Multi-criteria modelling of irrigation water market at basin level: A Spanish case study

European Journal of Operational Research 173 (2006) 313–336

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O.R. Applications

Multi-criteria modelling of irrigation water marketat basin level: A Spanish case study

Jose A. Gomez-Limon a,*, Yolanda Martınez b

a Department of Agricultural Economics, E.T.S.II.AA. Palencia, University of Valladolid, Avda. de Madrid 57, 34.071 Palencia, Spainb Department of Economic Analysis, University of Zaragoza, Gran Via 2-4, 50004 Zaragoza, Spain

Received 19 January 2004; accepted 16 December 2004Available online 13 February 2005

Abstract

This paper develops a multi-criteria methodology to simulate irrigation water markets at basin level. For this pur-pose it is assumed that irrigators try to optimise personal multi-attribute utility functions via their productive decisionmaking process (crop mix), subject to a set of constraints based upon the structural features of their farms. In this sense,farmers with homogeneous behaviour regarding water use have been grouped, such groups being established as ‘‘types’’to be considered in the whole water market simulation model. This model calculates the market equilibrium through asolution that maximises aggregate welfare, which is quantified as the sum of the multi-attribute utilities reached by eachof the participating agents. This methodology has been empirically applied for the Duero Basin (Northern Spain), find-ing that the implementation of this economic institution would increase economic efficiency and agricultural labourdemand, particularly during droughts.� 2005 Elsevier B.V. All rights reserved.

Keywords: Multi-criteria analysis; Water markets; Multi-attribute utility theory; Agriculture; Duero Valley (Spain)

1. Introduction

The constantly rising demand for water in Spain clearly demonstrates the growing relative shortage ofthis resource. In fact, most of Spanish basins are already in a situation known as a mature water economy(Randall, 1981). This has resulted in an intense debate about the efficiency of use of this natural good byirrigated farms, which account for 80 per cent of national water consumption (Ministry of the Environ-ment, 2000). The apparently poor management of water in Spanish irrigated areas has served as an

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* Corresponding author. Tel.: +34 979 108341; fax: +34 979 108301.E-mail address: [email protected] (J.A. Gomez-Limon).

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314 J.A. Gomez-Limon, Y. Martınez / European Journal of Operational Research 173 (2006) 313–336

argument for the implementation of demand water policies as an essential solution to this problem. Suchdemand policies should offer incentives for water conservation and resource reallocation in the direction ofmore value-added uses (Thobani, 1997). In this sense, the Spanish authorities have recently introduced anew legislative framework that will permit the operation of water markets.

The introduction of water markets has been traditionally thought of as a measure to improve, in a decen-tralised manner, the allocation of water resources among its potential users and to reduce the effects ofwater scarcity. Thus, the main characteristic that justifies the introduction of water markets is its abilityto reallocate water among various uses toward those with more value-added potential, while promotingmore rational utilisation of the resource in every use. In this way, as many authors agree (Randall,1981; Spulber and Sabbaghi, 1994; Easter and Hearne, 1995; Thobani, 1997; Lee and Jouravlev, 1998;Howe and Goemans, 2001), this economic instrument helps to alleviate the inefficiencies that public man-agement (allocation) of water has hitherto demonstrated. According to the literature, market institutionsmake it possible to achieve water allocation efficiency better than via of its alternatives, thus maximisingsocial welfare (Vaux and Howitt, 1984; Howe et al., 1986; Rosegrant and Binswanger, 1994; Hearne andEaster, 1995; Dinar et al., 1997).

Nevertheless, it is worth starting an analysis of water markets by properly conceptualising this economicinstrument. In this sense, water markets can be considered as being similar to any institutional frameworkthat allows rights holders, following some established rules, to give them voluntarily to another users inexchange for an economic compensation. As this definition points, the water markets that can be developedin the real world are not homogeneous, and a range of different organizational structures can be found.Indeed, the introduction of water markets, from the political economy point of view, allows us to determinea set of variables that define their basic characteristics, allowing the specific peculiarities of water manage-ment in the zones in which they are implemented to be faced (Lee and Jouravlev, 1998).

This paper focuses exclusively on the water market that has been introduced recently in Spain by theWater Act (Act no. 46/1999), the development of which is discussed in article 61 bis. In short, amongthe different alternative systems of water use rights transfers, Spanish legislation has opted to limit thesetransactions to leasing (sale and purchase of water and not of rights), water markets known as spot markets.

The objective of this research is thus to simulate a spot market for irrigation water for a whole basin, inorder to analyse the economic impact (increase in economic efficiency through measurement of profits) andsocial impact (change in demand for labour by the agricultural sector) that the effective application of thiseconomic instrument would generate. For this purpose we have developed a methodology within the Multi-Criteria Decision Making (MCDM) paradigm, based on the differences in the behaviour of irrigators withregard to the productive decisions that they take on their farms (crop mix decisions) and thus in the use ofagricultural inputs such as irrigation water. With this new approach we propose a mathematical program-ming model that simulates the market equilibrium for different scenarios of water availability, transactioncosts and water prices, quantifying for each case the socio-economic impacts identified above. This ap-proach has been empirically applied in the Duero Valley irrigation area in the north of Spain.

In order to achieve this objective, the second part of this paper explains the theoretical framework onwhich the multi-criteria model employed in the simulations is based, while the third section presents thecase study area (Duero basin). The fourth section describes the most important results. Finally, the last partof the paper offers some concluding remarks.

2. Methodology

The literature contains a number of empirical studies on modelling the economic, social and environ-mental impacts of water markets. For the concrete case of spot markets, we can cite those of Houstonand Whittlesey (1986) in the state of Idaho (USA), Dinar and Letey (1991) and Weinberg et al. (1993), both

J.A. Gomez-Limon, Y. Martınez / European Journal of Operational Research 173 (2006) 313–336 315

in the Californian valley of San Joaquin and Horbulyk and Lo (1998) in the Canadian province of Alberta.In general, these authors conclude that the implementation of water markets increase the allocation effi-ciency of this resource.

For the Spanish case, the works of Garrido (2000) and Calatrava and Garrido (2001) deserve attention.These authors employed mathematical models based on positive mathematical programming to simulatemarkets in the Guadalquivir Valley. The work of Arriaza et al. (2002) that simulates a spot water marketin the same basin should also be mentioned. This last paper introduces as a novel element the assumption ofconsidering irrigators� behaviour according to the principles of the Expected Utility Theory (EUT), i.e.maximising a utility function with several moments of profit. These three studies conclude that the imple-mentation of this economic instrument would bring moderate improvements to the allocation efficiency ofthe resource in the basin analysed.

Although our work has been influenced by the studies mentioned above, its major contribution is itsmethodological approach that tries to develop a simulation model based upon MCDM techniques. In fact,all previous studies have proposed mathematical models that assume that producers behave rationally interms of profit maximisation (or an utility function maximisation where profit is the only attribute), inaccordance with a classical economic theory (or of the EUT) hypothesis. According to this approach, farm-ers would use (via irrigation) or not (via sales) their water allowances depending on the productivity (mar-ginal value of water) that this resource generates in their farms, according to soil and climate conditions.According to this classical point of view of input allocation, the introduction of a water market would beexpected to move water from lower to higher marginal productivity uses. Thus, farmers could trade theirwater use rights and sell them to the point at which the marginal productivity of water equals its marketprice, thus improving water allocation efficiency.

We have assumed as starting point that, unlike the classical approach, the level of farmers� utility isdetermined not only by the profit but also by other relevant management criteria considered by them. Thus,this study supposes the amount of water that producers consume or sell depends on the multi-attribute util-

ity generated by this resource for these decision-makers, considering the relative importance that farmersassign to each of the different criteria that they try to optimise simultaneously (Gomez-Limon et al., 2003).

2.1. The Multi-Attribute Utility Theory (MAUT) approach

One of the basic principles of classical economic theory is that decision-makers behave as profit maxi-misers. According to this principle, the problem of agricultural producers could be adequately modelledby the maximisation of single-objective models. Real-life observations refute this simplification.

Expected Utility Theory (EUT) was a first step in the direction of broadening the profit maximiserassumption and including higher moments of the expected profit. However, EUT has been criticised forlimiting its application to a single attribute: the pay-off (or wealth). Many authors have shown the complex-ity of the farmers� decision-making process through empirical studies that have demonstrated that they con-sider more than one attribute in their utility functions: e.g. Harman et al. (1972), Gasson (1973), Smith andCapstick (1976), Harper and Eastman (1980), Kliebenstein et al. (1980), Patrick and Blake (1980) and Caryand Holmes (1982). More recent work of Berbel and Rodrıguez (1998), Costa and Rehman (1999), Willocket al. (1999) and Solano et al. (2001) is also of interest. All these studies suggest that farmers� decision-mak-ing processes are driven by various criteria, usually conflicting ones, related to their economic, social, cul-tural and natural environment situation, in addition to the expected profit (or higher moments). Suchcriteria include maximisation of leisure, minimisation of managerial problems, minimisation of indebted-ness, etc.

In this framework a decision-maker tries to satisfy, as far as possible, all these criteria at the same time.Considering then the existence of multiple objectives in farmers� decision making, it seems appropriateto focus a simulation of water markets within the Multi-Criteria Decision Making (MCDM) paradigm.


For discussions of MCDM techniques in agriculture see Hazell and Norton (1986), Hardaker et al. (1997)and Romero and Rehman (2003).

Recognising the convenience of including several objectives to simulate producer behaviour, we resort toMulti-Attribute Utility Theory (MAUT), an approach largely developed by Keeney and Raiffa (1976), inorder to overcome the limitations of the single-attribute utility function. The aim of MAUT is to reduce adecision problem with multiple criteria to a cardinal function that ranks alternatives according to a singlecriterion. Thus, the utilities of n attributes from different alternatives are captured in a quantitative way viaa utility function represented mathematically as U = U(r1, r2, . . . , rn), where U is the Multi-Attribute UtilityFunction (MAUF) and rj are the attributes regarded by the decision-maker as relevant to his decision-mak-ing process.

The level of achievement of each attribute can usually be expressed mathematically as a function of thedecision variables, that is, rj ¼ fjð~X Þ. Thus, decisions under MAUT are made by maximising U andresponding to the set of objectives that are simultaneously aimed at by the producer.

It is often argued that MAUT has the soundest theoretical structure of all the multi-criteria techniques(Ballestero and Romero, 1998). At the same time, from a practical point of view, the main drawback to thisapproach comes from the elicitation of the multi-attribute utility function (Herath, 1981; Hardaker et al.,1997, p. 162). In order to simplify this process, some assumptions need to be made about the mathematicalfeatures of the utility function.

In most cases, additive and linear utility functions have been adopted to simulate farmers� behaviour in amulti-attribute framework. The ranking of alternatives is obtained by adding contributions from each attri-bute. Since attributes are measured in terms of different units, normalisation is required to permit them tobe added. The weighting of each attribute expresses its relative importance. Mathematically the related util-ity function would be

1 ‘‘Aattribu

U i ¼Xn

j¼1

wjkjrij; i ¼ 1; . . . ;m; ð1Þ

where Ui is the value utility value of alternative i, wj is the weight of attribute j, kj is the factor normaliser ofthe attribute j and rij it is the value of the attribute j for alternative i.

Keeney (1974), Keeney and Raiffa (1976) and Fishburn (1982) explain the mathematical requirementsfor the assumption of an additive utility function. According to them, if attributes are mutually utility inde-pendent1 the utility function becomes separable (U = f{u1(r1), u2(r2), . . . , un(rn)}) and takes either the addi-tive form: Uðr1;r2; . . . ;rnÞ¼

PðKwjujðrjÞ, or multiplicative form: Uðr1;r2; . . . ;rnÞ¼f

QðKwjujðrjÞþ1Þ�1g=K,

where 0 6 wj 6 1 and K = f(wj). If the attributes are mutually utility-independent andP

wj ¼ 1, thenK = 0, and the utility function is additive. Although these conditions are somewhat restrictive, Edwards(1977) and Farmer (1987) have shown that the additive function yields extremely close approximationsto the hypothetical true function even when these conditions are not satisfied. In Hwang and Yoon�s words(1981, p. 103): ‘‘theory, simulation computations, and experience all suggest that the additive method yieldsextremely close approximations to very much more complicated non-linear forms, while remaining far eas-ier to use and understand’’.

Once the use of the additive utility function has been justified, we take a further step assuming that theindividual attribute utility functions are linear. Although this assumption of linearity is rather strong, andmay even be unrealistic (it implies linear utility-indifferent curves or constant partial marginal utility), itcan be regarded as a close enough approximation as long as the attributes vary within a narrow range

n attribute xi is utility independent of the other n � 1 attributes xj if preferences for lotteries involving different levels ofte xi do not depend on the levels of the other n � 1 attributes xj’’ (Huirne and Hardaker, 1998).


(Edwards, 1977; Hardaker et al., 1997, p. 165). There is some evidence for this hypothesis in agriculture.Thus, Huirne and Hardaker (1998) show how the slope of the single-attribute utility function has little im-pact on the ranking of alternatives. Likewise, Amador et al. (1998) have demonstrated how linear and qua-si-concave functions yield almost the same results. We therefore adopt this simplification in the elicitationof the additive utility functions.

2.2. Types of agents operating in the market

Given the practical impossibility of simulating a water market at hydrographical basin level consideringall irrigators as individual operating agents, it is necessary to aggregate these producers in homogeneousgroups that include irrigators with similar behaviour related to water use. This paper starts off with the ba-sic idea that farmers� behaviour (i.e. water use) is motivated by their productive potentialities (derived fromthe structural conditions of their farms) and by the relative importance that they attach to particular man-agement criteria, condensed in their respective MAUFs (Gomez-Limon et al., 2003). Thus, the homoge-neous groups that have been established in order to constitute types of agents in water marketmodelling are the result of a double entrance typology, in which operating agents (irrigators) are sortedaccording to the structural conditions of their holdings and the different weights given to the objectives con-sidered as classificatory variables. The following sections explain the way in which this binomial farm/farm-er typology was developed.

2.2.1. Structural diversity of farmsModelling agricultural systems at any level other than that of the individual farm implies problems of

aggregation bias. In fact, the introduction of a set of farms in a unique programming model overestimatesthe mobility of resources among production units, allowing combinations of resources that are not possiblein the real world. The final result of these models is that the value obtained for the objective function isalways upwardly biased and the values obtained for decision variables tend to be unobtainable in real life(Hazell and Norton, 1986, p. 145). This aggregation bias can only be avoided if the farms included in themodels fulfil strict criteria regarding homogeneity (Day, 1963): technological homogeneity (i.e. the samepossibilities of production, type of resources, technological level and management capacity), pecuniary pro-portionality (proportional profit expectations for each crop) and institutional proportionality (availabilityof resources to the individual farm proportional to average availability).

This study tries to approach a whole hydrographical basin, considering irrigated areas (Comunidades de

Riego, or irrigation districts) as basic geographical units of analysis. These units are relatively small areas(ranging from 1000 to 15,000 ha) that can be regarded as fairly homogeneous in terms of soil quality andclimate, and in which the same range of crops can be cultivated and will produce similar yields. Further-more, the whole set of farms that make up this agricultural system operates the same technology at a similarlevel of mechanization. Given these conditions, it can be assumed that the requirements regarding techno-logical homogeneity and pecuniary proportionality are basically fulfilled.

In view of the existence of efficient capital and labour markets, the constraints included in this systemhave been limited to the agronomic requirements (crop rotations) and the restrictions imposed by the Com-mon Agricultural Policy (set-aside land and sugar-beet quotas) that are similar for all farms. The require-ment of institutional proportionality may thus also be regarded as having been met.

We can thus see that agricultural systems of this kind can be modelled by means of a unique linear pro-gram with relatively small problems of aggregation bias. However, it is essential to note that the require-ments discussed above are outlined from the point of view of classical economic theory, which assumes thatthe sole criterion on which decisions are based is profit maximisation. If a multi-criteria perspective is uti-lised, an additional homogeneity requirement emerges in order to avoid aggregation bias; viz., homogeneity

related to choice criteria.


2.2.2. Diversity of farmers’ MAUFs

The experience that has been accumulated in this field leads us to suspect that the decision criteria offarmer homogeneity do not reflect the normal situation in real agricultural systems. In fact, the decisioncriteria are primarily based on the psychological characteristics of decision-makers, which differ signifi-cantly from farmer to farmer. According to this perspective, the differences in decision-making (cropmix) among farmers in the same production area (e.g. an irrigated area) must be primarily due to differencesin their objective functions (in which the weightings given to different criteria are condensed), even morethan other differences related to the profits of economic activities or disparities in resources requirementsor endowments (Gomez-Limon et al., 2003).

In order to avoid aggregation bias resulting from lumping together farmers with significantly differentobjective functions, a classification of all farmers into homogeneous groups with similar decision-makingbehaviour (similar MAUF) is required. For this issue we have taken the work of Berbel and Rodrıguez(1998) as our point of departure. These authors have pointed out that for this type of classification the mostefficient method is cluster analysis, taking farmers� real decision-making vectors (actual crop mix) as theclassification criterion.

As pointed out above, we can assume that in a homogeneous area, differences in the crop mix amongfarmers are mainly caused by their different management criteria (utility functions) rather than by otherconstraints such as land quality, capital, labour or water availability. Thus, the percentage area devotedto each crop can be considered as a proxy for the real criterion and shape of the MAUF. Thus, these per-centages can be used as classification variables to group farmers using the cluster technique, as required forour purposes.

In this sense, it is also important to note that the homogeneous groups obtained in this way can be re-garded as �fixed� in the short and medium terms. As noted above, the decision criteria are based on psycho-logical features of the decision-makers, which is why they may be regarded as producers� structuralcharacteristics. In fact, these psychological features, and thus the criteria, are unlikely to change in the shortterm. This means that the selection variables chosen allows farmers to be grouped into clusters irrespectiveof any change in the policy framework (i.e. water market). In other words, once homogeneous groups ofproducers have been defined on the basis of actual data (crop mix), we can assume that all elements insideeach group will behave in a particular way when the policy variables change; that is, crop-mix decisions willbe modified in a similar fashion by all farmers within a cluster, although such modifications would differamong the individual groups defined.

For a more concrete definition of the cluster analysis performed in this research, we may also note thatthe farmers were classified by considering the chi-squared distance among actual crop mixes, expressed inpercentages, as a measurement of distance, and using the Ward method (minimum variance) as the aggre-gation criterion.

This enable us to assume that each one of these clusters obtained, as a result of the binomial typology‘‘productive potentiality’’ (irrigated area)/‘‘shape of farmers� MAUF’’ (cluster), has sufficient internalhomogeneity to enable us to consider the average virtual farmers as representative cases of the differenttypes of agent operating in the water market, allowing them to be separately modelled without undesirablebias.

2.3. Elicitation of the multi-attribute utility functions

Once we agree to use additive and linear utility functions, the ability to simulate real decision-makers�preferences is based on the estimation of relative weightings. Sumpsi et al. (1997) and Amador et al.(1998) propose a method for assessing a farmer�s additive and linear MAUFs (weights vector) without di-rect interaction between farmers and the researcher. They show how it is possible to elicit the farmers� util-ity function by observing only the actual crop distribution on weighted goal programming. We adopt this


methodology in order to assess the utility function of a group of farmers as has previously been done byBerbel and Rodrıguez (1998), Gomez-Limon and Berbel (1999), Arriaza et al. (2002) and Gomez-Limonet al. (2002). This method may be summarised as follows:

1. Each attribute j is defined as a mathematical function of decision variables ~X (e.g. crop area); fj ¼ fjð~X Þ.These attributes are proposed a priori as the most relevant decision-making criteria used by farmers.Inour case study the following objectives were selected in order to explain farmers� behaviour:(a) Maximisation of Total Gross Margin (TGM), as a proxy for profit in the short term. Average crop

gross margins (gmc) are obtained from a time series of seven years (1993/1994 to 1999/2000); con-stant euros of 2000. Therefore, the TGM for each homogeneous group of farmers can be expressedas follows:

2 It szero). Tconsidconstaconsidassump(deficit

3 Thfarmerprogra

TGM ¼X

c

gmc � X c; ð2Þ

where c refers to each crop cultivated in the individual irrigable areas.(b) Minimisation of risk. Risk is an important factor in agricultural production. Farmers have a marked

aversion to risk, so the model should also include this objective. In this case risk was measured as thevariance of the TGM (VAR). The risk is thus computed as ~X

t

c½Cov�~X c), where [Cov] is the variance–covariance matrix of the crop gross margins during the seven-year period, and ~X is the crop decisionvector.2

(c) Minimisation of the Total Labour input (TL). This objective implies not only a reduction in the cost ofthis input but also an increase in leisure time and the reduction of managerial involvement (labour-intensive crops require more technical supervision). The expression of TL for each homogeneousgroup considered is obtained in the following way:

TL ¼X

c

lc � X c ð3Þ

where lc is the labour required (in Agricultural Work Units—AWUs) by each crop (c).This analysis enables us to assess the importance of each objective in the decision-making process for

each homogeneous group of farmers. In this way, TGM, VAR and TL will be the attributes that wouldbe included as arguments in the MAUFs of the individual clusters of farmers. In any case, it is conve-nient to point out that these attributes are the most relevant ones �a priori�, but is not improbable thatadditional attributes might be able to explain the real behaviour of farmers more accurately.3

2. A pay-off matrix that optimises each objective is obtained, in which fij is the value of the ith objectivewhen the jth objective is optimised. The main diagonal is the �ideal� point defined by the individuallyobtained optimum (a pay-off matrix for each agent ‘‘type’’ or binomial irrigated area-cluster).

The constraints taken into account in the various models (a model for agent ‘‘type’’) utilised to obtainthe pay-off matrices were:

hould be noticed that VAR is calculated using current situation data (i.e. without water market and thus with a water price ofhe same data (current [Cov] matrix) will be used to calculate VAR inside the water market framework to be modelled. We have

ered this option because it is assumed that the risk perceived by farmers for any particular crop-mix can be regarded as beingnt. Of course, when gmc varies for a modification in water price, the VAR of crop-mixes might change mathematically, but weer that the risk taken into account by farmers remains the same as in the current situation (baseline risk level). We think thistion is reasonable in simulations of farmers� behaviour, especially when variations in water quantity delivered for a single cropirrigation) are not considered as an option by the irrigators (Sunding et al., 1997; Schuck and Green, 2001).

e methodology has included the criteria more often considered by the literature in multi-criteria modelling for simulatings� decisions. Opposite, it has not included other hypothetical objectives that are difficult to be modelled through mathematicalmming (mainly dealing with psychological variables—e.g. social prestige), although they could be involved in the real MAUFs.


• Land constraint. The sum of decision variables (area devoted to each crop) must be equal to the totalarea available to the farm type in each cluster.

• Water availability.• European Common Agricultural Policy (CAP) constraints (set-aside requirements and sugar-beet

quotas).• Rotational constraints as expressed by the farmers questioned in the survey.• Market constraints that limit the amount of risky crops according to traditional practices.Each one of these restrictions has been built differently for each type of agent using the available infor-mation for each.

3. The following n + 1 system of equations is solved
Xn
j¼1

W jfij ¼ fi; i ¼ 1; 2; . . . ; n andXn

j¼1

W j ¼ 1; ð4Þ

where n is the number of a priori relevant objectives, Wj are the weights attached to each objective (thesolution), fij are the elements of the pay-off matrix and fi the real values of the observed behaviour offarmers (actual crop mix), as obtained by direct observation.

4. Normally, there is not an exact solution (Wj) for the system above and it is therefore necessary to solve aproblem by minimising the sum of deviational variables that find the closest set of weights:

MinXn

i¼1

ni þ pi

fi

s:t::Xn

j¼1

W jfij þ ni � pi ¼ fi; i ¼ 1; 2; . . . ; n andXn

j¼1

W j ¼ 1; ð5Þ

where ni and pi are negative and positive deviations respectively.Dyer (1977) demonstrated that the weights obtained in (5) are consistent with the following additive

and linear utility function:

U ¼Xn

j¼1

wjkjfjð~X Þ; ð6Þ

where kj is a normalising factor.

Precisely because this utility surrogate needs to fulfil the requirements of being an additive MAUF, itmust range between 0 and 1. For this reason, the following equivalent MAUF expression is used:

U ¼Xn

j¼1

wjfjð~X Þ � fj�

f �j � fj�: ð7Þ

The utility function (7) is thus normalised by taking the inverse of the difference between the maximum(f �j ) and minimum value (fj� ) of the different objectives in the pay-off matrix developed for the criteria con-sidered, and by choosing the mathematical expression of the attributes as their utility function, fj(X), minusthe minimum (fj� ).

The method proposed thus provides subrogated utility functions that can be used as an instrument capa-ble of reproducing the observed behaviour of farmers. In this way it is worth mentioning that this techniquewas used several times, once for every cluster defined (homogeneous group of producers or ‘‘agent type’’),in order to obtain the characteristic MAUF of each of them. Thus, these MAUFs are considered to bethose that the set of farmers in each of these groups always tries to maximise, despite the different possiblescenarios to be faced (e.g. different effective endowments of water). This is the key issue that allows a hypo-thetical water market framework to be simulated.


2.4. Modelling irrigation water market at basin level

Taking the above comments into account we may suggest that the problem of decision making that facesevery individual irrigator in the short term (i.e. annual crop mix decision) can be simulated through a math-ematical programming model whose objective function is the MAUF based on the weights vector (wj) cal-culated in each case, subject to the various technical and institutional constraints that need to be fulfilled.Therefore, beginning with the case where water exchanges are not possible (lack of water market), the prob-lem proposed would be outlined as follows:4

4 Inand th

Max Uð~X Þ ¼ wTGMkTGMTGMð~X Þ � wVARkVARVARð~X Þ � wTLkTLTLð~X Þ ð8Þs:t::

Xc

X c 6 s; ð8aÞX

c

wdcX c 6 wa � s; ð8bÞ

A~X 6 ~B; ð8cÞX c P 0 8c; ð8dÞ

where wTGM, wVAR and wTL are the weights estimated for the different objectives considered by the pro-ducer, kTGM, kVAR and kTL are the normalising factors, Xc is the area dedicated to crop c (in ha), s isthe total area available for cropping activities (in ha), wdc are the water demands for crop c (in m3/ha)and wa is the total endowment of water available (in m3/ha).

Thus, in this basic model the constraints linked with land (8a) and water (8b) availability are explicitlypointed out. The generic set of constraints (8c) is related to the rest of the constraints required to obtain thepay-off matrix (CAP limitations—set-aside requirements and sugar-beet quotas, crop frequencies and rota-tional requirements and market limitations).

If an individual producer were allowed to exchange water through a spot market, the optimisation modelexposed would become this:

Max Uð~X Þ ¼ wTGMkTGM TGMð~X Þ þX

j

wp � tcij

2

� �WSij

h i�X

j

wp þ tcji

2

� �WBij

h i( )

� wVARkVARVARð~X Þ � wTLkTLTLð~X Þ ð9Þs:t::

Xc

X c 6 s; ð9aÞX

c

wdcX c þX

j

WSij �X

j

WBij 6 wa s; ð9bÞ

A~X 6 ~B; ð9cÞX c P 0; WSij P 0; WBij P 0 8c 8i 8j; ð9dÞ

where wp is the market price of water (in €/m3), tcij are the transaction costs of a transfer of water from theirrigator (i) to other irrigators (j), (also in €/m3), WSij is the amount of water sold by i to j (in m3) and WBij

is the amount of water bought by i from j (in m3).It is worth mentioning that in this model wp is a parameter. This is because it is assumed that this water

market is a competitive one, in which a single producer cannot unilaterally modify the price fixed by thewhole market (interaction between the aggregated supply and demand); all agents operating in the market

order to clarify models specification, in all formula of this paper we have restricted the use of capital letters to identify variablese use of lower cases letters to distinguish parameters.


are ‘‘price-accepters’’. Since the water price is fixed exogenously, it should therefore be considered as aparameter by a single producer�s model.

In this respect, it is also worth pointing out that the transaction costs are parameters proposed at thestarting point and the end of each transfer. For this reason, tcij does not have to be equal to tcji. Thus,for our model definition these transaction costs take different values. It has been regarded as a minimumvalue (equal to 0.005 €/m3) when the water transactions are carried out inside an irrigated area. When thesetransfers are carried out among different irrigated areas using natural flows (down stream) as transportpaths, the transaction costs take a value of 0.01 €/m3. Finally, for all other cases, where no transport infra-structure exists (any transfer is physically impossible), a maximum value tending to infinity has been con-sidered (in an operative way 10 €/m3 has been used). In all cases, it has been assumed that the respectivetransaction costs (different tc depending on each particular case) are borne by the seller and by the pur-chaser equally (i.e. a half of the total cost is borne by each).

Vis-a-vis model (8), model (9) presents two significant changes. The first is related to the consideration ofreimbursement and payment (in €) for the water transferred inside the TGM attribute. In this sense it isassumed for the sake of simplification that the presence of the water market does not affect the value ob-tained for the rest of attributes. The other noteworthy change is the inclusion of sales and purchases ofwater within the hydraulic balance constraint (9b).

Widening the approach taken for the optimisation of an individual irrigator or type of agent i, the mar-ket equilibrium reached by interaction of all irrigators can be simulated through the following equation:

MaxX

i

awiU ið~X iÞ ¼X

i

awi wTGMi kTGMi TGMið~X iÞ þX

j

WP� tcij

2

� �WSij

h i((

�X

j

WPþ tcji

2

� �WBij

h i)�wVARi kVARi VARið~X iÞ � wTLi kTLi TLið~X iÞ

)

ð10Þ

s:t::X

c

X ci 6 si 8i; ð10aÞX

i

Xc

awiwdcX ci 6

Xi

awiwaisi; ð10bÞX

c

wdcX ci þX

j

WSij �X

j

WBij 6 waisi 8i; ð10cÞ

Uoi 6 U i 8i; ð10dÞ

Ai � ~X i 6~Bi 8i; ð10eÞ

X c P 0; WP P 0; WSij P 0; WBij P 0 8c 8i 8j; ð10fÞ

where awi (agent weights) are the normalising factors used to modulate each agent�s ‘‘type’’ (i) representa-tiveness. These factors have been equalised, for each case i, to the ratio of the total area represented by thetype of agent divided by the respective average area (sti/si).

This way of normalising utilities Ui inside the objective function needs to be further explained. In thiscase we have considered that every irrigated hectare should be considered as equally important. This iswhy the main idea underlying coefficient awi (sti/si) is that every hectare should count equally in the finalequilibrium solution, despite the cluster or farmer type considered. The objective function ought thereforebe the one that maximises aggregated utility for every hectare to its owner.

Because the values of Ui are obtained at farm level (expression between { } in Eq. (10)), we therefore needto estimate utility at hectare level (dividing by si clusters area). Furthermore, because it is necessary to take


into account every hectare inside each cluster, the average utility per hectare will have to be multiplied by sti

(total area represented by the type of agent). Only in this way will the utilities reached by each of them (Ui)be allowed to be summed in a homogeneous way. Therefore, the sum proposed as objective function prop-erly adds the utility generated by each irrigated hectare for the producers concerned.

As opposed to Eq. (9), in this case WP (the market price of water measured in €/m3) is treated as a var-iable in this model. In fact, water price is fixed endogenously inside this market model, being the key var-iable that allows equilibrium to be reached (water demand is equal to water supply).

The consideration of WP as a variable turns this model into a non-linear one. As is well known, in thesecases the search for ‘‘absolute’’ optima is much more demanding and requires a strong knowledge of thesystem that would be impossible to obtain in such a complex model. This is why we have opted to identify‘‘local’’ optima that can be reasonably considered as ‘‘absolute’’ optima. For this purpose we have paidspecial attention to the initial values and the validation of the results. Further details are provided in Sec-tion 4, which is devoted to the results of the case study.

This model assumes that market equilibrium is reached when the sum, properly weighted, of the utilitiesUi of all agents considered is maximised. Nevertheless, it is worth noting that in order to simulate the mar-ket in an appropriate way it was necessary to include two new constraints with regard to the model (9). Thefirst one, noted as (10b), related with the whole water balance, and ensured that the water consumed atbasin level is less than or equal to the total available resources.

In (10d) a set of constraints is also included in order to guarantee that the market operates without any-body ‘‘losing’’. In fact, when water exchanges are voluntary, the different agents would only participate inthe market as long as the transfers could increase their welfare (an increase in their utility function). For thisreason it is necessary that the utility reached by each agent (Ui) in the equilibrium should be superior, or atleast equal, to the utility that each one of them had obtained before the reallocation performed by the mar-ket has been implemented (Uoi), that is, where no market exists (utility values calculated in model 8).

Finally, it should be commented that the market equilibria obtained via this modelling approach implyin any case that the overall utility does not decline as a consequence of trading. Nevertheless, the optimaobtained by this approach cannot be considered as �best� options in terms of the classical economic effi-ciency and cost–benefit theory, since maximum total utility is not attained because of the set of constraints10d in the model. In fact, as a result of the operational rules legally imposed on water markets (voluntarytransfers based on individual utility gains), the equilibria obtained should be considered as �second best�options of overall utility, and sub-optimal in the perspective of total welfare. In any future research, there-fore, an interesting issue would be the analysis of possible efficiency gains that could be made by consider-ing the implementation of Kaldor�s compensating principle (transfers from gainers to those who could loseout). This theoretical possibility should allow different ways of �compensating/incentivising� users to free upmore water, thus increasing the total utility obtained in the market equilibria.

3. Case study

The Duero valley is a basin shared between Spain and Portugal. The case study analysed here considersonly the Spanish part, which occupies most of the basin (almost 78,000 km2). Within this area 555,582 hect-ares are dedicated to irrigated agriculture, which consumes an average of about 3500 hm3 of water annually(about 6300 m3/ha year). In fact, irrigation is the most important use of water in this basin, consuming 93%of the total available resources. The rest of the water is used for urban (6% of total resources availability)and industrial purposes (1%). This preponderance of irrigation suggests that the greatest potential forimproving resource allocation efficiency at basin level through the market would lie in transfers withinthe agricultural sector. Thus, by simulating the irrigation water market alone it should be possible to ana-lyse the lion�s share of the socio-economic impacts of this institution on the whole basin.


Irrigation in the Duero valley, as legally established by Spanish law, is divided into irrigated areas, inter-nally managed by Water User Associations known as ‘‘Comunidades de Regantes’’ (CR). For this research,given the practical impossibility of considering all them, we selected seven typical CRs at basin level, cov-ering 51,343 irrigated hectares (9.2% of the total irrigation in the Duero). Table 1 shows the basic featuresof each CR.

In the irrigated areas analysed we surveyed 367 farmers (an average of 52 producers per area) in order togather the information needed to develop the cluster technique, and subsequently feed the models. Produc-ers to be surveyed were selected at random using the CR�s databases. Once the sample had been selected,each farmer was individually interviewed in order to collect all the primary data needed by means of a ques-tionnaire. Individual information focused on the following aspects:

• Variables related with agricultural production, such as the surfaces devoted to each crop, yields obtained,fixed and variable costs by crop, irrigation water volume and number of irrigation events for each crop,etc. Other variables dealing with the constraints that limit the crop mix (sugar-beet quotas, rotationalconstraints, etc.) were also included.

• Socio-economic variables. These variables included the farmer�s age, family size, educational level, totalincome (from farming and non-farming activities), amount of land owned and leased, etc.

It is worth pointing out that our data are highly reliable, not only because of the way in which they wereobtained, but also because of the checking process used to validate them (data cross-checking with CR�sdatabases).

Using individual crop-mix vectors obtained through the questionnaires, we have implemented the clustertechnique explained above in order to generate homogeneous groups (defined as type of agents). Once thedendrogram charts were obtained for each case (irrigated area), they were �cut�, taking into account thenumber of groups that we regarded as being suitable for this research (2–4 groups per area). In this waya total of 22 different homogeneous groups were defined as types to be modelled. Each type of agent (group)is characterized in terms of the average data (cultivated surface, crop-mix, etc.) of its members. Table 2shows their basic features.

It is also worth noting that a set of statistical tests was carried out to determine the relationship betweenthe characteristics of the clusters and the various variables included in the survey. In the case of quantitativevariables (cultivated surface, crop-mix, age, etc.), we used analysis of variance (ANOVA), adopting equalityof averages among clusters as the null hypothesis. The Chi-square test (contingency tables) was used for thecategory variables (sex, educational level, etc.). v2 also tests the null hypothesis of equality of frequenciesamong the various clusters. The results confirmed that there were significant differences that justify distinc-tion between clusters.

For each cluster the multi-criteria methodology already described was employed to calculate the differentweighting vectors. For this purpose the basic models were built in a particular way for each type of agent,considering technical coefficients and constraints calculated as the average of the results obtained from thequestionnaires for the farmers in each cluster. The results of this procedure are also shown in Table 2.

It is worth noting, first, that there are important differences among the relative weights considered by thedifferent groups, demonstrating the existence of large disparities in the shape of the MAUFs that eachgroup tried to optimise (i.e. differences in behaviour). Secondly, it is also worth pointing out that for allcases the weighting obtained for the TL attribute was zero. This does not necessarily mean that farmersignore the objective of maximising their leisure time and minimising management complexity. Indeed, giventhe lack of conflict between the objective of minimising risk and that of minimising total labour, it is pos-sible that the weights assigned to the VAR attribute actually include the importance given by the farmers toboth objectives, min. VAR and min. TL, taken together (for further details see Berbel and Rodrıguez (1998)and Gomez-Limon and Riesgo (2004)).

Table 1General features of the seven irrigated areas analysed

Features CR CanalesBajo Carrion

CR CanalMargen Izda.del Porma

CR CanalGeneraldel Paramo

CR Canaldel Pisuerga

CR Canalde San Jose

CR de la Presade la Vegade Abajo

CR Virgendel Aviso

Province Palencia Leon Leon Palencia/Burgos Zamora/Valladolid Leon ZamoraAltitude (m a.s.l.) 775–825 750–830 800 760–830 645 800 645Average rainfall 527–448 732 498 427 364 498 364Irrigated surface (ha) 6588 12,386 15,554 9392 4150 1403 1870Number of landowners 899 3500 5950 2715 1406 1500 820Number of farmersa 137 251 488 223 166 82 118Average irrigated

farm area (ha)48.0 49.4 31.9 42.2 25.0 17.1 15.8

Water allotment(m3/ha Æ year)

5950 6250 6587 8100 8192 6105 8021

Irrigation system Surface irrigationand sprinklers onlyfor sugar-beet

Surface irrigationand sprinklersonly for sugar-beet

Surface irrigationand sprinklersonly for sugar-beet and beans

Surface irrigationand sprinklersonly for sugar-beet and alfalfa

Surfaceirrigation andsprinklers onlyfor sugar-beetand alfalfa

Surface irrigationand sprinklersonly for sugar-beet

Surfaceirrigationnd sprinklersonly forsugar-beet

Water tariff paid(€/ha Æ year)

40.06 66.10 85.34 60.59 85.94 36.06 Variable

Age of irrigation system 30 years 20 years 50 years 30 years 40 years 40 years 40 yearsIrrigation system

efficiency65% in surfaceirrigation and70% in sprinklersirrigation

75% in surfaceirrigation and80% in sprinklersirrigation





60% insurfaceirrigationand 65%in sprinklersirrigation

Number of interviews 52 54 61 32 68 34 66Number of clusters 4 4 2 3 3 3 3

a The irrigated farms are partly composed by farmer�s owned land and partly by leased land. This fact explains that the number of owners is bigger than the number offarmers.

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Table 2Main features of types of agent

Irrigated area No. Name % / No.farmers

% / Totalsurface

Main crops Weights

wTGM wVAR wTL

CR Canales Bajo Carrion 11 Part-time farmers 22.9 17.8 Maize, winter cereals and sugar-beet 0.724 0.276 0.00012 Livestock Farmers 21.3 24.2 Maize, alfalfa and winter cereals 0.465 0.535 0.00013 Small commercial farmers 27.8 8.9 Maize, alfalfa and winter cereals 1.000 0.000 0.00014 Risk-averse farmers 27.8 49.2 Winter cereals and maize 0.671 0.329 0.000

CR Canal Margen Izda.del Porma

21 Large-scale commercial farmers 40.7 45.8 Maize 1.000 0.000 0.00022 Part-time farmers 5.6 5.4 Winter cereals and maize 0.302 0.698 0.00023 Risk-averse farmers 16.7 16.6 Winter cereals, Maize and sunflowers 0.479 0.521 0.00024 Livestock farmers 37.0 32.1 Maize and alfalfa 0.852 0.148 0.000

CR Canal del Paramo 31 Risk-neutral farmers 72.0 69.6 Maize, sugar-beet and beans 1.000 0.000 0.00032 Risk diversification farmers 28.0 30.4 Maize, winter cereals and sugar-beet 0.785 0.215 0.000

CR Canal del Pisuerga 41 Conservative farmers 20.6 12.5 Winter cereals and alfalfa 0.000 1.000 0.00042 Large-scale commercial farmers 35.3 57.5 Winter cereals, sugar-beet and maize 0.425 0.575 0.00043 Livestock farmers 44.1 38.2 Alfalfa, winter cereals, sugar-beet

and maize0.623 0.377 0.000

CR Canal de San Jose 51 Risk diversification farmers 35.3 39.6 Maize, winter cereals and alfalfa 0.544 0.456 0.00052 Young commercial farmers 35.3 40.3 Maize and sugar-beet 0.955 0.045 0.00053 Maize growers 29.4 20.1 Maize 1.000 0.000 0.000

CR Presa de la Vega de Abajo 61 Small-scale elderly farmers 20.6 11.5 Maize and winter cereals 0.967 0.033 0.00062 Sugar-beet growers 29.4 31.4 Maize and sugar-beet 1.000 0.000 0.00063 Young commercial farmers 50.0 57.1 Maize, sugar-beet and winter cereals 1.000 0.000 0.000

CR Virgen del Aviso 71 Commercial farmers 45.5 23.2 Maize, sugar-beet and winter cereals 1.000 0.000 0.00072 Risk diversification farmers 24.2 33.4 Maize, winter cereals and sugar-beet 0.448 0.552 0.00073 Conservative farmers 30.3 43.4 Winter cereals, sunflowers and maize 0.197 0.803 0.000

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4. Results of water market simulation

This section analyses the results obtained by the simulations of alternative scenarios. For this purpose weset a base scenario that considered the existence of a water market (scenario ‘‘with market’’) in which waterexchanges are permitted. First, we analyse the economic and social impacts that would imply a reduction inwater availability for the whole basin for this base scenario, parameterising water allotments (wai). The re-sults of this scenario are compared with those obtained in the case where a water market system is not con-sidered (scenario ‘‘without market’’), in order to identify such improvements in economic efficiency(measured as the aggregated gross margin generated in the whole basin) and the social impact (consideredas the amount of labour demanded in all the irrigated areas studied) as the introduction of this institutioninvolves.

In addition to changes in availability of water, we simulate various possibilities related to transactioncosts and water pricing, also measuring their influence on the volume of water transferred, the aggregatedgross margin and the total demand for labour.

4.1. Influence of water availability at basin level

Although the Duero valley does not display great oscillations in water availability, it is necessary to indi-cate that water scarcity problems are liable to occur every seven or eight years. This makes it interesting toexamine the effects that a reduction in water availability would have on the amount of water transferredunder the ‘‘with market’’ scenario. To this end, we modified constraints (10b) and (10c) of the equilibriummodel substituting the following expressions:
X
i

Xc

awiwdcX ci 6

Xi

awikwaisi; ð10b:bisÞ

Xc

wdcX ci þX

j

WSij �X

j

WBij 6 kwaisi; ð10c:bisÞ

where the initial allotments (wai) are multiplied by a scarcity coefficient k that ranges between 0 and 1, insuch a way that the resources which agents could hypothetically dispose of are modified. For instance, whenk takes the value 1, the amount of water is equivalent to the theoretical allotment, whereas if coefficient ktakes the value 0, the availability of water is zero. Thus, by parameterising k, different equilibrium solutionsare reached, allowing us to obtain curves that reflect the path of the main variables when the availability ofirrigation water is progressively reduced.

At this point it may be worth explaining the procedure adopted to identify the optima for this non-linearmodel. In order to solve this model we used the solver CONOPT, run over GAMS software (Brooke et al.,1998). This solver produces only ‘‘local’’ optima. In order to deal with this limitation, we have paid specialattention to the starting values for model solving and have carefully validated the solutions obtained.

We fed the first run of the model (for k = 0.00) with an starting solution equal to the observed data(gathered in a year with full availability of water allocations—k = 0.00). The solution obtained in this firstrun (‘‘local’’ optimum) was then used as the starting solution in the next run (for k = 0.01), and so on. All‘‘local’’ optima obtained in this way were subsequently validated, first by checking their logical coherence,and secondly, by the opinion of a panel of experts that confirmed the results as ‘‘reasonable’’ and ‘‘believ-able’’. Thus, although the results reached are formally local optima only, we are confident enough to con-sider them as the ‘‘true’’ optima of the model solved.

Fig. 1 shows the variation in the volume of water transfers (line ‘‘TC0’’) and the evolution of total re-source consumption (line ‘‘water consumption’’) as k varies. In the absence of water scarcity (k = 1), thetotal consumption of water reaches 362 hm3, with 71 hm3 of this volume (19%) being bought and sold

Fig. 1. Impact of water availability on transfers.


on the market. When water availability is reduced (k diminishes), it can be seen that market transfers ofwater rise until they reach a peak that corresponds to a value of k of 0.5. In this situation the total volumeof water transferred is 117 hm3, equivalent to 64% of the water consumed in this particular situation(181 hm3). From that point on, because of the increasing scarcity of water (k values lower than 0.5), waterflows in the market fall in absolute terms until they reach zero.

A more detailed analysis of these results requires several additional comments. First, it is necessary topoint that the evolution of transfers reflects the aggregated effect of increasing scarcity on individual deci-sion making (crop mix). In fact, farmers must modify their cropping patterns due to water shortages byreducing the area devoted to crops with greater water requirements (those that produce greater profits),or purchase additional water on the market. In both cases the final result is a reduction in farmers� utility,because both possibilities imply a decrease in farmers� TGM.

In this sense, due to the utility maximisation behaviour of the farmers, the market allows water to bereallocated to uses that generate greater utility. Since the utility that this input generates is determinedby both ‘‘objective’’ (soil productivity and another structural features of farms) and ‘‘subjective’’ (TGMweight) aspects, water transfers move in the direction of more productive irrigation areas and farmers witha higher commercial profile, that is, to those who obtain greater increases in utility by the increase in profits(producers with greater values of wTGM).

This aspect is confirmed by observing the behaviour of different types of agents in the market, as shownin Table 3. We can observe the buyer (B) or seller (S) behaviour of the agents in four water availability sit-uations. From these non-aggregated results it can be deduced that the transfers do indeed go where waterprovides a greater utility, that is, preferentially towards the type of agents with better climatic and soil con-ditions (greater crop yields) and for those with greater wTGM values.

The above table shows that it is interesting to emphasise another element that determines the directionof water flows: the geographic localization of farms. As an adequate infrastructure for water transportdoes not exist in this basin, the only real possibility to transfer water is by using natural stream flows.For this reason irrigation areas located downstream (in our case the Canal de San Jose or Virgen delAviso districts) have a certain comparative advantage, because of their ability to buy water from all dis-tricts. This circumstance is not shared by upstream areas, where the farmers have fewer possibilities ofbuying water (smaller supply available). This circumstance can also be confirmed for the results shownin Table 3.

Table 3Position of type of agents in the market

Irrigation area No. Coefficient of scarcity (market price)

k = 1.00 k = 0.75 k = 0.50 k = 0.25Pm = 0.005 €/m3 Pm = 0.020 €/m3 Pm = 0.060 €/m3 Pm = 0.150 €/m3

CR Canales Bajo Carrion 11 B B NS NS12 NS NS B B13 B B B B14 NS NS S S

CR Canal Margen Izda. del Porma 21 B S S S22 S S B B23 S S B B24 B S S S

CR Canal del Paramo 31 B B B B32 B B B B

CR Canal del Pisuerga 41 S S S S42 S S S S43 B B B S

CR Canal de San Jose 51 S S B B52 S S B B53 NS NS B B

CR Presa de la Vega de Abajo 61 S S S S62 B B S S63 S S S S

CR Virgen del Aviso 71 NS NS B B72 S B B B73 S S B B

B: buyer, S: seller, NS: non-significant.


As already mentioned, if we consider that farmers maximise their respective utility functions, the marketwill reach equilibrium when the marginal utility of water for all users is equal to market price. Fig. 2 showsthe evolution of this water market price for different values of the coefficient k.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Wat

er p

rice

(/m

3 )

Water market pricecoefficient of scarcity

Fig. 2. Water market price.


As expected, increasing scarcity of water increases marginal utility for all users and as a result marketprice rises. The price of water rises from 0.005 €/m3 for the normal hydrological situation (k = 1), till0.29 € for the last cubic metre of available resource in the basin for agricultural uses (k = 0).

Another aspect to be pointed out is the result obtained for the normal water supply situation (k = 1),which indicates that water transfers could reach 19% of the total resources consumed. Nevertheless, itcan be confirmed this does not happen in real life, where no transfers are made. The causes of this marketparalysis in the Duero basin, as in other Spanish catchments, are several. The most important one nowa-days is the lack of a complete set of regulations that properly defines the practical rules that must governwater markets. In particular, there has been a long delay in the production of a definition of ‘‘consumptionquotas’’ (water traditionally consumed) for individual irrigation areas, that determines the maximumamount of water that rights holders can lease, despite the quantity of water rights that they have legallyregistered. Until these values are published, the administrative bodies of the basin cannot approve agricul-tural water transfers. Other causes that tend to make market operations difficult are:

• The legal insecurity that the water sales produce. The cause of this insecurity is that sales could be under-stood by the water management agency as evidence of farmers� �surplus� in water availability, so that irri-gators� water endowment could be cut in the future.

• Farmers tend to regard water as a common good. Historically water has been managed as a �common�,and has been used by sharing the available stocks between irrigators depending on aggregated needs.This is why nowadays water for irrigation is still judged by farmers as a non-negotiable good, and thusits trade is not considered correct in �ethical� terms within such rural communities.

Fig. 3 shows the evolution of the aggregated gross margin (sum of total gross margin of all the agentsproperly weighted) when the coefficient of scarcity is parametrised. This aggregated variable can be used asan indicator of total economic efficiency. Thus, it can be clearly observed that the efficiency produced by theintroduction of a water market (line ‘‘TCo’’) is greater than that generated by the scenario ‘‘without mar-ket’’. It can be verified that when there is no shortage of water, the aggregated gross margin ‘‘with market’’reaches 60 million euros, 18% more than the simulation with the scenario ‘‘without market’’, where only 49million euros are obtained. This improvement in economic efficiency also occurs for all possible values of k(shortage situations), with increases in the aggregated margin ranging from 12% to 20%.

30

35

40

45

50

55

60

65

70

75

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Agg

rega

ted

gros

s m

argi

n(m

illio

n of

eur

os)

TCo TC=0TC=2TCo Without market

Coefficient of scarcity

Fig. 3. Impact of water market on aggregated gross margin (economic efficiency).


The reason for these significant gains in global efficiency is that a water market permits different aggre-gated crop mixes (production decision making in the aggregate) compared with the ‘‘without market’’ sce-nario. In fact, for every value of k, the scenario ‘‘with market’’ devotes more area to the more profitablecrops, which have greater demands for water and labour (vegetables, sugar-beet or maize) than to moreextensive irrigation crops (winter cereals), which are less profitable and have smaller needs for water andlabour inputs. Consequently, although the irrigated area devoted to rain-fed crops (the least profitableones) is increased in order to balance global water balance requirements, the final result is clearly positive,and the aggregated profit at basin level rises. In this sense it should be noticed that output and inputchanges are assumed not to have market/price impacts. This is a reasonable assumption considering, first,the large dimension of the whole European market where this irrigated area is located, and second, the kindof crops considered, most of them non-perishable (storable crops), that allows an easier adjustment insidethe existing markets.

Due to the positive correlation between gross margin and labour input, the increase in the economic re-gional efficiency caused by the introduction of water markets also increases agricultural employment. Fig. 4shows the effects on labour demand for the two scenarios discussed above when coefficient k is para-metrised. First, as we can observe a fall in the aggregated labour demand as water availability drops in bothscenarios. Secondly, we can see how the ‘‘with market’’ scenario has a greater demand for agricultural la-bour than the ‘‘without market’’ scenario, with increases ranging from 20% to 45%. This water demandpolicy instrument is thus adequate from a social perspective, since it can improve the present under-employ-ment and high seasonability situations, favouring the population stability in rural districts.

4.2. Influence of transaction costs

A second group of simulations were performed, in which various levels of transaction costs were consid-ered, in order to compare the results achieved with initial costs (already introduced in Section 2.4; tc = tc0)with those obtained for a situation with no transaction costs (tc = 0) and with another situation in whichthese costs were doubled (tc = 2tc0). These simulations enabled us to determine the influence of the level oftransaction costs on the volume of transfers achieved by the market.

Fig. 1 shows the changes in the volume of water transfers as a result of parameterising k and for the dif-ferent transaction costs scenarios discussed above. Results indicate a similar path for all cost scenarios,

0

500

1000

1500

2000

2500

3000

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Tota

l lab

our d

eman

d(th

ousa

nd h

ours

)

TC=0Without marketTC=2TCo

TCo

Coefficient of scarcity

Fig. 4. Impact of water market on total labour use (social impact).


reaching maximum transfers when k = 0.5 in every case. However, we must point out that, as is logical, thequantity of transfers decreases when transaction costs are higher. For example, water transfers at maximumlevel with no costs exceed the initial cost situation by 8%, whereas when transaction costs are doubled,transfers are reduced by 25%.

The same trend is also reflected in aggregated gross margin and total labour demand levels (Figs. 3 and4). For different values of k, the aggregated margin without transaction costs rises to about 15% above theaggregated margin with initial costs, with an average increase in total demand for labour of 15%, whereaswith a double level of costs the aggregated gross margin is on average 16% below the initial one, with anoverall loss of labour of about 17%.

These results show the potential advantages of improving the legal framework that establishes the watermarket in order to keep transaction costs as low as possible. Only under such a condition can the economicand social benefits be optimised in a market situation.

4.3. Water markets and water tariffs

As is well known, the European Water Framework Directive requires the introduction of water pricingas an instrument for managing and controlling the growing demand for water. We can thus envisage a fu-ture scenario of increasing irrigation water prices through volumetric tariffs, rather than on the basis of irri-gated area as now. Such a scenario has been simulated in this paper in order to evaluate the effects that theintroduction of different irrigation water tariffs would generate.

The simulation of these water pricing scenarios requires a change in expression [10], which would thenappear as follows:

TableResult

Coeff.

WaterAggreTotal

MaxX

i

awiUið~X iÞ¼X

i

awi wTGMi kTGMi TGMið~X iÞþX

j

WP� tcij

2

� �WSij

h i((

�X

j

WPþ tcji

2

� �WBij

h i�Twaisi

)��wVARi kVARi VARið~X iÞ�wTLi kTLi TLið~X iÞ

);

ð10bisÞ

where T is the tariff paid by users in €/m3. The simulation considered four water availability situations andtwo values for T: 0.03 €/m3 and 0.06 €/m3. The results are shown in Table 4.

As might be expected, the introduction of a volumetric tariff reduces water consumption and watertransfers, with the result that profits and demand for labour decrease, as the above table shows. In the caseof T = 0.03 €/m3, transfers decrease by between 4% and 18%, depending on the value of k, and between26% and 37% for T = 0.06 €/m3. This reduction in the volume of water transferred would be accompaniedby a reduction in the aggregate gross margin, and therefore in the amount of labour demanded at basinlevel in comparison with the T = 0 situation. The average reductions in gross margin compared to the‘‘no tariff’’ situation are 10% and 27% for 0.03 and 0.06 €/ha respectively, resulting in average falls of7% and 21% in the total labour input.

4s with different water tariffs

of scarcity (k) T = 0.00 €/m3 T = 0.03 €/m3 T = 0.06 €/m3

1.00 0.75 0.50 0.25 1.00 0.75 0.50 0.25 1.00 0.75 0.50 0.25

transfers (hm3) 71.1 102.8 117.2 44.3 68.3 85.3 95.4 41.4 50.6 64.5 86.3 28.2gated gross margin (106 €) 60.0 50.5 48.3 47.4 52.2 46.3 44.7 42.2 39.0 36.1 42.1 31.7labour (103 h) 2110 1519 979 662 1870 1444 950 601 1644 1267 881 416


5. Conclusions

Two important conclusions can be drawn from this research. From the methodological point of view, isworth emphasising the advantages of the MCDM approach. Indeed, as the validation of the models thatsimulate the producers� individual behaviour (models (8)) has confirmed, the individual productive deci-sions they take (crop mix and input use) cannot be explained by assuming profit maximisation behaviourand considering only differences in their structural characteristics (climate, soil, etc.) and input availability(machinery, production quotas, etc). In order to correctly simulate the behaviour of these decision-makersit is necessary consider the different utility functions that they use, within a multi-criteria framework (seeArriaza and Gomez-Limon (2003) or Gomez-Limon and Riesgo (2004)). Assuming that it is necessaryto analyse farmers� decision making within the MCDM paradigm, is evident that water use (allocationto different crops and/or its transfer in the market) depends on the utility that this input offers them (con-tribution to MAUF value: achievement of the various objectives that farmers try to simultaneously opti-mise), and not only on its productivity (profit generation). In this sense we think that water marketmodelling is more realistic when we assume that water reallocations move this resource from the uses thatgenerates a relatively low level of utility towards those that generate greater utility, until an equilibriumpoint (i.e. fixing a market price for water) is reached, at which the marginal utilities provided by waterto all users (agents� ‘‘type’’ marginal utilities) are identical and equal to the marginal utility provided bywater to the whole market (aggregated marginal utility). This utilitarian approach supposes an extensionof classic economic theory, which assumes, as a particular case, that only profit maximisation is taken intoaccount as a unique management criterion, and that this defines market equilibrium when the value of themarginal product for all users is equal to the market price.

In any case, it should be also pointed out that the implementation of the methodology proposed in thispaper is based on certain assumptions (mainly the consideration of additive and linear MAUFs) that couldbe considered as important limitations on simulations of farmers� actual behaviour. Thus, further effortsshould be made in the future in order to improve operational modelling of MAUFs.

With regard to the case study discussed here, the interest of the mathematical model built for betterunderstanding and modelling of water markets in the real world is worth emphasising. On the basis ofour results, some interesting practical conclusions can also be drawn, the most important of which is thepotential of water markets to act as a demand policy instrument to improve economic efficiency and agri-cultural labour demand, particularly in periods of water scarcity. Our results confirm this positive impactfrom the economic and social points of view. These gains are due to transfers being made to those produc-ers with more highly commercial profiles (greater wTGM), enjoying greater competitive advantages (favour-able soil and climate conditions) and better geographic locations (downstream).

It is also worth remembering that achieving the positive impacts discussed here would require an appro-priate legal and social framework. In fact, the optimum transfer volume, as obtained from our model, willonly be obtained if enforceable regulations can ensure public control of externalities without puttingbureaucratic difficulties in the way of achieving effective transactions. For this purpose some measuresshould be taken in order to define market structures with minimum transaction costs. In this sense, theestablishment of transfer agencies could be useful; not only ‘‘bank’’ type agencies such as Spanish law estab-lishes for situations of exceptional shortage, but also agencies of the ‘‘stock exchange’’ type, which would bepublic centres in which users could resent their individual offers of and demands for water, which wouldensure that all transactions would be automatically made at competitive prices.

It would be more difficult to change the social framework, as pointed out above. In fact, as haspreviously been demonstrated (Garrido et al., 1996; Ortiz and Cena, 2001), irrigation water in Spainhistorically has been regarded as a common good, with the result that most farmers still believe that thisresource should not be exchanged inside a market environment (social values of water for irrigation mustnot be valued in monetary units). This attitude to irrigation water is even included in the printed water


management regulations, that establish sharing criteria that exclude any possibility of market-based ex-changes among irrigators. Therefore, in addition to the changes required in the internal regulations ofthe irrigation districts that would allow water markets to be operated, a slow evolution of farmers� mental-ity is required, in the direction of regarding water like any another economic good and, consequently,exchangeable in the market. Only when the prejudices of irrigation users against this institution have beenovercome will markets operate efficiently, as we have supposed them to do in the model developed here.

Finally, it should be noted that this paper is only a first approximation to modelling irrigation water mar-kets through the MCDM paradigm. Additional developments would be necessary within this area of knowl-edge in order to improve the modelling of the agronomic (e.g. the introduction of water and other inputproduction functions, the consideration of alternative irrigation systems, etc.) and hydraulic (e.g. waterrun-off recycling possibilities) aspects of the real world, that we have significantly simplified in this study.

Acknowledgments

Thanks are due to the anonymous reviewers of this paper, whose comments on possible methodologicalweaknesses led to improvements in the paper. The research was co-financed by the Spanish Ministry of Sci-ence and Technology (research project LEYA, REN2000-1079-C02-02), the Regional Government of Cas-tilla y Leon (Consejerıa de Educacion y Cultura research project MODERNA, UVA037/02) and theFundacion Centro de Estudios Andaluces (centrA:).

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Multi-criteria modelling of irrigation water market at basin level: A Spanish case study

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