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

European Journal of Operational Research 173 (2006) 313–336 www.elsevier.com/locate/ejor

O.R. Applications

Multi-criteria modelling of irrigation water market at basin level: A Spanish case study Jose´ A. Go´mez-Limo´n a

a,*

, Yolanda Martı´nez

b

Department of Agricultural Economics, E.T.S.II.AA. Palencia, University of Valladolid, Avda. de Madrid 57, 34.071 Palencia, Spain b Department of Economic Analysis, University of Zaragoza, Gran Via 2-4, 50004 Zaragoza, Spain Received 19 January 2004; accepted 16 December 2004 Available online 13 February 2005

Abstract This paper develops a multi-criteria methodology to simulate irrigation water markets at basin level. For this purpose it is assumed that irrigators try to optimise personal multi-attribute utility functions via their productive decision making 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 a solution that maximises aggregate welfare, which is quantified as the sum of the multi-attribute utilities reached by each of the participating agents. This methodology has been empirically applied for the Duero Basin (Northern Spain), finding that the implementation of this economic institution would increase economic efficiency and agricultural labour demand, 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 of this 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 by irrigated farms, which account for 80 per cent of national water consumption (Ministry of the Environment, 2000). The apparently poor management of water in Spanish irrigated areas has served as an *

Corresponding author. Tel.: +34 979 108341; fax: +34 979 108301. E-mail address: [email protected] (J.A. Go´mez-Limo´n).

0377-2217/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2004.12.009

314

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

argument for the implementation of demand water policies as an essential solution to this problem. Such demand policies should offer incentives for water conservation and resource reallocation in the direction of more value-added uses (Thobani, 1997). In this sense, the Spanish authorities have recently introduced a new 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 decentralised manner, the allocation of water resources among its potential users and to reduce the effects of water scarcity. Thus, the main characteristic that justifies the introduction of water markets is its ability to reallocate water among various uses toward those with more value-added potential, while promoting more 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 management (allocation) of water has hitherto demonstrated. According to the literature, market institutions make it possible to achieve water allocation efficiency better than via of its alternatives, thus maximising social welfare (Vaux and Howitt, 1984; Howe et al., 1986; Rosegrant and Binswanger, 1994; Hearne and Easter, 1995; Dinar et al., 1997). Nevertheless, it is worth starting an analysis of water markets by properly conceptualising this economic instrument. In this sense, water markets can be considered as being similar to any institutional framework that allows rights holders, following some established rules, to give them voluntarily to another users in exchange for an economic compensation. As this definition points, the water markets that can be developed in 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 determine a set of variables that define their basic characteristics, allowing the specific peculiarities of water management 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 the Water Act (Act no. 46/1999), the development of which is discussed in article 61 bis. In short, among the different alternative systems of water use rights transfers, Spanish legislation has opted to limit these transactions 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, in order to analyse the economic impact (increase in economic efficiency through measurement of profits) and social impact (change in demand for labour by the agricultural sector) that the effective application of this economic instrument would generate. For this purpose we have developed a methodology within the MultiCriteria Decision Making (MCDM) paradigm, based on the differences in the behaviour of irrigators with regard to the productive decisions that they take on their farms (crop mix decisions) and thus in the use of agricultural inputs such as irrigation water. With this new approach we propose a mathematical programming model that simulates the market equilibrium for different scenarios of water availability, transaction costs and water prices, quantifying for each case the socio-economic impacts identified above. This approach 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 on which the multi-criteria model employed in the simulations is based, while the third section presents the case study area (Duero basin). The fourth section describes the most important results. Finally, the last part of the paper offers some concluding remarks.

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

J.A. Go´mez-Limo´n, Y. Martı´nez / 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 efficiency 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 simulate markets in the Guadalquivir Valley. The work of Arriaza et al. (2002) that simulates a spot water market in the same basin should also be mentioned. This last paper introduces as a novel element the assumption of considering 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 implementation of this economic instrument would bring moderate improvements to the allocation efficiency of the resource in the basin analysed. Although our work has been influenced by the studies mentioned above, its major contribution is its methodological 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 in terms of profit maximisation (or an utility function maximisation where profit is the only attribute), in accordance with a classical economic theory (or of the EUT) hypothesis. According to this approach, farmers would use (via irrigation) or not (via sales) their water allowances depending on the productivity (marginal 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 be expected to move water from lower to higher marginal productivity uses. Thus, farmers could trade their water use rights and sell them to the point at which the marginal productivity of water equals its market price, thus improving water allocation efficiency. We have assumed as starting point that, unlike the classical approach, the level of farmers utility is determined 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 utility generated by this resource for these decision-makers, considering the relative importance that farmers assign to each of the different criteria that they try to optimise simultaneously (Go´mez-Limo´n 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 maximisers. According to this principle, the problem of agricultural producers could be adequately modelled by 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 maximiser assumption and including higher moments of the expected profit. However, EUT has been criticised for limiting its application to a single attribute: the pay-off (or wealth). Many authors have shown the complexity of the farmers decision-making process through empirical studies that have demonstrated that they consider more than one attribute in their utility functions: e.g. Harman et al. (1972), Gasson (1973), Smith and Capstick (1976), Harper and Eastman (1980), Kliebenstein et al. (1980), Patrick and Blake (1980) and Cary and Holmes (1982). More recent work of Berbel and Rodrı´guez (1998), Costa and Rehman (1999), Willock et al. (1999) and Solano et al. (2001) is also of interest. All these studies suggest that farmers decision-making processes are driven by various criteria, usually conflicting ones, related to their economic, social, cultural and natural environment situation, in addition to the expected profit (or higher moments). Such criteria include maximisation of leisure, minimisation of managerial problems, minimisation of indebtedness, 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 appropriate to focus a simulation of water markets within the Multi-Criteria Decision Making (MCDM) paradigm.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

316

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 to Multi-Attribute Utility Theory (MAUT), an approach largely developed by Keeney and Raiffa (1976), in order to overcome the limitations of the single-attribute utility function. The aim of MAUT is to reduce a decision problem with multiple criteria to a cardinal function that ranks alternatives according to a single criterion. Thus, the utilities of n attributes from different alternatives are captured in a quantitative way via a utility function represented mathematically as U = U(r1, r2, . . . , rn), where U is the Multi-Attribute Utility Function (MAUF) and rj are the attributes regarded by the decision-maker as relevant to his decision-making process. The level of achievement of each attribute can usually be expressed mathematically as a function of the ~Þ. Thus, decisions under MAUT are made by maximising U and decision variables, that is, rj ¼ fj ðX responding 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 this approach 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 mathematical features of the utility function. In most cases, additive and linear utility functions have been adopted to simulate farmers behaviour in a multi-attribute framework. The ranking of alternatives is obtained by adding contributions from each attribute. Since attributes are measured in terms of different units, normalisation is required to permit them to be added. The weighting of each attribute expresses its relative importance. Mathematically the related utility function would be n X Ui ¼ wj k j rij ; i ¼ 1; . . . ; m; ð1Þ j¼1

where Ui is the value utility value of alternative i, wj is the weight of attribute j, kj is the factor normaliser of the 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 requirements for the assumption of an additive utility function. According to them, if attributes are mutually utility independent1 the utility function Pbecomes separable (U = f{u1(r1), u2(r2), . . . , un(rn)}) and Q takes either the additive form: U ðr1 ;r2 ;...;rn Þ ¼ ðKwj uj ðrj Þ, or multiplicative form: U ðr1 ;r2 ;...;rn Þ ¼ f ðKwj uj ðr j Þ þ 1Þ  1g=K, P where 0 6 wj 6 1 and K = f(wj). If the attributes are mutually utility-independent and wj ¼ 1, then K = 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 approximations to the hypothetical true function even when these conditions are not satisfied. In Hwang and Yoons words (1981, p. 103): ‘‘theory, simulation computations, and experience all suggest that the additive method yields extremely close approximations to very much more complicated non-linear forms, while remaining far easier to use and understand’’. Once the use of the additive utility function has been justified, we take a further step assuming that the individual attribute utility functions are linear. Although this assumption of linearity is rather strong, and may even be unrealistic (it implies linear utility-indifferent curves or constant partial marginal utility), it can be regarded as a close enough approximation as long as the attributes vary within a narrow range

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

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

317

(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 impact on the ranking of alternatives. Likewise, Amador et al. (1998) have demonstrated how linear and quasi-concave functions yield almost the same results. We therefore adopt this simplification in the elicitation of 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 considering all irrigators as individual operating agents, it is necessary to aggregate these producers in homogeneous groups that include irrigators with similar behaviour related to water use. This paper starts off with the basic idea that farmers behaviour (i.e. water use) is motivated by their productive potentialities (derived from the structural conditions of their farms) and by the relative importance that they attach to particular management criteria, condensed in their respective MAUFs (Go´mez-Limo´n et al., 2003). Thus, the homogeneous groups that have been established in order to constitute types of agents in water market modelling are the result of a double entrance typology, in which operating agents (irrigators) are sorted according to the structural conditions of their holdings and the different weights given to the objectives considered as classificatory variables. The following sections explain the way in which this binomial farm/farmer typology was developed. 2.2.1. Structural diversity of farms Modelling 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 overestimates the mobility of resources among production units, allowing combinations of resources that are not possible in the real world. The final result of these models is that the value obtained for the objective function is always 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 the models fulfil strict criteria regarding homogeneity (Day, 1963): technological homogeneity (i.e. the same possibilities of production, type of resources, technological level and management capacity), pecuniary proportionality (proportional profit expectations for each crop) and institutional proportionality (availability of 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 and climate, and in which the same range of crops can be cultivated and will produce similar yields. Furthermore, the whole set of farms that make up this agricultural system operates the same technology at a similar level of mechanization. Given these conditions, it can be assumed that the requirements regarding technological homogeneity and pecuniary proportionality are basically fulfilled. In view of the existence of efficient capital and labour markets, the constraints included in this system have been limited to the agronomic requirements (crop rotations) and the restrictions imposed by the Common Agricultural Policy (set-aside land and sugar-beet quotas) that are similar for all farms. The requirement 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 program with relatively small problems of aggregation bias. However, it is essential to note that the requirements discussed above are outlined from the point of view of classical economic theory, which assumes that the sole criterion on which decisions are based is profit maximisation. If a multi-criteria perspective is utilised, an additional homogeneity requirement emerges in order to avoid aggregation bias; viz., homogeneity related to choice criteria.

318

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

2.2.2. Diversity of farmers’ MAUFs The experience that has been accumulated in this field leads us to suspect that the decision criteria of farmer homogeneity do not reflect the normal situation in real agricultural systems. In fact, the decision criteria are primarily based on the psychological characteristics of decision-makers, which differ significantly from farmer to farmer. According to this perspective, the differences in decision-making (crop mix) among farmers in the same production area (e.g. an irrigated area) must be primarily due to differences in their objective functions (in which the weightings given to different criteria are condensed), even more than other differences related to the profits of economic activities or disparities in resources requirements or endowments (Go´mez-Limo´n et al., 2003). In order to avoid aggregation bias resulting from lumping together farmers with significantly different objective functions, a classification of all farmers into homogeneous groups with similar decision-making behaviour (similar MAUF) is required. For this issue we have taken the work of Berbel and Rodrı´guez (1998) as our point of departure. These authors have pointed out that for this type of classification the most efficient method is cluster analysis, taking farmers real decision-making vectors (actual crop mix) as the classification criterion. As pointed out above, we can assume that in a homogeneous area, differences in the crop mix among farmers are mainly caused by their different management criteria (utility functions) rather than by other constraints such as land quality, capital, labour or water availability. Thus, the percentage area devoted to each crop can be considered as a proxy for the real criterion and shape of the MAUF. Thus, these percentages can be used as classification variables to group farmers using the cluster technique, as required for our purposes. In this sense, it is also important to note that the homogeneous groups obtained in this way can be regarded as fixed in the short and medium terms. As noted above, the decision criteria are based on psychological features of the decision-makers, which is why they may be regarded as producers structural characteristics. In fact, these psychological features, and thus the criteria, are unlikely to change in the short term. This means that the selection variables chosen allows farmers to be grouped into clusters irrespective of any change in the policy framework (i.e. water market). In other words, once homogeneous groups of producers have been defined on the basis of actual data (crop mix), we can assume that all elements inside each group will behave in a particular way when the policy variables change; that is, crop-mix decisions will be modified in a similar fashion by all farmers within a cluster, although such modifications would differ among the individual groups defined. For a more concrete definition of the cluster analysis performed in this research, we may also note that the farmers were classified by considering the chi-squared distance among actual crop mixes, expressed in percentages, as a measurement of distance, and using the Ward method (minimum variance) as the aggregation 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 internal homogeneity to enable us to consider the average virtual farmers as representative cases of the different types of agent operating in the water market, allowing them to be separately modelled without undesirable bias. 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 farmers additive and linear MAUFs (weights vector) without direct interaction between farmers and the researcher. They show how it is possible to elicit the farmers utility function by observing only the actual crop distribution on weighted goal programming. We adopt this

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

319

methodology in order to assess the utility function of a group of farmers as has previously been done by Berbel and Rodrı´guez (1998), Go´mez-Limo´n and Berbel (1999), Arriaza et al. (2002) and Go´mez-Limo´n et al. (2002). This method may be summarised as follows: ~ (e.g. crop area); fj ¼ fj ðX ~Þ. 1. Each attribute j is defined as a mathematical function of decision variables X These attributes are proposed a priori as the most relevant decision-making criteria used by farmers.In our 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); constant euros of 2000. Therefore, the TGM for each homogeneous group of farmers can be expressed as follows: X TGM ¼ gmc  X c ; ð2Þ c

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 the ~t ½CovX ~c ), where [Cov] is the variance– variance of the TGM (VAR). The risk is thus computed as X c ~ is the crop decision covariance matrix of the crop gross margins during the seven-year period, and X vector.2 (c) Minimisation of the Total Labour input (TL). This objective implies not only a reduction in the cost of this input but also an increase in leisure time and the reduction of managerial involvement (labourintensive crops require more technical supervision). The expression of TL for each homogeneous group considered is obtained in the following way: X TL ¼ lc  X c ð3Þ c

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 would be included as arguments in the MAUFs of the individual clusters of farmers. In any case, it is convenient to point out that these attributes are the most relevant ones a priori, but is not improbable that additional 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 objective when the jth objective is optimised. The main diagonal is the ideal point defined by the individually obtained 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 obtain the pay-off matrices were:

2 It should be noticed that VAR is calculated using current situation data (i.e. without water market and thus with a water price of zero). The same data (current [Cov] matrix) will be used to calculate VAR inside the water market framework to be modelled. We have considered this option because it is assumed that the risk perceived by farmers for any particular crop-mix can be regarded as being constant. Of course, when gmc varies for a modification in water price, the VAR of crop-mixes might change mathematically, but we consider that the risk taken into account by farmers remains the same as in the current situation (baseline risk level). We think this assumption is reasonable in simulations of farmers behaviour, especially when variations in water quantity delivered for a single crop (deficit irrigation) are not considered as an option by the irrigators (Sunding et al., 1997; Schuck and Green, 2001). 3 The methodology has included the criteria more often considered by the literature in multi-criteria modelling for simulating farmers decisions. Opposite, it has not included other hypothetical objectives that are difficult to be modelled through mathematical programming (mainly dealing with psychological variables—e.g. social prestige), although they could be involved in the real MAUFs.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

320

• Land constraint. The sum of decision variables (area devoted to each crop) must be equal to the total area 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 information for each. 3. The following n + 1 system of equations is solved n n X X W j fij ¼ fi ; i ¼ 1; 2; . . . ; n and W j ¼ 1; ð4Þ j¼1

j¼1

where n is the number of a priori relevant objectives, Wj are the weights attached to each objective (the solution), fij are the elements of the pay-off matrix and fi the real values of the observed behaviour of farmers (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 a problem by minimising the sum of deviational variables that find the closest set of weights: n X ni þ p i Min fi i¼1 n n X X s:t:: W j fij þ ni  pi ¼ fi ; i ¼ 1; 2; . . . ; n and W j ¼ 1; ð5Þ j¼1

j¼1

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: n X ~Þ; U¼ wj k j fj ðX ð6Þ j¼1

where kj is a normalising factor. Precisely because this utility surrogate needs to fulfil the requirements of being an additive MAUF, it must range between 0 and 1. For this reason, the following equivalent MAUF expression is used: n X ~Þ  fj fj ðX U¼ wj  : ð7Þ fj  fj j¼1 The utility function (7) is thus normalised by taking the inverse of the difference between the maximum (fj ) and minimum value (fj ) of the different objectives in the pay-off matrix developed for the criteria considered, and by choosing the mathematical expression of the attributes as their utility function, fj(X), minus the minimum (fj ). The method proposed thus provides subrogated utility functions that can be used as an instrument capable of reproducing the observed behaviour of farmers. In this way it is worth mentioning that this technique was 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 be those that the set of farmers in each of these groups always tries to maximise, despite the different possible scenarios to be faced (e.g. different effective endowments of water). This is the key issue that allows a hypothetical water market framework to be simulated.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

321

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 faces every individual irrigator in the short term (i.e. annual crop mix decision) can be simulated through a mathematical programming model whose objective function is the MAUF based on the weights vector (wj) calculated 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 problem proposed would be outlined as follows:4 Max s:t::

~Þ ¼ wTGM k TGM TGMðX ~Þ  wVAR k VAR VARðX ~Þ  wTL k TL TLðX ~Þ U ðX X X c 6 s;

ð8Þ ð8aÞ

c

X

wd c X c 6 wa  s;

ð8bÞ

c

~6~ AX B; X c P 0 8c;

ð8cÞ ð8dÞ

where wTGM, wVAR and wTL are the weights estimated for the different objectives considered by the producer, kTGM, kVAR and kTL are the normalising factors, Xc is the area dedicated to crop c (in ha), s is the 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 explicitly pointed out. The generic set of constraints (8c) is related to the rest of the constraints required to obtain the pay-off matrix (CAP limitations—set-aside requirements and sugar-beet quotas, crop frequencies and rotational requirements and market limitations). If an individual producer were allowed to exchange water through a spot market, the optimisation model exposed would become this: ( ) i X h i   X h tc tc ij ji ~Þ ¼ wTGM k TGM TGMðX ~Þ þ Max U ðX wp  wp þ WSij  WBij 2 2 j j s:t::

X

~Þ  wTL k TL TLðX ~Þ  wVAR k VAR VARðX

X

ð9aÞ

X c 6 s;

c

wd c X c þ

c

ð9Þ

X j

WSij 

X

WBij 6 wa s;

ð9bÞ

j

~6~ AX B;

ð9cÞ

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

ð9dÞ

3

where wp is the market price of water (in €/m ), tcij are the transaction costs of a transfer of water from the irrigator (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 the whole market (interaction between the aggregated supply and demand); all agents operating in the market 4 In order to clarify models specification, in all formula of this paper we have restricted the use of capital letters to identify variables and the use of lower cases letters to distinguish parameters.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

322

are ‘‘price-accepters’’. Since the water price is fixed exogenously, it should therefore be considered as a parameter by a single producers model. In this respect, it is also worth pointing out that the transaction costs are parameters proposed at the starting 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 minimum value (equal to 0.005 €/m3) when the water transactions are carried out inside an irrigated area. When these transfers are carried out among different irrigated areas using natural flows (down stream) as transport paths, the transaction costs take a value of 0.01 €/m3. Finally, for all other cases, where no transport infrastructure exists (any transfer is physically impossible), a maximum value tending to infinity has been considered (in an operative way 10 €/m3 has been used). In all cases, it has been assumed that the respective transaction costs (different tc depending on each particular case) are borne by the seller and by the purchaser 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 of reimbursement and payment (in €) for the water transferred inside the TGM attribute. In this sense it is assumed for the sake of simplification that the presence of the water market does not affect the value obtained for the rest of attributes. The other noteworthy change is the inclusion of sales and purchases of water within the hydraulic balance constraint (9b). Widening the approach taken for the optimisation of an individual irrigator or type of agent i, the market equilibrium reached by interaction of all irrigators can be simulated through the following equation: ( ( i X X X h tcij  ~i Þ ¼ Max awi U i ðX awi wTGMi k TGMi TGMi ðX~i Þ þ WP  WSij 2 i i j ) ) i X h tcji  ~i Þ  wTLi k TLi TLi ðX ~i Þ  WP þ WBij wVARi k VARi VARi ðX 2 j

s:t::

X

ð10Þ 8i;

X ci 6 si

ð10aÞ

c

XX i

X

awi wd c X ci 6

c

wd c X ci þ

X

c

Uoi 6 U i ~i 6 ~ Bi Ai  X

j

X i

WS ij 

ð10bÞ

awi wai si ;

X

WBij 6 wai si

8i;

ð10cÞ

j

8i;

ð10dÞ

8i;

X c P 0; WP P 0; WSij P 0; WBij P 0

ð10eÞ 8c 8i 8j;

ð10fÞ

where awi (agent weights) are the normalising factors used to modulate each agents ‘‘type’’ (i) representativeness. These factors have been equalised, for each case i, to the ratio of the total area represented by the type 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 this case we have considered that every irrigated hectare should be considered as equally important. This is why the main idea underlying coefficient awi (sti/si) is that every hectare should count equally in the final equilibrium solution, despite the cluster or farmer type considered. The objective function ought therefore be 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 need to estimate utility at hectare level (dividing by si clusters area). Furthermore, because it is necessary to take

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

323

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 properly 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 variable in this model. In fact, water price is fixed endogenously inside this market model, being the key variable 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 these cases the search for ‘‘absolute’’ optima is much more demanding and requires a strong knowledge of the system 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 paid special attention to the initial values and the validation of the results. Further details are provided in Section 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 utilities Ui of all agents considered is maximised. Nevertheless, it is worth noting that in order to simulate the market in an appropriate way it was necessary to include two new constraints with regard to the model (9). The first one, noted as (10b), related with the whole water balance, and ensured that the water consumed at basin 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 anybody ‘‘losing’’. In fact, when water exchanges are voluntary, the different agents would only participate in the market as long as the transfers could increase their welfare (an increase in their utility function). For this reason it is necessary that the utility reached by each agent (Ui) in the equilibrium should be superior, or at least equal, to the utility that each one of them had obtained before the reallocation performed by the market 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 imply in any case that the overall utility does not decline as a consequence of trading. Nevertheless, the optima obtained by this approach cannot be considered as best options in terms of the classical economic efficiency and cost–benefit theory, since maximum total utility is not attained because of the set of constraints 10d in the model. In fact, as a result of the operational rules legally imposed on water markets (voluntary transfers 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, therefore, an interesting issue would be the analysis of possible efficiency gains that could be made by considering the implementation of Kaldors compensating principle (transfers from gainers to those who could lose out). This theoretical possibility should allow different ways of compensating/incentivising users to free up more 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 considers only the Spanish part, which occupies most of the basin (almost 78,000 km2). Within this area 555,582 hectares 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 for improving resource allocation efficiency at basin level through the market would lie in transfers within the agricultural sector. Thus, by simulating the irrigation water market alone it should be possible to analyse the lions share of the socio-economic impacts of this institution on the whole basin.

324

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

Irrigation in the Duero valley, as legally established by Spanish law, is divided into irrigated areas, internally 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, covering 51,343 irrigated hectares (9.2% of the total irrigation in the Duero). Table 1 shows the basic features of each CR. In the irrigated areas analysed we surveyed 367 farmers (an average of 52 producers per area) in order to gather the information needed to develop the cluster technique, and subsequently feed the models. Producers to be surveyed were selected at random using the CRs 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 questionnaire. 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, rotational constraints, etc.) were also included. • Socio-economic variables. These variables included the farmers age, family size, educational level, total income (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 were obtained, but also because of the checking process used to validate them (data cross-checking with CRs databases). Using individual crop-mix vectors obtained through the questionnaires, we have implemented the cluster technique explained above in order to generate homogeneous groups (defined as type of agents). Once the dendrogram charts were obtained for each case (irrigated area), they were cut, taking into account the number of groups that we regarded as being suitable for this research (2–4 groups per area). In this way a 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 2 shows their basic features. It is also worth noting that a set of statistical tests was carried out to determine the relationship between the characteristics of the clusters and the various variables included in the survey. In the case of quantitative variables (cultivated surface, crop-mix, age, etc.), we used analysis of variance (ANOVA), adopting equality of averages among clusters as the null hypothesis. The Chi-square test (contingency tables) was used for the category variables (sex, educational level, etc.). v2 also tests the null hypothesis of equality of frequencies among the various clusters. The results confirmed that there were significant differences that justify distinction between clusters. For each cluster the multi-criteria methodology already described was employed to calculate the different weighting 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 the questionnaires 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 the different groups, demonstrating the existence of large disparities in the shape of the MAUFs that each group tried to optimise (i.e. differences in behaviour). Secondly, it is also worth pointing out that for all cases the weighting obtained for the TL attribute was zero. This does not necessarily mean that farmers ignore the objective of maximising their leisure time and minimising management complexity. Indeed, given the lack of conflict between the objective of minimising risk and that of minimising total labour, it is possible that the weights assigned to the VAR attribute actually include the importance given by the farmers to both objectives, min. VAR and min. TL, taken together (for further details see Berbel and Rodrı´guez (1998) and Go´mez-Limo´n and Riesgo (2004)).

Features

CR Canales Bajo Carrio´n

CR Canal Margen Izda. del Porma

CR Canal General del Pa´ramo

CR Canal del Pisuerga

CR Canal de San Jose´

CR de la Presa de la Vega de Abajo

CR Virgen del Aviso

Province Altitude (m a.s.l.) Average rainfall Irrigated surface (ha) Number of landowners Number of farmersa Average irrigated farm area (ha) Water allotment (m3/ha Æ year) Irrigation system

Palencia 775–825 527–448 6588 899 137 48.0

Leo´n 750–830 732 12,386 3500 251 49.4

Leo´n 800 498 15,554 5950 488 31.9

Palencia/Burgos 760–830 427 9392 2715 223 42.2

Zamora/Valladolid 645 364 4150 1406 166 25.0

Leo´n 800 498 1403 1500 82 17.1

Zamora 645 364 1870 820 118 15.8

5950

6250

6587

8100

8192

6105

8021

Surface irrigation and sprinklers only for sugar-beet

Surface irrigation and sprinklers only for sugar-beet

Surface irrigation and sprinklers only for sugarbeet and beans

Surface irrigation and sprinklers only for sugarbeet and alfalfa

Surface irrigation and sprinklers only for sugar-beet

Water tariff paid (€/ha Æ year) Age of irrigation system Irrigation system efficiency

40.06

66.10

85.34

60.59

Surface irrigation and sprinklers only for sugar-beet and alfalfa 85.94

36.06

Surface irrigation nd sprinklers only for sugar-beet Variable

30 years 65% in surface irrigation and 70% in sprinklers irrigation

20 years 75% in surface irrigation and 80% in sprinklers irrigation

50 years 65% in surface irrigation and 70% in sprinklers irrigation

30 years 60% in surface irrigation and 65% in sprinklers irrigation

40 years 65% in surface irrigation and 70% in sprinklers irrigation

40 years 65% in surface irrigation and 70% in sprinklers irrigation

52 4

54 4

61 2

32 3

68 3

34 3

Number of interviews Number of clusters

40 years 60% in surface irrigation and 65% in sprinklers irrigation 66 3

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

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

Table 1 General features of the seven irrigated areas analysed

325

326

Irrigated area

No.

Name

% / No. farmers

% / Total surface

Main crops

Weights wTGM

wVAR

wTL

CR Canales Bajo Carrio´n

11 12 13 14

Part-time farmers Livestock Farmers Small commercial farmers Risk-averse farmers

22.9 21.3 27.8 27.8

17.8 24.2 8.9 49.2

Maize, winter cereals and sugar-beet Maize, alfalfa and winter cereals Maize, alfalfa and winter cereals Winter cereals and maize

0.724 0.465 1.000 0.671

0.276 0.535 0.000 0.329

0.000 0.000 0.000 0.000

CR Canal Margen Izda. del Porma

21 22 23 24

Large-scale commercial farmers Part-time farmers Risk-averse farmers Livestock farmers

40.7 5.6 16.7 37.0

45.8 5.4 16.6 32.1

Maize Winter cereals and maize Winter cereals, Maize and sunflowers Maize and alfalfa

1.000 0.302 0.479 0.852

0.000 0.698 0.521 0.148

0.000 0.000 0.000 0.000

CR Canal del Pa´ramo

31 32

Risk-neutral farmers Risk diversification farmers

72.0 28.0

69.6 30.4

Maize, sugar-beet and beans Maize, winter cereals and sugar-beet

1.000 0.785

0.000 0.215

0.000 0.000

CR Canal del Pisuerga

41 42 43

Conservative farmers Large-scale commercial farmers Livestock farmers

20.6 35.3 44.1

12.5 57.5 38.2

Winter cereals and alfalfa Winter cereals, sugar-beet and maize Alfalfa, winter cereals, sugar-beet and maize

0.000 0.425 0.623

1.000 0.575 0.377

0.000 0.000 0.000

CR Canal de San Jose´

51 52 53

Risk diversification farmers Young commercial farmers Maize growers

35.3 35.3 29.4

39.6 40.3 20.1

Maize, winter cereals and alfalfa Maize and sugar-beet Maize

0.544 0.955 1.000

0.456 0.045 0.000

0.000 0.000 0.000

CR Presa de la Vega de Abajo

61 62 63

Small-scale elderly farmers Sugar-beet growers Young commercial farmers

20.6 29.4 50.0

11.5 31.4 57.1

Maize and winter cereals Maize and sugar-beet Maize, sugar-beet and winter cereals

0.967 1.000 1.000

0.033 0.000 0.000

0.000 0.000 0.000

CR Virgen del Aviso

71 72 73

Commercial farmers Risk diversification farmers Conservative farmers

45.5 24.2 30.3

23.2 33.4 43.4

Maize, sugar-beet and winter cereals Maize, winter cereals and sugar-beet Winter cereals, sunflowers and maize

1.000 0.448 0.197

0.000 0.552 0.803

0.000 0.000 0.000

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

Table 2 Main features of types of agent

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

327

4. Results of water market simulation This section analyses the results obtained by the simulations of alternative scenarios. For this purpose we set a base scenario that considered the existence of a water market (scenario ‘‘with market’’) in which water exchanges are permitted. First, we analyse the economic and social impacts that would imply a reduction in water availability for the whole basin for this base scenario, parameterising water allotments (wai). The results of this scenario are compared with those obtained in the case where a water market system is not considered (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 (considered as the amount of labour demanded in all the irrigated areas studied) as the introduction of this institution involves. In addition to changes in availability of water, we simulate various possibilities related to transaction costs and water pricing, also measuring their influence on the volume of water transferred, the aggregated gross 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 indicate that water scarcity problems are liable to occur every seven or eight years. This makes it interesting to examine the effects that a reduction in water availability would have on the amount of water transferred under the ‘‘with market’’ scenario. To this end, we modified constraints (10b) and (10c) of the equilibrium model substituting the following expressions: XX X awi wd c X ci 6 awi kwai si ; ð10b:bisÞ i

X c

c

wd c X ci þ

i

X j

WSij 

X

WBij 6 kwai si ;

ð10c:bisÞ

j

where the initial allotments (wai) are multiplied by a scarcity coefficient k that ranges between 0 and 1, in such a way that the resources which agents could hypothetically dispose of are modified. For instance, when k takes the value 1, the amount of water is equivalent to the theoretical allotment, whereas if coefficient k takes the value 0, the availability of water is zero. Thus, by parameterising k, different equilibrium solutions are reached, allowing us to obtain curves that reflect the path of the main variables when the availability of irrigation water is progressively reduced. At this point it may be worth explaining the procedure adopted to identify the optima for this non-linear model. 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 special attention 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 first run (‘‘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 ‘‘believable’’. Thus, although the results reached are formally local optima only, we are confident enough to consider 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 resource consumption (line ‘‘water consumption’’) as k varies. In the absence of water scarcity (k = 1), the total consumption of water reaches 362 hm3, with 71 hm3 of this volume (19%) being bought and sold

328

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

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 of water rise until they reach a peak that corresponds to a value of k of 0.5. In this situation the total volume of 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), water flows 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 to point that the evolution of transfers reflects the aggregated effect of increasing scarcity on individual decision making (crop mix). In fact, farmers must modify their cropping patterns due to water shortages by reducing 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 be reallocated to uses that generate greater utility. Since the utility that this input generates is determined by both ‘‘objective’’ (soil productivity and another structural features of farms) and ‘‘subjective’’ (TGM weight) aspects, water transfers move in the direction of more productive irrigation areas and farmers with a 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 shown in Table 3. We can observe the buyer (B) or seller (S) behaviour of the agents in four water availability situations. From these non-aggregated results it can be deduced that the transfers do indeed go where water provides a greater utility, that is, preferentially towards the type of agents with better climatic and soil conditions (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 direction of water flows: the geographic localization of farms. As an adequate infrastructure for water transport does 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 del Aviso districts) have a certain comparative advantage, because of their ability to buy water from all districts. This circumstance is not shared by upstream areas, where the farmers have fewer possibilities of buying water (smaller supply available). This circumstance can also be confirmed for the results shown in Table 3.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

329

Table 3 Position of type of agents in the market Irrigation area

No.

Coefficient of scarcity (market price) k = 1.00 Pm = 0.005 €/m3

k = 0.75 Pm = 0.020 €/m3

k = 0.50 Pm = 0.060 €/m3

k = 0.25 Pm = 0.150 €/m3

CR Canales Bajo Carrio´n

11 12 13 14

B NS B NS

B NS B NS

NS B B S

NS B B S

CR Canal Margen Izda. del Porma

21 22 23 24

B S S B

S S S S

S B B S

S B B S

CR Canal del Pa´ramo

31 32

B B

B B

B B

B B

CR Canal del Pisuerga

41 42 43

S S B

S S B

S S B

S S S

CR Canal de San Jose´

51 52 53

S S NS

S S NS

B B B

B B B

CR Presa de la Vega de Abajo

61 62 63

S B S

S B S

S S S

S S S

CR Virgen del Aviso

71 72 73

NS S S

NS B S

B B B

B B B

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

As already mentioned, if we consider that farmers maximise their respective utility functions, the market will reach equilibrium when the marginal utility of water for all users is equal to market price. Fig. 2 shows the evolution of this water market price for different values of the coefficient k. 0.35

Water price ( /m3)

0.30 0.25 0.20 0.15 0.10 0.05 0.00 1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

coefficient of scarcity Water market price Fig. 2. Water market price.

0.2

0.1

0.0

330

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

As expected, increasing scarcity of water increases marginal utility for all users and as a result market price rises. The price of water rises from 0.005 €/m3 for the normal hydrological situation (k = 1), till 0.29 € 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, it can be confirmed this does not happen in real life, where no transfers are made. The causes of this market paralysis in the Duero basin, as in other Spanish catchments, are several. The most important one nowadays is the lack of a complete set of regulations that properly defines the practical rules that must govern water markets. In particular, there has been a long delay in the production of a definition of ‘‘consumption quotas’’ (water traditionally consumed) for individual irrigation areas, that determines the maximum amount of water that rights holders can lease, despite the quantity of water rights that they have legally registered. Until these values are published, the administrative bodies of the basin cannot approve agricultural 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 understood by the water management agency as evidence of farmers surplus in water availability, so that irrigators 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 thus its 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 agents properly weighted) when the coefficient of scarcity is parametrised. This aggregated variable can be used as an indicator of total economic efficiency. Thus, it can be clearly observed that the efficiency produced by the introduction of a water market (line ‘‘TCo’’) is greater than that generated by the scenario ‘‘without market’’. 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 49 million 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%.

Aggregated gross margin (million of euros)

75 70 65 60 55 50 45 40 35 30 1.0

0.9

TCo TC=2TCo

0.8

0.7

0.6 0.5 0.4 0.3 Coefficient of scarcity

0.2

0.1

0.0

TC=0 Without market

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

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

331

The reason for these significant gains in global efficiency is that a water market permits different aggregated crop mixes (production decision making in the aggregate) compared with the ‘‘without market’’ scenario. In fact, for every value of k, the scenario ‘‘with market’’ devotes more area to the more profitable crops, which have greater demands for water and labour (vegetables, sugar-beet or maize) than to more extensive irrigation crops (winter cereals), which are less profitable and have smaller needs for water and labour inputs. Consequently, although the irrigated area devoted to rain-fed crops (the least profitable ones) 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 input changes 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 kind of crops considered, most of them non-perishable (storable crops), that allows an easier adjustment inside the existing markets. Due to the positive correlation between gross margin and labour input, the increase in the economic regional efficiency caused by the introduction of water markets also increases agricultural employment. Fig. 4 shows the effects on labour demand for the two scenarios discussed above when coefficient k is parametrised. First, as we can observe a fall in the aggregated labour demand as water availability drops in both scenarios. Secondly, we can see how the ‘‘with market’’ scenario has a greater demand for agricultural labour than the ‘‘without market’’ scenario, with increases ranging from 20% to 45%. This water demand policy instrument is thus adequate from a social perspective, since it can improve the present under-employment 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 considered, 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 which these costs were doubled (tc = 2tc0). These simulations enabled us to determine the influence of the level of transaction 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 different transaction costs scenarios discussed above. Results indicate a similar path for all cost scenarios,

Total labour demand (thous and h our s)

3000 2500 2000 1500 1000 500 0 1.0

TCo TC=2TCo

0.9

0.8

0.7

0.6 0.3 0.5 0.4 Coefficient of scarcity

0.2

0.1

TC=0 Without market

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

0.0

332

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

reaching maximum transfers when k = 0.5 in every case. However, we must point out that, as is logical, the quantity of transfers decreases when transaction costs are higher. For example, water transfers at maximum level 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 and 4). For different values of k, the aggregated margin without transaction costs rises to about 15% above the aggregated margin with initial costs, with an average increase in total demand for labour of 15%, whereas with a double level of costs the aggregated gross margin is on average 16% below the initial one, with an overall loss of labour of about 17%. These results show the potential advantages of improving the legal framework that establishes the water market in order to keep transaction costs as low as possible. Only under such a condition can the economic and 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 pricing as an instrument for managing and controlling the growing demand for water. We can thus envisage a future scenario of increasing irrigation water prices through volumetric tariffs, rather than on the basis of irrigated area as now. Such a scenario has been simulated in this paper in order to evaluate the effects that the introduction of different irrigation water tariffs would generate. The simulation of these water pricing scenarios requires a change in expression [10], which would then appear as follows: ( ( i X X X h tcij  ~i Þ ¼ ~i Þ þ Max awi U i ðX awi wTGMi k TGMi TGMi ðX WP  WSij 2 i i j ) ) i X h tcji  ~i Þ  wTLi k TLi TLi ðX ~i Þ ; WP þ  WBij  Twai si  wVARi k VARi VARi ðX 2 j ð10bisÞ 3

where T is the tariff paid by users in €/m . The simulation considered four water availability situations and two 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 water transfers, with the result that profits and demand for labour decrease, as the above table shows. In the case of T = 0.03 €/m3, transfers decrease by between 4% and 18%, depending on the value of k, and between 26% and 37% for T = 0.06 €/m3. This reduction in the volume of water transferred would be accompanied by a reduction in the aggregate gross margin, and therefore in the amount of labour demanded at basin level 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 of 7% and 21% in the total labour input. Table 4 Results with different water tariffs Coeff. of scarcity (k) 3

Water transfers (hm ) Aggregated gross margin (106 €) Total labour (103 h)

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

71.1 60.0 2110

102.8 50.5 1519

117.2 48.3 979

44.3 47.4 662

68.3 52.2 1870

85.3 46.3 1444

95.4 44.7 950

41.4 42.2 601

50.6 39.0 1644

64.5 36.1 1267

86.3 42.1 881

28.2 31.7 416

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

333

5. Conclusions Two important conclusions can be drawn from this research. From the methodological point of view, is worth emphasising the advantages of the MCDM approach. Indeed, as the validation of the models that simulate the producers individual behaviour (models (8)) has confirmed, the individual productive decisions they take (crop mix and input use) cannot be explained by assuming profit maximisation behaviour and 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-makers it is necessary consider the different utility functions that they use, within a multi-criteria framework (see Arriaza and Go´mez-Limo´n (2003) or Go´mez-Limo´n and Riesgo (2004)). Assuming that it is necessary to analyse farmers decision making within the MCDM paradigm, is evident that water use (allocation to different crops and/or its transfer in the market) depends on the utility that this input offers them (contribution to MAUF value: achievement of the various objectives that farmers try to simultaneously optimise), and not only on its productivity (profit generation). In this sense we think that water market modelling is more realistic when we assume that water reallocations move this resource from the uses that generates a relatively low level of utility towards those that generate greater utility, until an equilibrium point (i.e. fixing a market price for water) is reached, at which the marginal utilities provided by water to all users (agents ‘‘type’’ marginal utilities) are identical and equal to the marginal utility provided by water to the whole market (aggregated marginal utility). This utilitarian approach supposes an extension of classic economic theory, which assumes, as a particular case, that only profit maximisation is taken into account as a unique management criterion, and that this defines market equilibrium when the value of the marginal 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 this paper is based on certain assumptions (mainly the consideration of additive and linear MAUFs) that could be considered as important limitations on simulations of farmers actual behaviour. Thus, further efforts should 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 better understanding and modelling of water markets in the real world is worth emphasising. On the basis of our results, some interesting practical conclusions can also be drawn, the most important of which is the potential of water markets to act as a demand policy instrument to improve economic efficiency and agricultural labour demand, particularly in periods of water scarcity. Our results confirm this positive impact from the economic and social points of view. These gains are due to transfers being made to those producers with more highly commercial profiles (greater wTGM), enjoying greater competitive advantages (favourable soil and climate conditions) and better geographic locations (downstream). It is also worth remembering that achieving the positive impacts discussed here would require an appropriate legal and social framework. In fact, the optimum transfer volume, as obtained from our model, will only be obtained if enforceable regulations can ensure public control of externalities without putting bureaucratic difficulties in the way of achieving effective transactions. For this purpose some measures should be taken in order to define market structures with minimum transaction costs. In this sense, the establishment of transfer agencies could be useful; not only ‘‘bank’’ type agencies such as Spanish law establishes for situations of exceptional shortage, but also agencies of the ‘‘stock exchange’’ type, which would be public centres in which users could resent their individual offers of and demands for water, which would ensure 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 has previously been demonstrated (Garrido et al., 1996; Ortiz and Cen˜a, 2001), irrigation water in Spain historically has been regarded as a common good, with the result that most farmers still believe that this resource should not be exchanged inside a market environment (social values of water for irrigation must not be valued in monetary units). This attitude to irrigation water is even included in the printed water

334

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

management regulations, that establish sharing criteria that exclude any possibility of market-based exchanges among irrigators. Therefore, in addition to the changes required in the internal regulations of the irrigation districts that would allow water markets to be operated, a slow evolution of farmers mentality 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 been overcome 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 markets through the MCDM paradigm. Additional developments would be necessary within this area of knowledge in order to improve the modelling of the agronomic (e.g. the introduction of water and other input production functions, the consideration of alternative irrigation systems, etc.) and hydraulic (e.g. water run-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 methodological weaknesses led to improvements in the paper. The research was co-financed by the Spanish Ministry of Science and Technology (research project LEYA, REN2000-1079-C02-02), the Regional Government of Castilla y Leo´n (Consejerı´a de Educacio´n y Cultura research project MODERNA, UVA037/02) and the Fundacio´n Centro de Estudios Andaluces (centrA:).

References Amador, F., Sumpsi, J.M., Romero, C., 1998. A non-interactive methodology to assess farmers utility functions: An application to large farms in Andalusia, Spain. European Review of Agricultural Economics 25 (1), 92–109. Arriaza, M., Go´mez-Limo´n, J.A., Upton, M., 2002. Local water markets for irrigation in southern Spain: A multicriteria approach. The Australian Journal of Agricultural and Resource Economics 46 (1), 21–43. Arriaza, M., Go´mez-Limo´n, J.A., 2003. Comparative performance of selected mathematical programming models. Agricultural Systems 77, 155–171. Ballestero, E., Romero, C., 1998. Multiple Criteria Decision Making and Its Applications to Economic Problems. Kluwer Academic Publishers, Dordrecht. Berbel, J., Rodrı´guez, A., 1998. An MCDM approach to production analysis: An application to irrigated farms in Southern Spain. European Journal of Operational Research 107, 108–118. Brooke, A., Kendrick, D., Meeraus, A., Raman, R., 1998. GAMS. A Users Guide. GAMS Development Corporation, Washington, DC. Calatrava, J., Garrido, A., 2001. Ana´lisis del efecto de los mercados de agua sobre el beneficio de las explotaciones, la contaminacio´n por nitratos y el empleo eventual agrario. Economı´a Agraria y Recursos Naturales 1 (2), 153–173. Cary, J.W., Holmes, W.E., 1982. Relationships among farmers goals and farm adjustment strategies: Some empirics of a multidimensional approach. The Australian Journal of Agricultural Economics 26, 114–130. Costa, F.P., Rehman, T., 1999. Exploring the link between farmers objectives and the phenomenon of pasture degradation in the beef production systems of Central Brazil. Agricultural Systems 61, 135–146. Day, R.H., 1963. On aggregating linear programming models of production. Journal of Farm Economics 45, 797–813. Dinar, A., Letey, J., 1991. Agricultural water marketing, allocative efficiency, and drainage reduction. Journal of Environmental Economics and Management 20 (3), 210–223. Dinar, A., Rosegrant, M.W., Meinzen-Dick, R., 1997. Water Allocation Mechanisms—Principles and Examples. The World Bank, Washington. Dyer, J.S., 1977. On the relationship between goal programming and multiattribute utility theory. Discussion paper 69, Management Study Center, University of California, Los Angeles. Easter, W.K., Hearne, R., 1995. Water markets and decentralized water resources management: International problems and opportunities. Water Resources Bulletin 31 (1), 9–20. Edwards, W., 1977. Use of multiattribute utility measurement for social decision making. In: Bell, D.E., Keeney, R.L., Raiffa, H. (Eds.), Decisions. John Wiley & Sons, Chichester.

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

335

Farmer, P.C., 1987. Testing the robustness of multiattribute utility theory in an applied setting. Decision Sciences 18, 178–193. Fishburn, P.C., 1982. The Foundations of Expected Utility. Reidel Publishing Company, Dordrecht. Garrido, A., 2000. A mathematical programming model applied to the study of water markets within the Spanish agricultural sector. Annals of Operations Research 94, 105–123. Garrido, A., Iglesias, E., Blanco, M., 1996. Ana´lisis de la actitud de los regantes ante el establecimiento de polı´ticas de precios pu´blicos y de mercados de agua. Revista Espan˜ola de Economı´a Agraria 178, 139–162. Gasson, R., 1973. Goals and values of farmers. Journal of Agricultural Economics 24, 521–537. Go´mez-Limo´n, J.A., Berbel, J., 1999. Multicriteria analysis of derived water demand functions: A Spanish case study. Agricultural Systems 63, 49–71. Go´mez-Limo´n, J.A., Riesgo, L., 2004. Irrigation water pricing: Differential impacts on irrigated farms. Agricultural Economics 31, 47–66. Go´mez-Limo´n, J.A., Arriaza, M., Berbel, J., 2002. Conflicting implementation of agricultural and water policies in irrigated areas in the EU. Journal of Agricultural Economics 53, 259–281. Go´mez-Limo´n, J.A., Riesgo, L., Arriaza, M., 2003. Multi-criteria analysis of factors use level: The case of water for irrigation. In: 25th International Conference of IAAE, Durban, South Africa. Hardaker, J.B., Huirne, R.B.M., Anderson, J.R., 1997. Coping with Risk in Agriculture. CAB International, Wallingford, UK. Harman, W.L., Hatch, R.E., Eidman, V.R., Claypool, P.L., 1972. An evaluation of factors affecting the hierarchy of multiple goals. Ohla. Agric. Ext. Stn. Tech. Bull., T-134. Harper, W.H., Eastman, C., 1980. An evaluation of goal hierarchies for small farm operations. American Journal of Agricultural Economics 62 (4), 742–747. Hazell, P.B.R., Norton, R.D., 1986. Mathematical Programming for Economic Analysis in Agriculture. MacMillan Publishing Company, New York. Hearne, R., Easter, K., 1995. Water Allocation and Water Markets. An Analysis of Gains-from-Trade in Chile. The World Bank, Washington. Herath, H.M.G., 1981. An empirical evaluation of multiattribute utility theory in peasant agriculture. Oxford Agrarian Studies 10 (2), 240–254. Horbulyk, T.M., Lo, L.J., 1998. Welfare gains from potential water markets in Alberta, Canada. In: Easter, K.W., Rosegrant, M.W., Dinar, A. (Eds.), Markets for Water. Potential and Performance. Kluwer Academic Publishers, New York. Houston, J.E., Whittlesey, N.K., 1986. Modelling agricultural water markets for hydropower production in the Pacific Northwest. Western Journal of Agricultural Economics 11, 221–231. Howe, C., Goemans, C., 2001. The effects of economic and social conditions on the functioning of water markets: A comparative study of the benefits and costs of water transfers in the South Platte and Arkansas River basins in Colorado. In: EAERE Annual Conference, Southampton, UK. Howe, C., Schurmeier, D., Shaw Jr., W., 1986. Innovative approaches to water allocation: The potential for water markets. Water Resources Research 22 (4), 439–445. Huirne, R.B.M., Hardaker, J.B., 1998. A multi-attribute model to optimise sow replacement decisions. European Review of Agricultural Economics 25 (4), 488–505. Hwang, C.L., Yoon, K., 1981. Multi Attribute Decision Making. Springer-Verlag, New York. Keeney, R.L., 1974. Multiplicative utility functions. Operations Research 22 (1), 22–34. Keeney, R.L., Raiffa, H., 1976. Decisions with Multiple Objectives: Preferences and Value Trade Offs. John Wiley & Sons, New York. Kliebenstein, J.B., Barrett, D.A., Hefferman, W.D., Kirtley, C.L., 1980. An analysis of farmers perceptions of benefit received from farming. North Central Journal of Agricultural Economics 2, 131–136. Lee, T.R., Jouravlev, A.S., 1998. Los precios, la propiedad y los mercados en la asignacio´n del agua. CEPAL (Naciones Unidas), Santiago de Chile. Ministerio de Medio Ambiente, 2000. Libro blanco del agua en Espan˜a, Ministerio de Medio Ambiente, Madrid. Ortiz, D., Cen˜a, F., 2001. Los derechos de propiedad en la agricultura de regadı´o: Su situacio´n frente al cambio institucional. Economı´a Agraria y Recursos Naturales 1 (2), 93–110. Patrick, F., Blake, B.F., 1980. Measurement and modelling of farmers goals: An evaluation and suggestions. Southern Journal of Agricultural Economics 1, 23–56. Randall, A., 1981. Property entitlements and pricing policies for a maturing water economy. The Australian Journal of Agricultural Economics 25 (3), 195–220. Romero, C., Rehman, T., 2003. Multiple Criteria Analysis for Agricultural Decisions. Elsevier Science Publishers, Amsterdam. Rosegrant, M.W., Binswanger, H.P., 1994. Markets in tradable water rights: Potential for efficiency gains in developing country water resource allocation. World Development 22 (11), 1613–1625. Schuck, E.C., Green, G.P., 2001. Field attributes, water pricing, and irrigation technology adoption. Journal of Soil and Water Conservation 56, 293–298.

336

J.A. Go´mez-Limo´n, Y. Martı´nez / European Journal of Operational Research 173 (2006) 313–336

Smith, B., Capstick, D.F., 1976. Establishing priorities among multiple management goals. Southern Journal of Agricultural Economics 2, 37–43. Solano, C., Leo´n, H., Pe´rez, E., Herrero, M., 2001. Characterising objective profiles of Costa Rican dairy farmers. Agricultural Systems 67, 153–179. Spulber, N., Sabbaghi, A., 1994. Economics of Water Resources: From Regulation to Privatization. Kluwer Academic Publishers, New York. Sumpsi, J.M., Amador, F., Romero, C., 1997. On farmers objectives: A multi-criteria approach. European Journal of Operational Research 96, 64–71. Sunding, D., Zilberman, D., Howitt, R., Dinar, A., MacDougall, N., 1997. Modelling the impacts of reducing agricultural water supplies: Lessons from Californias Bay/Delta problem. In: Parker, D., Tsur, J. (Eds.), Decentralization and Coordination of Water Resource Management. Kluwer, New York. Thobani, M., 1997. Formal water markets: Why, when, and how to introduce tradable water rights. The World Bank Research Observer 12 (2), 161–179. Vaux, H.J., Howitt, R.E., 1984. Managing water scarcity: An evaluation of interregional transfers. Water Resources Research 20 (7), 785–992. Weinberg, M., Kling, C.L., Wilen, J.E., 1993. Water markets and water quality. American Journal of Agricultural Economics 75 (2), 278–291. Willock, J., Deary, I.J., Edwards-Jones, G., Gibson, G.J., Mcgregor, M.J., Sutherland, A., Dent, J.B., Morgan, O., Grieve, R., 1999. The role of attitudes and objectives in farmer decision making: Business and environmentally-oriented behaviour in Scotland. Journal of Agricultural Economics 50 (2), 286–303.