1. Introduction
Over the past 30 years, European countries have carried out major policy reforms in the water sector by implementing new legislative frameworks to meet the increasing demand for water [
1] and to transpose the EU’s Water Framework Directive (WFD) into national legislation [
2,
3]. However, most of these countries have failed to achieve the WFD’s objectives as indicated in Article 9 Point 1 [
4,
5,
6,
7] namely the Incentive Pricing Principle (IPP), the Polluter Pays Principle (PPP) and Full Cost Recovery (FCR).
Water pricing is considered to be one of the most important instruments used to affect the demand for water, as encouraged by the WFD [
8,
9] and by the Blueprint to Safeguard Europe’s Water [
10]. In fact, the “implementability” and the effectiveness of water pricing depends on several factors [
11,
12] and needs to take into account eventual disproportionality issues [
13]. Among factors affecting implementability, water metering is considered the most important for irrigated agriculture [
8]. For most European agricultural regions, however, water for irrigation is delivered through surface irrigation networks (with surface irrigation networks, we indicate an open canal system for water delivery) [
8,
14]. In this distribution system, metering individual water use is difficult since it requires costly technologies like a hydraulic device to measure the flow at the head of each farm [
15,
16] and this may not work without adequate control of farmers to prevent cheating. As a result, costs associated with monitoring water flows are prohibitive unless the water is pressurized and meters can be installed [
17]. This condition hinders the ability to meter the volumes actually used and to implement volumetric pricing as a way of allocating supply costs and of ensuring efficient water use [
18,
19,
20,
21,
22].
Proxies of volumetric pricing are possible, i.e., per hectare tariffs varying with the type of cultivated crops, but such alternative incentive pricing options usually entail high transaction costs. Transaction costs include the costs of administration, implementation, enforcement and monitoring [
21]. Transaction costs related to administration and implementation involve costs that the Water Authority (WA) must administer, manage or establish along with collecting tariffs from water users in a given irrigation area.
As a result of the above, the use of incentive pricing in the absence of water metering determines a typical agency problem between WAs and farmers, as farmers hold private information about water use, profit and cost structures that cannot be fully verified by the WA and other farmers. This undermines the efficiency of such pricing options unless the WA sets up strategies that partially reveal farmers’ water use and/or its related costs/profitability.
The literature on asymmetric information issues highlights two essential incentive problems: hidden information and hidden action [
23]. Hidden information or adverse selection is characterized by a situation in which the agent has some private information about their cost that is unknown to the principal [
24,
25]. Hidden action, also referred to as moral hazard, is characterized by a situation in which the agent can take an action that is not observable by the principal while affecting her/his utility [
26,
27].
In this paper, we deal with hidden information, deliberately disregarding the moral hazard problem, for which important implications on water pricing for irrigation in the absence of water metering have been recently investigated in other papers (e.g., see Lika et al. [
8]). The problem of hidden information is a core element in understanding market failure [
23], and that understanding has changed significantly since Akerlof’s paper in 1970 and those of other scholars who further developed this theory. The authors who contributed most and who played a particular role in enriching the literature were Mirrlees [
24], with the general income taxation model; Spence [
25], who illustrated how signalling improves the information gap between parties; and Stiglitz [
26], who demonstrated screening theory by examining the distribution of profits and costs under situations of full information and imperfect information. Whereas, Rothschild and Stiglitz [
27] discuss how sellers’ prices and quantities affect the equilibrium in the insurance market and highlight the importance of information availability in determining optimal contracts. Another major step was the introduction of the revelation principle thanks to which the procedure required to achieve a contract solution was simplified [
28]. Furthermore, the literature was enriched by introducing a mechanism design, first shown by Hurwicz. [
29] and by Harsayni. [
30]. Later, Fudenberg and Tirole [
31] provided a description of mechanism design through the treatment of games with incomplete information.
The hidden information problem in irrigated agriculture was first addressed by Smith and Tsur [
22] and later by Gallerani et al. [
32], Viaggi et al. [
20], Galioto et al. [
15] and Lika et al. [
18]. These authors analysed how the presence of hidden information can affect the way WAs design their pricing mechanisms. The authors emphasized the WA’s need to identify a strategy to optimize the allocation of water and supply costs among heterogeneous groups of farmers served by an irrigation network, minimizing possible negative externalities associated with water uses.
In particular, Smith and Tsur [
22] developed a direct revelation mechanism to soften the level of information asymmetry between farmers and the WA. The authors argued that transaction costs affect the WA’s capacity to achieve expected policy goals. Moreover, they show that, beyond a certain level of transaction costs, mechanism design is not effective and leads to a failure of the policy regulations.
Gallerani et al. [
32] analysed the incentive pricing strategy and compared with flat rate option. The authors highlighted that information costs and transaction costs play a crucial role not only in designing payment levels but also in influencing the acceptability of the correct policy instrument, especially concerning equity considerations attached to highly differentiated payments.
Viaggi et al. [
20] provided a comparison between a flat rate and a menu of contracts. The authors noted a high variability (hence less political feasibility) in the menu of contract option, where payment differentiation for incentive reasons associated with the differentiation of the share of irrigable land is the key component determining the self-selection on the part of farmers.
Later, Galioto et al. [
15] analysed pricing policies with the purpose of verifying whether existing area-based tariff strategies are efficient economic instruments for water policy and how area-based alternative instruments can help in better complying with European water policy principles. The authors found that the existing flat rate policies are justified if transaction costs, which are due to the need to monitor at least irrigated areas under no metering conditions, are lower than the differences in benefits between the two opposite pricing scenarios.
Recently, Lika et al. [
18] developed a water pricing scheme under hidden information and unmetered irrigation water. A nonlinear model of social welfare maximizing was used based on a menu of contracts and compared with flat rates. The authors found that second-best incentive pricing might yield improved social welfare compared with traditional flat rate water pricing.
Previous studies have used various modelling techniques for analysing the impact of hidden information in irrigated agriculture under a single or a large number of farms. In their analysis, the main focus of the authors has been on how different levels of water supply costs and transaction costs affect policy significance. They have overlooked analysing the interaction of various forms of profit and cost functions and their effect on the optimal solution, eventually failing to detect under what conditions adverse selection actually occurs.
In this respect, the objective of this paper is to analyse WAs’ choices among different incentive pricing policies under hidden information and to assess their economic performance compared with the flat rate option under different hypotheses of cost and profit functions and degree of differentiation among farm types.
The research addresses the prominent inefficiencies coming from information asymmetries in irrigated agriculture. We consider this issue important because of how these inefficiencies influence the way water is priced and used with direct consequences in terms of social benefits.
The foundation of this paper relies on an early study conducted by Lika et al. [
18], which considered four farm types in their optimization process by using a mechanism design approach. The authors attempted to design discriminating contracts to different farm types in the absence of water metering. In this study, we offer a theoretical approach more formalized than the one offered by Lika et al. [
18] and generalizable to a number of conditions that help to understand the extent to which proxies of volumetric pricing are applicable in the absence of water metering.
Our analysis enriches the existing literature by focusing on the efficiency of different water pricing options under different conditions as regards the properties of water cost functions, profit functions and levels of transaction costs with an eye to identifying the best theoretical contract solution. In particular, we address the relative differences in cost and profit function among farms in order to identify conditions under which the first-best solution is still feasible under asymmetric information. In addition, we study how this interacts with transaction costs and cost recovery constraints. The main contribution of the paper is then in providing a categorization of empirical situations (based on the parameters above) that can allow to hint at the actual meaningful instrument in terms of irrigation water pricing. The results indeed corroborate the use of a menu of contracts based on first-best solutions even under asymmetric information.
The remainder of the paper is organized as follows:
Section 2 describes the general formulation of a principal-agent problem under adverse selection in water pricing.
Section 3 presents the flat rate model of water pricing.
Section 4 describes the incentive pricing strategies and includes three subsections. The first one concerns the general model setting; the second develops and derives results for the model under full information, whilst the third subsection addresses asymmetric information.
Section 5 is devoted to the discussion of the results projected in the context of different irrigation conditions and related policy considerations. Finally,
Section 6 presents the main conclusions.
2. Formulation of the Problem
In this section, we describe a typical agency problem between a WA (the principal) and agents (farmers) in the absence of water metering. The choice of the pricing option by the WA depends on the WA’s goal, which can be assumed to be that of maximizing social benefits. We assume these social benefits can be measured by the algebraic sum of farmers’ profits, water supply costs and transaction costs.
Farm profits are private profits by farmers but are also a frequent social objective linked, for example, to competitiveness and welfare in rural areas. Water use costs are costs generated by water use by farmers; the transfer of this cost through water tariffs to farmers is the main purpose of water pricing, especially if intended to recover costs, and when aimed at providing economic incentives for efficient water use, whereas transaction costs are costs borne by the WA for this pricing/water tariff collection activity.
This may look not consistent with the WFD. Indeed, consistently with the WFD FCR principle (Article 9) [
4] also environmental and resource costs should be considered when analysing social benefits. Actually, several cases consider this explicitly when modelling fees/subsidies (see Berbel et al. [
33]). However, our main point is about the overall cost structure and not on its components. Therefore, the cost we assume may well include resource and environmental costs (as it is a cost caused by farmers but perceived by the WA), but we do not distinguish the different components. In this sense, our exercise remains relevant and in the direction of the WFD.
In this paper there is a fundamental distinction between the common per-area pricing method generally found in the literature (see Tsur et al. [
34] and FAO [
35]) and the one applied here. Here, under incentive pricing, we consider the irrigated area as a proxy of water use but with a relationship partly unknown to the WA; hence, it is used as an observable parameter for designing a menu of contracts and not as the only tariff parameter. This is better explained in the next section of the paper. The pricing options considered here are (1) a flat rate proportional to the total farmland and (2) a tariff based on a menu of contracts connected to the share of irrigated area. The first option is the most commonly applied to price water supplied through surface irrigation networks in most European countries [
14], whilst the second is an approximation of future suitable alternatives for possible adaptation. However, the implications of using one or the other are very different. With flat rates, the distribution of supply costs among farmers is disconnected from the amount of water used by each farmer (farmers pay the same per hectare tariff regardless of whether they are irrigating) but the cost of implementing such a pricing option is low. With tariffs connected to the share of irrigated farmland, the distribution of supply costs among farmers is partly connected to the farm’s water use (the irrigated area is indeed a proxy of actual water uses) but the cost of implementing such a pricing option is higher compared with flat rates. The main reason from an economic point of view is that marginal social costs do not match marginal social benefits. Then, heterogeneity in farms implies that tariffs are difficult to estimate and cannot be accommodated easily for every farmer [
8,
36]. The characteristics of the typologies of farms served by WAs and their distribution are usually common knowledge, but the WA is unable to observe each farm [
18]. The characteristics of the population of end-users is a crucial issue that affects the WA’s pricing strategies and especially its decisions with regard to whether to set a flat rate or an incentive pricing strategy (e.g., a menu of differentiated contracts). Heterogeneity may concern the type of crops cultivated, which is easily observable even by the WA. The crop mix includes irrigated and non-irrigated crops that influence the demand for water (some examples of the methodologies used to estimate the demand function for irrigation water are provided by [
18,
32,
37]). Other differences across farms may involve land quality, the depth of the water table, the type and efficiency of the irrigation system adopted by the farmer, the quality of production and related price, and the type of marketing channels, which are more difficult to observe. Finally, differences may concern individual management capacities of the farmer or individual risk-coping strategy in water use, which is not observable at all by the WA. All of these non-observable (by the WA) factors contribute influencing differences in water uses and profitability across farmers (which are unobservable), even when the observed irrigated area is the same. Hence, even in cases when farm variables are not fully observable, high heterogeneity in water uses urges the imposition of incentive pricing mechanisms which lead to a more coherent allocation of supply costs among farmers.
In the following, we assume that the irrigated share of farmland in each farm is the main observable regulatory variable, which is also an imperfect proxy of water use costs and farm profit from water use (hence water demand). Under full information, the WA knows the demand for water of each farmer as driven by the way costs and profits provide incentives to determine the optimal share of irrigated farmland. Under hidden information, the irrigated share and the characteristics (profit and cost) of each typology of farmers supplied by the irrigation network is common knowledge, but only the irrigated share can be observed by the WA for a specific farm while costs and profits generated (and the related amount of water uses) remain the farmer’s private information. Hence, the WA can observe and control the irrigated share of each farm but is unable to set an incentive-compatible price for that specific farm unless the WA designs contracts that are able to encourage self-selection by farmers.
3. Flat Rate Model
In this section, we develop a flat rate version of the model. This model provides a mathematical representation of the most common solution for water tariffs actually used in agriculture when water is delivered through open canals (as discussed above). It also makes it possible to identify a benchmark for the modelling solutions discussed in the subsequent sections. With flat rates, farmers pay the same price for the supply service offered by the WA, whether they are irrigating or not [
8,
15,
16,
32]. Tariffs merely play the role of recovering supply costs and are usually paid by farmers at the end of the irrigation season [
32]: namely, under flat rate regimes for surface irrigation networks, ex-ante, before and during the irrigation season, the farmer decides what crop to cultivate and how much to irrigate and ex-post; at the end of the irrigation season, the WA sets the tariff that each farmer must pay for the water supplied. The level of the tariff depends on the overall costs from the total amount of water supplied, which is distributed equally across the total farmland in the area. The payment for an individual farm is hence independent of the individual amount of water used and is actually only related to the total farmland managed. Without loss of generality and to simplify notation, in the following, we assume that all the farms are equal to 1 ha of farmland. We begin our analysis assuming the existence of a large number of farm types (indicated by the subscript
i with
i = 1, n).
First, we focus on modelling the decision-making problem of the farm and assume at all times that the farmer seeks to maximize the net profit
as represented in Equation (1):
The farm profit
is represented as a function of the share of irrigated farmland
and is estimated by subtracting from farm revenue all input costs for crop production except the cost of water which is primarily borne by the WA and transferred through the tariff
, as indicated in Equation (1). The revenue can be estimated from crop yield and market prices. The crop yield can be expressed as a function of several inputs (i.e., water use per unit of area, fertilizer, ploughing and machinery) and contextual variables (e.g., soil, salt concentration, climate, etc.) [
38]. The profit function is assumed to be continuous and twice differentiable in each point with
,
. These assumptions are consistent with most of the literature (see [
18,
20,
39]) estimating profitability from water use and accounting for variable crop mixes and differentiated profits for the same crops. For more detail about approaches aimed at estimating water use profits and costs, see Viaggi et al. [
20] and Lika et al. [
18].
By taking the First-Order Condition (FOC) of Equation (1) with respect to the irrigated share,
, the optimal share of irrigated area is obtained when the marginal profit equals zero:
From Equation (2), it can be inferred that the value of the flat rate tariff does not affect the farm choice about the share of irrigated area , where the superscript FR indicates the irrigated share under the flat rate scenario, given by solving Equation (2).
The WA’s objective function under the flat rate system, based on the problem setting illustrated in
Section 2, can be written as the social welfare maximizing problem (Note that
is the reduced form of
. The first term between the square brackets is the net profit of the farmer; the second is the net profit of the WA) given by:
subject to
The maximization of the social benefit S given by the sum of farm profit, individual farm water supply costs and transaction costs is subject to the cost recovery constraint (CR); indicates the number of farms involved in the scheme and is a natural number.
The function under flat rates indicates costs incurred by the WA to supply water for irrigation to meet the demand estimated based on the farms’ observed characteristics; we assume that this function is twice differentiable such that and , i.e., it is linear. Linearity is assumed to simplify the problem and corresponds to the idea that each farm has an increase in the use of water proportional to its irrigated area (which is often compatible with practice) and that there are no increased marginal costs to be borne by the WA for water supply (which is less plausible for large changes in water uses but close to reality for small changes, especially if the amount of water used is below the capacity of existing irrigation infrastructure). is the probability that the water supplied by the WA is requested by the farm type i, with ; indicates transaction costs, considered to be costs due for the implementation and enforcement of the tariff system, and is always strictly positive (i.e., in this study, we assume only the linear transaction costs to the tariff and not exploiting options of nonlinearity which might drive to other results solutions). The CR condition in Equation (4) is added to ensure that water costs and transaction costs are covered by water tariffs, on average.
The result of the model for the flat rate scenario is rather straightforward. The only decisional variable in this problem is t, which does not differ among farm types as the WA is not assumed to be capable of recognizing differences in water uses. Hence, the irrigated share is determined as a solution of the farm problem in Equation (2) and is not linked to any WA decisional variables in Equation (3). As farm profits and water supply costs are not affected by , the maximisation problem becomes the same as minimizing , subject to (4). As a result, CR is always satisfied with strict equality. Therefore, the level of social benefits achieved in the regulator problem is given by assuming the optimal solution of the farm problem as provided, with , and by minimising transaction costs linked to the tariff.
There are qualifications to this result. From the point of view of the regulator, the problem in Equation (3) also indicates that, if transaction costs are very high (in relative terms), cost recovery may become very costly. One could even question the social desirability of cost recovery based on the potential (dis)proportionality with respect to the cost of water use. In practice, this can happen when water is very cheap for the WA or when water use in a given area is very low.
In terms of farm participation, there are at least two regulatory options. First, if farmers can be forced to participate in the scheme in the case that they face very high water tariffs, some farms will have positive net profits due to irrigation while others could have negative net profits. Still, everybody will irrigate at the optimal level (because tariffs are not connected to individual amounts of water use).
The second option is that farmers can drop out of the scheme, for example, by giving up the option to irrigate. If this is admitted, no tariff will apply to them, which also implies that the tariff will be recalculated on the subsample of farmers that continue to irrigate .
5. Discussion
This paper provides a formal analysis of incentive water pricing policies in irrigated agriculture. The mechanism design refers to a case where irrigation water is supplied through open canals and is unmetered. The study considers a principal-agent model that allows the WA to develop pricing strategies aimed at maximizing social benefits. The paper further develops the model used in Lika et al. [
18].
This is also the only paper that, strictly speaking, is comparable to this one. Our results are consistent with the empirical results by Lika et al. [
18]; however, in our model, the costs here are assumed to be linear and are analysed with a broader set of assumptions. This allows us to identify a set of general cases that can be used in a more straightforward way for policy prescriptions. Here, we also consider more explicitly the role of incentive constraints, transaction costs and cost recovery constraints.
One lesson learned from the insights above is that incentive pricing in different contexts can be more or less efficient and desirable from a social point of view. The practicability of incentive pricing strategies in the absence of water metering depends on the existence of suitable proxies of water use to design pricing schemes, such as tariffs proportional to the share of irrigated area, and on the potential improvement of the “allocative” efficiency, which is linked to farm heterogeneity including in terms of costs and profits. The impact of heterogeneity on the optimal tariff design option is illustrated in
Figure 4 by showing how different combinations of profits and costs fit with pricing policies. We identify four cases.
Farms are homogeneous both in profits and costs. Under these conditions, there is no need to provide an incentive strategy to differentiate tariffs because the costs of guaranteeing price discrimination might not be justified compared with the benefit from differentiation. With such a hypothesis, the regulator can simply apply a flat rate or, better, a tariff proportional to the irrigated area without applying a more complex incentive pricing strategy.
Farms are heterogeneous in profits but not in costs. Under this condition, the adverse selection problem will occur and the WA will impose tariff differentiation only if the efficiency gain by differentiating is higher than the costs arising from the implementing incentive strategy.
Farmers are heterogeneous in profits and in costs. The existence of different supply costs among farm types provides the motivation to verify the possibility of differentiating tariff options in such a way as to encourage farmers to self-qualify through the choice of the contract. This possibility is influenced by the level of transaction costs faced to implement such a tariff option and by the additional cost imposed on farmers to ensure incentive-compatible contract design to face adverse selection. This cost decreases with increasing differences in profits among efficient and inefficient farm types.
Farms are heterogeneous in costs but not in profits. If the population of farmers is located on the lower right of the figure, the WA faces an adverse selection problem. This requires the design of suboptimal contracts, including the provision of incentives, which means the pricing policy is more costly than it would be in conditions of perfect information. This option is extensively analysed above, where the achievement of efficient solutions depends on the degree of heterogeneity among farmers and transaction cost levels.
Overall, as a result of this discussion, it can be concluded that the ability to implement incentive pricing depends on (1) the characteristics of the irrigation network that affects the implementation costs (direct transaction costs); (2) the characteristics of the community of farmers served by the network that affects the economic losses caused by the presence of information biases between principals and agents (indirect transaction costs); and (3) the identification of priorities motivating the implementation of incentive mechanisms by the WA (policy, environmental and equity issues).
Several limitations do exist for this study. An important limitation is the approximation of farm water use through an irrigated share of farmland, i.e., irrigated share assumed as a proxy of water use. The use of proxy measures is considered a limitation because of imperfect estimates of water demand. Actually, the paper precisely addresses the issue that measuring irrigated area cannot fully account for the information about water use (the area can be measured and this is needed to have it as part of the contract, but it remains unknown how it relates to costs and profits for each individual farmer). However, different and better proxies can be identified.
Another limitation can be found in the fact that we considered the effect of an adverse selection problem in the presence of information asymmetries between the WA and the farmers whilst not considering the presence of the moral hazard.
Also, we left aside the effect of climate change on the water supply and ultimately its effects on water costs and the consequent implication for designing pricing schemes. As climate change is one of the main drivers of current adaptations, this could be a priority topic to be addressed in further research.
Moreover, we assumed that transaction costs are simply proportional to water tariffs when there might also be a fixed and nonlinear variable component that contributes to further complicating the WA’s incentive pricing policy. Certainly, there may be other cases in which transaction costs differ in their form and among types.
In addition, in our analysis, we did not explicitly discuss compatibility with the Polluter Pays Principle (PPP), a very important issue for water policy. Knowing that PPP is closely interlinked with the other two principles (Incentive Pricing Policies (IPP) and Cost Recovery (CR)) [
42] by means of incentive pricing policy designs in this study, it is possible to boost rational water uses that might contribute to softening related negative environmental effects. However, direct interlinkages with PPP are out of the scope of this paper but could be further investigated.
However, our model can be expanded to consider these costs related to PPP by simply including them in the WA’s cost for water delivery to farmers (). However, as environmental and resource costs may have different behaviours (both because they follow different functional forms with respect to water abstraction and because they often have the nature of public goods), it would be preferable to work with them through a different item of the objective function and potentially a different constraint in future developments of this model.
Other limitations are related to the fact that we consider a limited set of hypotheses of combinations of profit and cost functions. For example, assuming a quadratic cost function in the modelling approach could lead to different results from the ones introduced thus far. Addressing these issues could be considered in future research.
6. Conclusions
The provision of water resources through open canals and the potential inefficiencies in its use by farmers under flat rate pricing motivates research on the design of alternative pricing strategies that provide incentives for the rational use of water resources according to the WFD requirements, IPP and CR.
The mechanism design for incentive pricing, overall, matches two of the requirements of Article 9 of the Directive 2000/60/EC [
4]. The IPP is addressed by developing an incentive strategy that connects farms’ water tariffs (indirectly) with the farms’ water uses. In addition, water tariffs cover water supply costs and associated transaction costs (i.e., cost recovery).
Through our analysis, we demonstrate that incentive pricing options are possible even under asymmetric information conditions, though the related efficiency gains and losses are highly case specific. By separating hypotheses about costs and profit functions, we also show that first-best incentive contracts can be implemented even under asymmetric information, in particular, when differences in costs for water use are small compared to differences in irrigation profits across farms and/or when transaction costs related to tariff implementation are low.
The main policy prescription remains that incentive pricing strategies via menus of contracts need to be designed in such a way that the features of each particular region are taken into consideration. On the other hand, the feasibility of these contract solutions may be greater than usually expected, even when water is not measured. This can include first-best solutions that are not just theoretical options but can actually be the best solution for a class of real-life situations. In order to exploit these opportunities, the policy would need to be more carefully designed, taking into account farmers’ heterogeneity and incentive compatibility.
An obvious extension of this methodology could be in the direction of an empirical application. In addition, the investigation of the joint problem of adverse selection and moral hazard in irrigated agriculture might be a further step forward as a way of bringing models closer to a realistic assessment of the economic efficiency of different policy instruments. Another potential extension of this method (alone or combined with those listed above) could be an assessment of the effects of different transaction cost structures (fixed and variable transaction costs) on optimal policy design.