2. Literature review: agricultural water economics and nonlinear pricing

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 used for irrigation in accordance with the climatic conditions.

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 they do not encourage saving water.

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

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]).

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

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:

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

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

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

at European Union level of the Water Framework Directive (see e.g., [4]).

uses and that it cannot be used by a single sector of the economy.

order to adapt them more precisely to the available water.

30

economic, social, and environmental.

Drought - Detection and Solutions

demand in the high blocks will be more elastic than demand in the low blocks, resulting in a net decrease in water use when compared to a uniform pricing. Although there is widespread consensus that IBT have many advantages, this type of tariff still deserves more careful examination since an incorrect structure of the IBTs leads to several shortcomings as argued in [19]. Some of them are difficulties to set the initial block; mismatch between prices and marginal costs; conflict between revenue sufficiency and economic efficiency; absence of simplicity, transparency, and implementation; incapacity of solving shared connections; etc.

function of the volume Ci of the water he consumes. This production function is

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

take into account these two variables and to display some properties.

• Si is the volume reserved by agent i during the considered year.

• hi(Ci) is agent i's production function, which depends on the consumed

The pricing scheme is a common knowledge for all farmers and is the same for all of them. Parameter a represents a kind of sharing of the price between, on the first hand, the reservation part and, on the other hand, the consumption part. As D = λB, the role of parameter λ is to ensure a balanced budget, under the financial conditions of the WUA, for example, by adjusting the value of this parameter by trial and error year after year, if a temporary budget imbalance is permissible. We will return to this point in Section 3.3, examining in particular the case where a minimum of revenue each year is required. The role of parameter b is to incite to reserve at least the forecasted consumption divided by b. For a Si given, when

<sup>i</sup> which appears in the pricing formula incites to diminish water

A deterministic approach, without acquisition of information between the reservation date and the consumption date, is sufficient in order to study some of the properties of this pricing. Of course other properties directly linked to stochastic variables (as the climate) cannot be studied here and are the object of further

But we must note that since Ci depends on Si, we must take this relationship into

When choosing the values of his control variables Si and Ci, the farmer must decide of the optimal value of Ci knowing the optimal value of Si previously

account in optimizing the volumes reserved and consumed by the farmer i.

Cimax Ci ð Þ ; bSi Si (1)

• Ci is the volume consumed by agent i during the same year.

• F ¼ F Si ð Þ ;Ci is the sum agent i must pay (his water bill).

F Si ð Þ¼ ;Ci D aSi þ ð Þ 1 � a

Each year, each farmer firstly reserves a water volume Si, for example, before choosing his planting and then consumes another volume Ci for the field irrigation, Ci being either inferior or superior to Si. The pricing formula is designed in order to

private information, known only by the farmer himself.

The notations we use are the following:

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

For each agent i, the pricing formula is

3.2 The maximization problem of farmer i

announced. Therefore each farmer must solve

with a ∈ [0, 1] and b ∈ [0, 1].

water Ci.

Ci > bSi, the C<sup>2</sup>

consumption.

researches.

33

• B is the total water user association expenses.

• D is proportional to B: D = λB, with a constant λ>0.

The decreasing block tariff (DBT) is, unlike the preceding one, in accordance with the proposition that high-value goods "should" be bought at higher price than low-value goods. Water will be first purchased for uses with high values and then only for uses which will lead to less welfare increases. Concerning equity, this type of tariff is "not advisable". "The consumers who acquire smaller amounts of the good and/or service because of their low incomes would be bearing a higher price than those who can afford to consume greater amounts" (see [20]). But it can be justified in the following circumstances:


A two-part tariff combines a fixed and a volumetric rate (or a mix of fixed and variable elements). "Under this system, consumers must pay an entry charge that entitles them to consume the good. Subsequently they will pay an additional smaller amount for each extra unit consumed." "Two-part tariff is easy to explain and easy to understand" is mentioned in [20]. But in practice, it fails to reach the efficiency objective and suffer from the fact that it does not allow to reveal information on water demand, which may be at the origin of sudden discrepancy between water supply and demand.

In the following sections, we study the properties of a different pricing structure, in which farmers make a water reservation (e.g., during wet period or before planting) and then pay a water bill which is an increasing function of water reservation and of real water consumption (e.g., during dry period or during peak vegetation). This allows the WUA manager to forecast disequilibrium between water demand and supply. The water pricing is parameterized, in order to adapt the price to the actual WUA situation and to the available water supply.
