Drought Effects in Temperate Countries? DOI: http://dx.doi.org/10.5772/intechopen.86529

minimum flow rates in the nearby rivers). Finally, we show that it is possible to modify the volumes consumed globally by varying the parameters.

In a way, by creating value not only from the water resources but also simultaneously from public and private information, this makes it easier to resolve conflicts of use, by reducing the frequency of crises. This approach combines mechanism design, game theory, and nonlinear pricing results.

In the rest of this chapter, we give a very short overview of some of the literature on irrigation water resource pricing (see [7] for some aspects), as well as on nonlinear pricing (see [8]). Then we develop a mathematical model to show different properties of this pricing formula and in particular why volume subscription by farmers makes it possible to anticipate their consumption.
