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Water Policy 14 (2012) 470–489

The Polluter Pays Principle as a policy tool in an externalitymodel for nitrogen fertilizer pollution

doi: 10.

© IWA

Yaron Fishmana, Nir Beckerb and Mordechai Shechterc

aNatural Resources and Environmental Research Center, University of Haifa, Haifa 31905, Israel

bCorresponding author. Department of Economics and Management, Tel-Hai College, Upper Galilee 12210, Israel.

E-mail: nbecker@telhai.ac.ilcDepartment of Economics and Natural Resources and Environmental Research Center, University of Haifa, Haifa 31905, Israel

Abstract

A policy based on the Polluter Pays Principle (PPP) with respect to the subject of contamination by nitrogenfertilizer is proposed. The mechanism is tested via a cost-efficient input tax policy to supply clean drinkingwater that is subject to contamination by nitrogen fertilizer and to quantify the welfare change due to public con-trol. The paper proposes, for different water scarcity conditions, a policy that supports the legal principle of thePPP, by compensating the victim for the residual pollution not abated by the cost efficient solution, withoutany effects on the efficiency criterion. By introducing a Welfare Change Index (WCI) which measures the signifi-cance of an authority’s intervention in dealing with externalities, we suggest that for relatively high and moderatewater scarcity conditions, welfare change supports public intervention. However, for low scarcity conditions, wel-fare change is low, which discourages public intervention.

Keywords: Economic incentives; Groundwater contamination; Polluter Pays Principle; Water policy tools;Welfare change

1. Introduction and literature review

Nitrogen fertilizer is used as a main input in growing crops because of its ability to enhance agricul-tural productivity. Although agricultural production can be considered a green activity, there is agrowing concern over the negative external effects of the use of nitrogen fertilizer on the environment.One of the major concerns is the growing amount of nitrogen in the soil and its concentration in ground-water. Nitrate concentration in groundwater has increased in Canada, the United States, Europe, Africa,India and other areas of the world as a result of the intensification of farming practices (WHO, 1993;USEPA, 1994; Kapoor & Virarghavan, 1997; EEA, 1999, 2005; Brouwer, 2001; Bartram et al.,2002; Krysanova & Haberlandt, 2002; Brady, 2003; Von Blottnitz et al., 2006; Ibendahl & Fleming,

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Y. Fishman et al. / Water Policy 14 (2012) 470–489 471

2007; Lewandowski et al., 2008). This trend has raised concerns because nitrates in amounts greaterthan the acceptable health standard can be fatal to infants under six months of age (a presumablecause of blue baby syndrome).Contamination of groundwater with nitrogen concentrations above the health standard requires auth-

orities to either treat water before supplying it as drinking water, or to prohibit its use as such (ex postpolicy). Authorities may also choose to impose restrictions on the use of nitrogen fertilizer in agricul-tural activities through command-and-control or economic incentives (ex ante policy) (Moxey et al.,1999; Kampas & White, 2002; Berntsen et al., 2003; Roeseta-Palma, 2003; Pan & Hodge, 2004;Rao & Puttanna, 2006; Almasri, 2007; Lehtonen et al., 2007).Modeling the externality problem of nitrogen fertilizer in the literature has been achieved using a

typical social net benefit function that is formulated in several ways. Yadav (1997) and Conrad &Olson (1992) formulated private net benefits from nitrogen and pesticide application, respectively,minus a social aggregate damage function of groundwater contaminated by these inputs. Other formu-lations consist of private net benefit from nitrogen application minus one of three taxes: anenvironmental tax on the contaminated nitrogen input (Fleming & Adams, 1997; Picazo-Tadeo &Reig-Martinez, 2007); an environmental tax on nitrogen contamination exceeding the acceptablestandard (Fleming et al., 1995); or a tax on total nitrogen leaching (Feinerman & Falkovitz, 1997;Sumelius et al., 2005).Solving nitrogen externalities by using economic incentive policies is thoroughly discussed in the lit-

erature. A direct environmental policy, in the form of a tax on nitrogen fertilizer prices and a pollutiontax in the form of a tax on nitrogen percolation, is presented in Feinerman & Falkovitz (1997) and inHaruvy et al. (1997) and Haruvy et al. (2000). Using economic incentives to deal with the well-knownagricultural problem of non-point source pollution is presented in Xepapadeas (1997); Ribaudo et al.(1999) and Borisova et al. (2005).The agricultural sector is characterized by low profitability (Blank, 1998) and is subject to conditions

of water scarcity (Seckler et al., 1999). These problems raise important questions:

1. What is the most cost-effective policy to supply clean drinking water subject to continued contami-nation: an ex-ante prevention policy or an ex-post treatment policy, or a combination of them both?

2. What is the welfare change resulting from authority intervention and is this welfare changesignificant?

3. How can input taxes be used to deal with externalities from agricultural contamination inputs in thelow profitability agricultural sector?

4. How can we support the legal approach of the Polluter Pays Principle (PPP) without affecting theefficiency criterion? In other words, can a government use a contamination input tax and then usethe tax payments to cover the groundwater contamination treatment costs (a principle of justice),while not affecting the optimal emission level (a principle of efficiency) or becoming subject to stra-tegic behavior by the victims, who can misrepresent their true damage due to private information(Huber & Wirl, 1998)?

5. How do the answers to the above questions change with respect to varying water scarcity conditions?

In this study, we try to give some answers and suggest policies to deal with the above questions. Todo this, we first present a discussion on the PPP policy (Section 2). We then employ an optimizationmodel (Section 3) with a typical social net benefit function – agricultural private net benefit (Section

Y. Fishman et al. / Water Policy 14 (2012) 470–489472

3.1) – minus the cost of treating groundwater contamination (Section 3.2) from the use of nitrogenfertilizer in crop production. We integrate the economic section with an equation of motion fornitrogen concentration in groundwater – specifically modified by Fishman et al. (2009) from ahydrological model based on Mercado (1976, 1980), and Tsur (1991), (presented in Section 3.3)– and reveal the influence of water flow on nitrogen concentrations in groundwater. We obtainsteady state social optimum quantities of nitrogen fertilizer and a concentration of nitrogen ingroundwater to maximize the net present-value social benefit function and identify ex-ante andex-post policies to get this equilibrium (Section 3.4). We then introduce an input tax policymodel that maintains social optimal equilibrium, with a profitable agricultural sector (Section3.5.1). We present the absolute welfare change when moving to social planner equilibrium insteady state and present a Welfare Change Index (WCI) that measures the significance of an author-ity’s intervention in dealing with externalities (Section 3.5.2). This index can help determine,indirectly, the relative importance of the implementation cost of the economic incentives becauseimplementation cost is not usually considered directly in welfare analysis (either in the literature orin this study). Implementation costs may be significant and could result in a Pareto irrelevance situ-ation in which the potential welfare change is swept away by the high implementation costs. Wepresent the empirical results and suggest some policies for various water scarcity conditions by simu-lating different water allocations between irrigation consumption and drinking water consumption(Section 4). Section 5 concludes the paper.

2. Polluter Pays Principle policy

The Polluter Pays Principle (PPP) has many interpretations, and the principle often has differentmeanings in the different contexts in which it appears. Bugge (1996) identifies four versions of thePPP that have found expression in various contexts: (1) an economic principle – a principle of effi-ciency; (2) a legal principle – a principle of ‘just’ distribution of costs; (3) a principle of internationalharmonization of national environmental policy; and (4) a principle of allocation of costs betweenstates. In this paper, we will focus on Bugge’s first two interpretations and suggest a policy that ful-fills economic efficiency but which also relates to the principle of justice. Another way of stating theprinciple is as follows: what level of pollution does the principle seek to achieve? The OECD’sinterpretations, for example, can be seen as calling for polluters to internalize the costs of reducingtheir pollution emissions to the levels established by government (Bugge, 1996; Nash, 2000).Today, an increasing number of policy makers understand the principle, as if the government is torequire internalization of costs in order to achieve the optimal level of pollution (Nash, 2000).While this interpretation refers to an economic efficiency that internalizes ex-ante the pollution costand seeks to find the social optimal level of pollution, and therefore enable the existence of somedegree of residual pollution, current interpretations of the PPP introduce an equitable side to the prin-ciple. These interpretations are concerned with the fact that specific polluters bear responsibility fortheir contribution to a particular pollution problem by internalizing at least the pollution abatementcosts. Nash (2000) defined this interpretation as ‘equitable internalization’. Equitable internalizationallocates abatement costs and the costs of residual pollution among polluters, and between pollutersand victims. It calls for the proper apportionment of the costs of abatement and of residual pollutionbetween the polluter and the victim, with the polluter bearing those costs. Put differently, the main

Y. Fishman et al. / Water Policy 14 (2012) 470–489 473

difference between the economic efficiency and the legal principle of justice is that economic effi-ciency could fail on the grounds of leaving residual pollution to continue rather than to be abated.The principle of justice could not be efficient from an economic point of view if it legally obligesthe abatement of all the pollution units in cases where it is socially optimal to abate only partof the pollution (for example in cases where it is not efficient to abate the last units of pollutionwhere the marginal abatement cost is higher than the marginal benefit).In the current study, we present an optimal social planner solution with a treatment process that

causes the farmer (the polluter), with the aid of a fixed input tax, to absorb only a part of thegroundwater contamination treatment cost. It leaves a positive amount of nitrogen concentrationto be removed by the drinking water consumers (the victims) which are not responsible for the pol-lution in the first place. While this policy is consistent with the economic principle of efficiency, asit allows for a cost-effective level of nitrogen concentration in groundwater, it is nonetheless incon-sistent with the principle of justice as it leaves some positive nitrogen concentration above the healthstandard to be removed by the drinking water consumers.While economists are more concerned with efficiency than justice, in this study we also suggest

an economic efficiency solution but also suggest a policy to compensate victims for the unabatedresidual pollution. We suggest using economic incentives in the form of an input tax. Thiswould then allow a government to compensate drinking water consumers from its federal budget,depending on its overall budget priorities, whilst also considering transferring nitrogen tax payments(part of or even all of them) plus an additional amount to cover the groundwater contaminationtreatment cost. This depends, of course, on the total compensation, total nitrogen tax payments,groundwater treatment cost and the government’s overall budget. It should be noted, however,that this is a distributional matter and not an efficiency requirement. That is, the social optimallevel of pollution will not change. A policy of transferring the tax payment to the pollution victimsis an issue in debate. It could affect the optimal emission level due to the fact that the victimsoffended by pollution may defend themselves against the consequences of pollution (Shibata &Winrich, 1983; McKitrick & Collinge, 2002). It is also associated with asymmetric informationwhich enables victims to act strategically, mainly by misrepresenting the true damage (Huber &Wirl, 1998).While theoretically these arguments are valid, there are cases, such as the one in this study, where the

issue has little relevance. In the current case study, we seek a second-best policy in which the healthstandard should be met. The optimal steady state in this model is achieved by using an empirical deter-ministic treatment cost1. Therefore, it could not be subject to defensive or strategic behavior because thedefensive behavior is empirically known and is already taken into consideration in the optimal steadystate. While the first-best solution is more general, including the damage cost (the cost associatedwith consuming drinking water that doesn’t meet the health standard), it is also less applicable as auth-orities are more flexible in cost-effectiveness policies (such as meeting a certain standard) than inchanging the standard itself (Goetz et al., 2006).

1 Groundwater nitrogen concentration converged to steady state is presented in Fishman et al. (2009) and in Section D of theAppendix to this paper, available online at http://www.iwaponline.com/wp/014/139.pdf.

Y. Fishman et al. / Water Policy 14 (2012) 470–489474

3. The model

3.1. The Farmer optimization problem

The optimization problem faced by a farmer is to maximize private net benefit (ΠP), and is given by:

MAX PP(Nfert(t), Wir(t)) ¼ PY � Y(Nfert(t);Wir(t))� TPC(Nfert(t); Wir(t)) (1)

The terms on the right-hand side are the private net benefit per hectare, where PY is the price per tonof yield net of variable costs except for nitrogen and irrigation costs, while Y(Nfert(t),Wir(t)) and TPC(Nfert(t),Wir(t)) are an agricultural response function and a total production (private) cost function,respectively, for quantities of Nfert(t) and of irrigation water (Wir(t)). For empirical reasons, we use1.5 polynomial production functions that were statistically estimated by Feinerman & Falkovitz(1997). This function is given by:

Y(Nfert, Wir) ¼ �a0 þ a1 � Nfert(t)þ a2 �Wir � a3(Nfert(t))1:5 � a4 � (Wir)

1:5 � a5 � Nfert(t) �Wir

where aj. 0 for j¼ 1, 2, 3, 4, 5. The agricultural response function is an inverse U shape for each inputand Nfert(t) and Wir(t) were identified empirically as substitutes

@Y(�)=@Nfert(t)@Wir(t)

¼ @Y(�)=@Wir(t)@Nfert(t)

¼ �a5 , 0

� �

The total production cost function is given by: TPC(·)¼ PN · Nfert(t)þ PW ·Wir(t)þ FC where PN andPW are the nitrogen fertilizer price in $ per kg and irrigation water price in $ per m3, respectively, and FC isthe production fixed cost. Solving Equation (1) with the first order conditions for the ‘private’ solution ofthe profit maximizing farmer results in the optimal amount of irrigation water (W ir

of) and nitrogen fertilizer(N fert

of ). The mathematical modeling of the ‘private’ solution of the profit maximizing farmer is presentedin Section A of the Appendix (available online at http://www.iwaponline.com/wp/014/139.pdf).

3.2. Cost of treating groundwater contamination

We present a groundwater contamination total treatment cost (TTC) function using selective electro-dialysis (EDA) technology. EDA technology is commonly used to treat contaminated groundwaterworldwide. Using data received from a private firm that relies on this technology, we were able tomodel the connection between the nitrogen concentration in groundwater (Q(t)) and the cost of remov-ing it (TTC). We use two kinds of treatments: a primary treatment stage for low nitrogen concentrationin the groundwater (up to 32.26 ppm of NO3-N) and primary plus secondary treatment stages for highnitrogen concentrations (between 32.26 and 92.2 ppm of NO3-N)

2. Primary plus secondary treatmentstages refer to using two treatment plants with the same technology.

2 The calculation of these intervals is presented in Fishman et al. (2009).

Y. Fishman et al. / Water Policy 14 (2012) 470–489 475

The total cost of treating groundwater contamination (TTC) is given in Equation (2):

TTC ¼0; 0 � Q(t) � ~Qur

(aþ b � Q(t)) � Wur1; ~Qur , Q(t) � ~Qurv

(cþ d � Q(t)) � Wur2;~Qurv , Q(t) � ~Qur

v2

8><>: (2)

where a, b, c and d are positive constants, ~Qur is the health standard nitrogen concentration for drinkingwater, (Wuri) is the treated quantity of drinking water to be supplied where i¼ 1,2 stands for primary andprimary plus secondary treatment stages, respectively; (~Qur=v) is the maximum nitrogen concentration,in the primary treatment stage, v is a fixed rate of nitrogen concentration residual in the water after thetreatment and (~Qur=v

2) is the maximum nitrogen concentration, in the primary treatment plus secondarytreatment stages for high nitrogen concentrations. The mathematical modeling of the total cost of TTCpresented in Equation (2) and its economic interpretation is presented in Section B of the Appendix(http://www.iwaponline.com/wp/014/139.pdf).

3.3. The equation of motion for nitrogen concentration in groundwater

The equation of motion for nitrogen concentration in groundwater is derived from water and nitrogenpercolation, and from pumping between land surface and groundwater. It is based on a hydrologicalmodel that was specifically modified by Fishman et al. (2009) from a hydrological model developedby Mercado (1976, 1980). It outlines the nitrogen fertilizers’ influence on groundwater nitrogen concen-tration in steady state. The equation of motion represents the rate of change over time of groundwaternitrogen concentration ( _Q(t)) and is given by:

_Q(t) ¼ a � R � QR

W|fflfflfflfflffl{zfflfflfflfflffl}Contribution ofnitrogen in rain

þ [a � �W ir � �Wp]W

� Q(t)|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Contribution of nitrogenin irrigation water; net of thecontribution of nitrogenin pumping water

þ a � 1000 � (1� h)W

� Nfert(t)|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Contribution of nitrogen fertilizer ð3Þ

where the first term on the right-hand side of the equation is the contribution of nitrogen in rain to nitro-gen concentration in groundwater, R is the constant amount of annual average rain in m3/hectare, QR isnitrogen concentration in rain in ppm, α is the rate of nitrogen that reaches the water table from all nitro-gen sources that percolate into the unsaturated zone and W is groundwater stock at time t in m3/hectare.The second term on the right-hand side is the contribution of nitrogen in irrigation water, net of the con-tribution of nitrogen in pumping water to nitrogen concentration in groundwater, where �Wp is thepumping water from the groundwater in m3/hectare/year. The third term on the right-hand side is thecontribution of nitrogen fertilizer to nitrogen concentration in groundwater, where (1� η) is the rateof the applied nitrogen fertilizer that percolates beneath the root zone into the unsaturated zone andthe number 1,000 is the conversion factor from kg to g.The contribution of nitrogen fertilizer to nitrogen concentration in groundwater represents the polluter’s

emission that reaches the water table. Other sources of positive and negative nitrogen contribution to the

Y. Fishman et al. / Water Policy 14 (2012) 470–489476

nitrogen concentration in groundwater are horizontal inflow and outflow of water, and nitrogen to andfrom the groundwater, respectively. These sources were neglected from Equation (3) because empiricaldata for the Israeli coastal aquifer (Israel Ministry of National Infrastructure, 2001) show that due toheavy pumping, horizontal outflow of water and nitrogen approach zero. They also reveal that horizontalinflow of water and nitrogen are marginal; we have therefore assumed them to equal 0 as well. In theabsence of any human activity, horizontal outflow of water and nitrogen .0 and Q(t) could also reacha steady state.

3.4. Social planner economic optimization problem

The highest net present-value social benefit (ΠS) is chosen out of three alternatives presented in thefollowing decision rule:

PS¼MAX

Ð10e�r�t �{PY �Y(Nosb1

fert , �W ir)�TPC(Nosb1fert , �W ir)}dt; Q(t)¼Qosb1¼ ~Qur

Ð10e�r�t�{PY �Y(Nosb2

fert , �W ir)�TPC(Nosb2fert , �W ir)

�TTC(Qosb2, �Wur)}dt; ~Qur ,Q(t)¼Qosb2, ~Qur=vÐ10e�r�t�{PY �Y(Nosb3

fert , �W ir)�TPC(Nosb3fert , �W ir)

�TTC(Qosb3, �Wur)}dt; Q(t)¼Qosb3¼ ~Qur=v

8>>>>>>>>>>>><>>>>>>>>>>>>:

(4)

where (Nosbjfert ,Q

osbj), j¼ 1, 2, 3 are three possible Optimal Social Benefit (OSB) quantities of nitrogenfertilizers applied (Nosbj

fert ), and a concentration of nitrogen in groundwater (Qosbj), respectively; r is thediscount rate, and t is the time. The decision rule in Equation (4) is used here due to the discontinuity ofthe treatment cost function presented in Equation (2). Equation (4) is presented in a reduced formfor only three possible points (Q(t)¼ ~Qur,Q(t)¼ ~Qur=v and the interval between them~Qur ,Q(t), ~Qur=v), because empirical results for different water allocation between irrigation waterand drinking water show no maximization of the other two points. The decision rule in Equation (4)is presented regardless of the transaction or implementation costs that are discussed in more detail inthe welfare analysis section below (Section 3.5.2).The possible points, (Nosb1

fert , Qosb1) and (Nosp3

fert , Qosp3), which fall where the treatment cost function is

discontinuous and is not differential, are solved with a strict restriction on the farmer, namely to usequantities of nitrogen fertilizer equal to Nosb1

fert or Nosb3fert . By using these quantities, the nitrogen concen-

tration in the groundwater converges to Qosb1 or Qosb3, respectively. Note that by using Nosb1fert , the

nitrogen concentration in groundwater meets the health standard concentration for drinking water(~Qur) and therefore does not require a treatment process. The mathematical modeling of solving thepossible points (Nosb1

fert , Qosb1) and (Nosp3

fert , Qosp3) is presented in Section C of the Appendix (http://

www.iwaponline.com/wp/014/139.pdf).The possible point (Nosb2

fert , Qosb2), which falls in the continuous and differential open interval of the treat-

ment cost function is solved in a dynamic optimization of net present-value social benefit in the frameworkof a continuous-time optimal control model. The mathematical modeling of solving the possible point(Nosb2

fert , Qosb2) is presented in Section D of the Appendix (http://www.iwaponline.com/wp/014/139.pdf).

Y. Fishman et al. / Water Policy 14 (2012) 470–489 477

3.5. Economic incentives and welfare analysis

3.5.1. Economic incentives: an input tax policy. We introduce an input tax policy by imposing a fixedtax rate on the nitrogen fertilizer price (taxPN) to induce farmers to use nitrogen fertilizer amounts thatare equal to the social planner amounts. It is important, however, to note that due to low profitability inthe farming sector, issuing an input tax in cases of high water scarcity conditions could result in negativelong-term private net benefit, causing an exit from the industry of less efficient farmers; the policy ques-tion as to whether or not to maintain low profitability agricultural activities in cases of high waterscarcity conditions is outside the scope of this study, and we assume that authorities would want tokeep agricultural activities due to its benefits for society that are not explicitly considered in thisstudy. In this study, we internalize the environmental cost of nitrogen fertilizer in the price of thisinput to obtain an efficient application of nitrogen fertilizer, and deal with two important questions:

1. In a low profitability farming sector, do we really need to impose the fixed tax rate on the nitrogenfertilizer price from the first unit in order to achieve economic efficiency?; and

2. is it fair to impose a tax where the cost for society from nitrogen fertilizer contamination is zero (upto the ~N

urfertunit)?

To deal with these questions, we suggest using an input tax policy by using a tax bracket for nitrogenquantity, below which the price of nitrogen fertilizer is free of tax, and above which it is not. We suggestenforcing a tax bracket from the ~N

urfert unit because, at this level and below it, groundwater nitrogen con-

centration is equal or lower than the drinking water health standard concentration, and therefore thegroundwater treatment cost is zero. This input tax policy is both efficient and fair from a farmer’s pointof view. It is efficient because it induces farmers to use nitrogen fertilizer amounts that are equal to thesocial planner amounts. That is, the efficient social planner solution does not change between enforcinga fixed tax rate from the first nitrogen fertilizer unit and the ~N

urfert unit. It is fair because it does not

impose a tax where the cost for society from nitrogen fertilizer contamination is zero (up to the ~Nurfert unit).

The new nitrogen fertilizer price will be PtaxN ¼ PN þ taxPN . Solving for taxPN with the aid of

Equation (A4) of Section A of the Appendix, we get:

taxPN ¼0; Nfert � ~N

urfert

PY � a1 � a5 � �W ir �ffiffiffiffiffiffiffiffiffiffiNosbjfert

q� 1:5 � a3

� �� PN ; Nfert . ~N

urfert

8<: (5)

For a positive tax interval, Equation (5) represents an optimal equilibrium where the farmer’s mar-ginal net benefit (the right-hand side of Equation (5)) equals the marginal tax payment (the left-handside of the equation). The total tax payments are TaxPN ¼ taxPN � Nosbj

fert . This policy is presented inFigure 1.It should be noted, however, that a farmer has other options to respond to the imposed input tax, such

as crop rotation, changing technology, or even reducing the land under cultivation. Evaluation of theseoptions is out of the scope of this paper.

Fig. 1. Social planner optimal condition in steady state, with an input tax policy and welfare change.

Y. Fishman et al. / Water Policy 14 (2012) 470–489478

3.5.2. Welfare analysis. Imposing a social planner solution (optimal social net benefit) includes anoverall positive welfare change. That is, internalizing the cost of contamination ex-ante results in thereduction of the treatment cost on the one hand and loss of private (agricultural) net benefit on theother hand. The difference between these two terms is defined as welfare change, and is positive.Another definition of welfare change could be derived by internalizing the cost of contamination ex-ante. This policy results in a higher net benefit (private net benefit minus cost of contamination)than the net benefit in which the cost of contamination is not internalized ex-ante and is calculatedex-post only. The latter net benefit could be defined as ‘no contamination, internalized net benefit’. Wel-fare change calculations are summarized in Equation (6).

{Welfare change} ¼ {Treatment cost reduction}� {Private (agricultural) net benefit lost}

¼ {Optimal social net benefit}� {No contamination internalized net benefit}(6)

The mathematical condition for maximizing the welfare change is presented in Section E of theAppendix (http://www.iwaponline.com/wp/014/139.pdf). Figure 1 presents a graphical illustration ofsocial planner optimal condition in steady state, an input tax policy and walfare change.Solving the welfare change for a social planner solution raises the question: is the welfare change

sufficient to warrant intervention by authorities? This question is important because the tax managementscheme presented above is costly to implement and thus could fail to improve efficiency, especially ifthe welfare change due to authority intervention is not significant. These costs may include, according toFeinerman & Falkovitz (1997), information gathering on economic and physical parameters, monitoringwater quality, tax administration, enforcement cost and greater management authorities or power. Whilethese costs are considered mainly in states’ budgets, they are not explicitly considered in welfare analy-sis in the literature, and in this study.To identify if the welfare change points out on intervention or not with no need to explicitly calculate

tax management scheme costs, we suggest, in Equation (7), a WCI which could help authorities to

Y. Fishman et al. / Water Policy 14 (2012) 470–489 479

decide if the welfare change is sufficient to intervene. We suggest looking not only at the absolute valueof the welfare change (the nominator of Equation (7)) but also at its relative value with respect to theeconomic aspects of the initial situation in which the polluters do not internalize their contaminationex-ante, i.e. at the no contamination internalized net benefit (the denominator of Equation (7)).

{WCI} ¼ {welfare change}{no contamination inernalized net benefit}

� 100����

���� (7)

4. Empirical results

4.1. The study area

We employed the outcome of our hydrological economic optimization model to corn productionabove the nitrogen-contaminated coastal aquifer in Israel. The coastal aquifer is a major joint sourceof Israel’s water for drinking and irrigation. It supplies about one quarter of the water consumed inIsrael, with long-term annual average water production of about 400 million m3 (Israel Ministryof National Infrastructure, 2003). The coastal aquifer in Israel is heavily contaminated with nitrogen,mainly introduced through agricultural activity. Nitrate concentration varies from less than 10 ppmin some areas of the aquifer to around 130 ppm in other areas, far exceeding the 50 ppm healthstandard recommended by the World Health Organization (WHO, 2011) and by the European Union(EU, 1998).Israel is becoming more urbanized over the years, at the expense of farming areas. This is especially

true in the area above the coastal aquifer, which consists of Tel-Aviv and its neighbouring towns alongthe coast. In 2009, more than 3 million people were living in this area (out of Israel’s total population of7.4 million). In Israel, irrigated agriculture occupies about 180,000 hectares, out of which about 40,000are located just over the coastal aquifer. In 2010, the area cultivated with corn was estimated at about3,300 hectares out of which about one third is grown over the coastal aquifer (Israel Central Bureau ofStatistics, 2010). Table 1 lists the parameters of the study area used in this paper.

4.2. Simulation of the model

Twenty different water allocation ratios between irrigation and drinking purposes were simulated. Thefirst of these allocated 0% of the total pumped water to irrigation purposes and 100% to drinking waterpurposes3. The other allocations differed by 5% each. We calculated 20 different optimal social steadystate equilibriums for the model and were thus able to obtain a comprehensive examination of policiesregarding varying nature states of water allocation in varying water scarcity conditions. We considerwater scarcity to be relatively high if drinking water needs are relatively high with respect to irrigationwater, and vice versa. Analyzing the outcome of the different water allocations yielded the followingresults and policy options.

3 Groundwater here represents the only water source which, of course, is usually not the case in reality.

Table 1. Parameters of the applied study area

Parameter Value Units Parameter Value Units

Hydrological model Pricesg

_WðtÞ 0 m3/ta PY 107.4 $/tonW(t) 2889.4 m3/hab PN 0.84 $/kgR 5160 m3/ha/yearc FC 326.9 $/ha/yearQR 1.2 NO3-N ppmd r 7 %η 0.473 Rated Response function coefficientsh

α 0.32 Rated �a0 1.9135~Qur 11.29 ppm of NO3-N

e a1 0.0545EDA treatment processf a2 0.0059v 0.35 Rate �a3 0.0013z 0.05 Rate �a4 0.000045θ 0.69 Rate �a5 0.0000036

Treatment cost function coefficientsi

a 0.0451b 0.0090

aThe average water table in the Israeli coastal aquifer was quite stable from the early 1970s until the early 1990s. Since thenthe water table has fluctuated due to rainy and dry years (Israel Ministry of National Infrastructure, 2003). For simplicity, weassume a steady state in the water table.b1.25 times greater than �Wp. Based on Malul’s (1988) argument that only a small percentage of the saturated coastal aquiferin Israel (about 25� 109 m3) is available for use. 2% of this amount gives 500 million m3 which is 1.25 greater than theapproximately actual 400 million m3 annually used (Israel Ministry of National Infrastructure, 2003).cLong-term average rain in a representative cell in the Israeli coastal aquifer for 1971–1997 (Israel Ministry of NationalInfrastructure, 1998).dSource: approximately the values in Mercado (1976).eBased on WHO standards for drinking water (WHO, 2011) and equivalent to 50 ppm of NO3.fSources: data received from commercial water treatment companies and Semiat & Hasson (2000).gSource: data received from commercial manufacturing company of nitrogen fertilizer and Israel Ministry of Agriculture (2000).hSource: Feinerman & Falkovitz (1997). The t values of �a0, a1, a2, �a3, � a4, � a5 are �32.21, 165.15, �92.86, 122.9,�8355.9, �11522.5, respectively; and R2¼ 0.981.iBased on data received from a commercial water treatment company. b is significant at 1% and R2¼ 0.959.

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4.3. Results and policy options

4.3.1. Option 1: ex-ante prevention and ex-post treatment policies. We found that, for relatively lowwater scarcity conditions when a relatively low quantity of drinking water is needed (below 40% in thisstudy) and a relatively high quantity of irrigation water could be supported (above 60% in this study),the preferred policy is to have restrictions on nitrogen use together with a drinking-water treatment pro-cess. In that case, the treatment process proves to be economically efficient due to the low water quantitythat is treated. The associated optimal nitrogen fertilizer amount is relatively high; nitrogen concen-tration in the groundwater is higher than the 11.29 ppm health standard (the nitrogen concentrationexceeding the health standard has to be removed by the treatment process). The cost of treating thegroundwater is positive but the private net benefit is relatively high (Table 2). For relatively highwater scarcity conditions, when a relatively high quantity of drinking water is needed (above 45% inthis study) and a relatively low quantity of irrigation water could be supported (below 55% in this

Table 2. Social steady state equilibrium: major variables (units per hectare)

Irrigationwaterallocation (%)

Private net benefit(in a socialsolution) ($/year)

Price perm3 treated($/m3)

Drinking-watertreatment cost($/year)

Social netbenefit($/year)

Net presentvalue of socialbenefits ($)

Highest net present-value social benefitis achieved from

0 �109 0.00 0 �109 �1,555 First term ofEquation (4)5 �90 0.00 0 �90 �1,287

10 �70 0.00 0 �70 �99415 �48 0.00 0 �48 �68520 �25 0.00 0 �25 �36025 �2 0.00 0 �2 �2630 23 0.00 0 23 32535 48 0.00 0 48 69040 75 0.00 0 75 1,06745 101 0.00 0 101 1,44150 129 0.00 0 129 1,83855 158 0.00 0 158 2,255

60 482 0.32 286 196 2,801 Second term ofEquation (4)65 504 0.32 257 247 3,527

70 525 0.33 226 300 4,28175 546 0.33 194 352 5,033

80 568 0.34 159 409 5,841 Third term ofEquation (4)85 588 0.34 121 467 6,667

90 608 0.34 82 526 7,51895 628 0.34 42 586 8,370

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study), the optimal policy changes calls for restrictions on nitrogen use only. This exclusion of thegroundwater treatment process is economically efficient because of the high quantity of water thatneeds to be treated. In this case, the farmer has to reduce nitrogen use by a considerable amountbefore groundwater nitrogen concentrations will meet the health standard concentrations in steadystate (11.29 ppm). The associated private net benefit is relatively small but the cost of treating ground-water is zero (Table 2).

4.3.2. Option 2: authority externality intervention policy. We found that welfare change is subject todifferent water scarcity conditions. It decreases with respect to water allocation for irrigation (andincreases with respect to water allocation for drinking water). It ranges from $363 per hectare peryear for an allocation of 0% for irrigation water and 100% for drinking water (a relatively high waterscarcity condition) to only $3 per hectare per year for an allocation of 95% for irrigation water and5% for drinking water (a relatively low water scarcity condition) (Table 3). The need to allocatemore water for drinking purposes and, therefore, less water for irrigation, results in using more nitrogenfertilizer because of the substitution effect between nitrogen fertilizer and irrigation water. The extern-ality effect will therefore increase due to the use of a higher quantity of nitrogen fertilizer and due to theneed to supply higher quantities of drinking water (to the given health standard).We suggest that under relatively high water scarcity conditions, when a relatively low or a medium

quantity of irrigation water could be supplied, there are strong and moderate incentives for the auth-orities to intervene, respectively, because the welfare change and the WCI are significant and

Table 3. Social steady state equilibrium: welfare analysis (units per hectare)

Welfare analysis

Columnnumber

1 2 3 45¼ 1–2¼3–4 6¼ |(5/4)� 100|

Irrigationwaterallocation(%)

Treatment costreduction($/year)

Private(agricultural) netbenefit lost ($/year)

Optimal socialnet benefit($/year)

No contaminationinternalized netbenefit ($/year)

Welfarechange($/year) WCI (%)

0 895.8 532.4 �108.9 �472.2 363.4 76.95 855.0 516.1 �90.1 �428.9 338.8 79.010 813.8 499.8 �69.6 �383.6 314.0 81.915 772.5 483.6 �48.0 �336.9 289.0 85.820 730.3 467.0 �25.2 �288.4 263.2 91.325 687.9 450.5 �1.8 �239.1 237.3 99.330 645.4 434.2 22.7 �188.5 211.2 112.135 601.4 417.3 48.3 �135.7 184.1 135.640 557.4 400.6 74.7 �82.1 156.8 190.945 513.5 384.1 100.8 �28.6 129.4 453.150 468.9 367.5 128.6 27.1 101.5 373.955 423.2 350.5 157.8 85.2 72.7 85.360 91.9 38.2 196.0 142.3 53.7 37.765 75.1 30.3 246.9 202.2 44.7 22.170 59.2 23.1 299.6 263.5 36.1 13.775 44.9 16.7 352.3 324.1 28.2 8.780 32.2 11.3 408.8 388.0 20.9 5.485 22.6 8.3 466.7 452.4 14.3 3.290 14.0 5.7 526.3 518.0 8.3 1.695 6.4 3.6 585.9 583.0 2.9 0.5

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moderate, respectively (up to 450%) (Table 3). Under relatively low water scarcity conditions, when arelatively high quantity of irrigation water could be supplied, there is a weak incentive for the authoritiesto intervene and eliminate the externality of nitrogen fertilizer because the welfare change is low andsocial net benefit could be negative if implementation costs are considered. The WCI is also low(less than 10%) (Table 3).

4.3.3. Option 3: an input tax policy. For high water scarcity conditions when a relatively low quan-tity of irrigation water could be supplied (below 55% in this case study), imposing restrictions onnitrogen use by economic incentives in the form of input tax from the first unit will result in negativeprivate net benefit (Table 4). For low water scarcity conditions, when relatively medium and highquantities of irrigation water could be supplied (above 60% in this study), tax collection from thefirst nitrogen fertilizer unit as well as from the health standard unit (~N

urfert) creates positive private

net benefit.We suggest that under high water scarcity conditions, when a relatively low quantity of irrigation

water could be supplied (below 55% in this study) and where tax collection from the first nitrogen fer-tilizer unit results in negative private net benefit, the authorities could enforce an input tax policy by

Table 4. Social steady state equilibrium: economic incentives (units per hectare)

Economic incentives

Tax collections from the nitrogen fertilizerhealth standard unit

Tax collections from the first nitrogenfertilizer unit

Irrigationwaterallocation(%)

Fixed tax rateon nitrogenfertilizerprice ($/kg)

Total taxpayments($/year)

Private netbenefit inoptimal socialsteady state($/year)

Rate of taxpayments totreatmentcosts (%)

Total taxpayments($/year)

Private netbenefit inoptimal socialsteady state($/year)

Rate of taxpayments totreatmentcosts (%)

0 2.7 0.0 �108.9 329.3 �438.25 2.7 0.0 �90.1 323.8 �413.910 2.6 0.0 �69.6 318.2 �387.815 2.6 0.0 �48.0 312.5 �360.520 2.6 0.0 �25.2 306.7 �331.925 2.5 0.0 �1.8 300.7 �302.530 2.5 0.0 22.7 294.8 �272.035 2.4 0.0 48.3 288.5 �240.240 2.4 0.0 74.7 282.2 �207.545 2.3 0.0 100.8 275.8 �175.050 2.3 0.0 128.6 269.3 �140.755 2.3 0.0 157.8 262.6 �104.760 0.6 139.9 341.9 49.0 214.3 267.5 75.065 0.6 126.8 376.8 49.4 192.8 310.8 75.170 0.5 112.5 412.9 49.8 169.8 355.6 75.275 0.4 97.4 448.5 50.3 145.9 400.0 75.480 0.4 81.5 486.5 51.2 121.3 446.7 76.285 0.3 69.6 518.0 57.5 103.5 484.1 85.690 0.3 57.5 550.6 70.3 85.5 522.5 104.695 0.2 45.3 582.3 108.7 67.3 560.3 161.5

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creating a tax bracket of nitrogen quantity. Below this bracket the price of nitrogen fertilizer is free oftax, and above this bracket, it is not. Enforcing a tax bracket from the ~N

urfert unit (where at this level and

below the groundwater nitrogen concentration is equal to or lower than the groundwater health standardconcentration, and therefore the groundwater treatment cost is zero) is efficient and fair as presentedabove. Note, however, that if the irrigation water allocation is below 30%, government authoritiescould provide a minimum allocation of irrigation water to maintain agricultural activities and to preventfarmers from facing bankruptcy (Table 4). For a medium supply of irrigation water, tax collection fromthe first nitrogen fertilizer unit creates a positive private net benefit but could be considered not fair, aspresented above; therefore, the input tax policy is also preferred. No tax policy is suggested for a highquantity of irrigation water (above 75% in this study) because the welfare change and WCI are low, asshown above in Policy Option 2.

4.3.4. Option 4: Polluter Pays Principle policy. For moderate and high quantities of irrigation water(above 60% in this study), the nitrogen concentration in groundwater, in the social steady state, is higherthan the health standard, and the cost of treating groundwater is positive. Tax payments could cover thevariable treatment cost (as presented in Figure 1) but they are not large enough to cover the total

Y. Fishman et al. / Water Policy 14 (2012) 470–489484

treatment cost in all water scarcity conditions due to the existence of fixed capital costs in the treatmenttechnology presented above.Government could compensate drinking water consumers from its federal budget, depending on its

overall budget priorities, and consider also transferring the nitrogen tax payments (part of them, oreven more than the collected amount) to cover cost of groundwater contamination treatment. Thetotal compensation therefore depends on the total nitrogen tax payments, the cost of groundwater treat-ment and on the government’s overall budget.Authorities could use the input tax policy presented above and transfer tax payments to cover the

groundwater contamination treatment cost. By doing so, they could support the legal principle (a principleof justice) of PPP without affecting the economic principle (a principle of efficiency). For a moderatequantity of irrigation water (between 60–75% in this study), the cover ratio of tax payments to treatmentcost is 50% if tax collection starts from the health standard unit. Note, however, that it increases to 75% iftax collection starts from the first nitrogen fertilizer unit (Table 4) and that it also remains a positive pri-vate net benefit at this water allocation interval. One could argue that it would be fair for drinking waterconsumers to induce the tax payments from the first unit rather than from the health standard unit as pre-sented above – thus providing support for the principle of justice of the PPP. While there is no uniqueequilibrium to this situation, the tax policy could range between inducing it from the health standardunit (which is fairness from the farmer’s point of view) to inducing it from the first unit (which is fairnessfrom the point of view of drinking water consumers). The compensation policy also depends on the gov-ernment’s overall budget allocation policy, as discussed above. No tax policy is suggested for a relativelyhigh quantity of irrigation water (above 75% in this study) because the welfare change and WCI are low,as shown above in Policy Option 3. For a relatively low quantity of irrigation water (below 55% in thisstudy), the social steady state and the tax policy (the principle of efficiency of the PPP) completely fulfillthe principle of justice of the PPP because they reduce the cost of treating groundwater to 0. A summary ofthe results and policy options is presented in Table 5.

5. Concluding remarks

This paper has focused on finding an optimal social steady state equilibrium, to provide decisionmakers with an economic tool to deal with the conflict between the need for nitrogen fertilizers in agri-cultural production and the requirements for a clean drinking water supply.We have employed an optimization model with a typical agricultural private net benefit function for

the use of nitrogen fertilizer in crop production and calculated the associated externalities. This wasdone using a direct environmental treatment cost function, based on a specific drinking water nitrogentreatment technology, and with a hydrological model that included the important influence of waterflow, with a given nitrogen concentration, into the groundwater. We used direct environmental policyin the form of a tax on nitrogen fertilizer prices in order to induce farmers to internalize the negativeexternal effects of using nitrogen fertilizer. We then analyzed the welfare change in the model. Weapplied the empirical analysis to corn production above the nitrogen contaminated coastal aquifer inIsrael and suggested the following policy options:

1. In a joint water source area that has to supply a relatively high quantity of irrigation water and alow quantity of drinking water, the preferred policy is to combine restrictions on nitrogen use

Table 5. Summary of results and policy options in the model

Water scarcitycondition

High Low

Irrigation waterallocation (%) 0–25 30–55 60–75 80–95

I. Ex-ante prevention and ex-post treatment policies (see Table 2)Results Nitrogen concentration in groundwater in social steady state is

equal to the health standardNitrogen concentration in groundwater in social steady state is higher

than the health standardPolicy Impose restrictions on nitrogen use only (ex-ante) Combine a policy that imposes restrictions on nitrogen use (ex-ante)

together with a drinking-water treatment process (ex-post)II. Authority externality intervention policy (see Table 3)Results Welfare change and Welfare Change Index are significant Welfare change and Welfare Change Index

are moderateWelfare change andWelfare ChangeIndex are low

Policy Strong incentive for the authorities to intervene Moderate incentive for the authorities tointervene

Weak incentive for theauthorities tointervene

III. An input tax policy (Table 4)Results Tax collection from the first nitrogen fertilizer unit results in

negative private net benefitTax collection from the first nitrogen

fertilizer unit still allows for a positiveprivate net benefit

Welfare change andwelfare changeindex are low

Policy Tax collection from the nitrogen fertilizer health standard unitis preferred if authorities want to maintain agriculturalactivities and to prevent farmers from facing bankruptcy

Tax collection from the first nitrogenfertilizer unit as well as from the healthstandard unit might be involved, and issubject to fairness preferences betweenthe farmer and drinking waterconsumers

No tax policy issuggested becausethe welfare changeand the welfarechange index arelow

(Continued.)

←

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485

Table 5. (Continued.)

Water scarcitycondition

High Low

Irrigation waterallocation (%) 0–25 30–55 60–75 80–95

IV. Polluter Pays Principles policy (see Tables 2, 3, 4)Results Farmers have to reduce nitrogen use by a considerable amount

before groundwater nitrogen concentration will meet thehealth standard concentration in steady state. The cost oftreating groundwater for drinking water consumers is zero

Nitrogen concentration in groundwater insocial steady state is higher than thehealth standard. The cost of treatinggroundwater is positive

Welfare change andWelfare ChangeIndex are low

Policy The social steady state and the tax policy fully fulfill theprinciple of justice of the Polluter Pays Principle

Government could compensate drinkingwater consumers from its federal budgetdepending on its overallbudget allocation policy, and alsoconsider transferring part of the nitrogentax payments, or even more than justpart, to cover the groundwatercontamination treatment cost. By doingso they can support the principle ofjustice of the Polluter Pays Principle.The ratio of tax payments to treatmentcost is 50% if tax collection is from thehealth standard unit (which is fairnessfrom a farmer point of view) andincreases to 75% if tax collection isfrom the first nitrogen fertilizer unit(which is fairness from the drinkingwater consumers’ perspective)

No tax policy issuggested becausethe welfare changeand Welfare ChangeIndex are low

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486

Y. Fishman et al. / Water Policy 14 (2012) 470–489 487

together with a drinking-water treatment process. On the other hand, in a joint water source area thathas to supply a relatively low quantity of irrigation water and high quantity of drinking water, theoptimal policy changes because it is economically more efficient to impose restrictions on nitrogenuse only.

2. In a joint water source area that has to supply a relatively low quantity of irrigation water and a highquantity of drinking water, there is a strong incentive for the authorities to intervene because the wel-fare change and the WCI is significant and reaches a maximum where 45% of water is allocated forirrigation. In a joint water source area that has to supply a relatively high quantity of irrigation waterand a low quantity of drinking water, there is a weak incentive for the authorities to intervene becausethe welfare change is low and could be negative if implementation costs are considered.

3. For a relatively low quantity of irrigation water, tax collection from the first nitrogen fertilizer unitwill result in negative private net benefit. Authorities could enforce a tax bracket from the healthstandard unit. For a moderate quantity of irrigation water, tax collection from the first nitrogen fer-tilizer unit as well as from the health standard unit could be considered, and is subject to fairnesspreferences between farmers and drinking water consumers.

4. Governments could compensate drinking water consumers from their federal budget depending ontheir overall budget priorities and also consider transferring the nitrogen tax payments (either partof them, or even more than the payments) to cover the cost of groundwater contamination treatment.By doing so, they can support the principle of justice in the PPP.

Policymakers have to consider other variables in their decision-making process, such as croprotations, the marginal treatment costs for nitrogen, the value of the marginal product of the cropsfor nitrogen and water, using wastewater irrigation and hydrological parameters reflecting the nitrogen’seffects on groundwater nitrogen concentration. The influences of these variables on the policy chosencould be a subject for future research.

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