large-scale desalination and the external impact on

0

חקלאית בכלכלה למחקר המרכז

Agricultural for Center TheResearch Economic

וניהול סביבה לכלכלת המחלקה Environmental of Department

Management and Economics

Discussion Paper No. 4.20

Large-Scale Desalination and the External Impact on Irrigation-Water

Salinity: Economic Analysis for the Case of Israel

By

Yehuda Slater, Israel Finkelshtain, Ami Reznik and Iddo Kan

נמצאים המחלקה חברי של מאמרים :שלהם הבית באתרי גם

Papers by members of the Department can be found in their home sites:

http://departments.agri.huji.ac.il/economics/index.html

P.O. Box 12, Rehovot 76100, Israel 76100 רחובות ,12 .ד.ת

http://departments.agri.huji.ac.il/economics/index.html

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Yehuda Slater, Israel Finkelshtain, Ami Reznik and Iddo Kan

Department of Environmental Economics and Management, The Robert H. Smith Faculty

of Agriculture, Food and Environment, The Hebrew University of Jerusalem, P.O.B. 12,

Rehovot 761001, Israel

Corresponding Author: Iddo Kan [email protected]

Key Points:

Subsidizing desalination is socially warranted because the associated irrigation-

water salinity reduction is an external effect of water consumption by all sectors

Irrigation with desalinated water is found optimal for Israel due to the large share of

water-intensive salinity-sensitive high-value crops

Ignoring the damage entailed by irrigation-water salinity benefits water suppliers at

the expense of consumers of water and agricultural products

mailto:[email protected]

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Abstract

Recent agro-economic studies in water-scarce countries such as Spain, Australia, Saudi

Arabia, and Israel have revealed the economic viability of irrigating high-value crops

with desalinated water. However, the worldwide growth of large-scale desalination

capacities is primarily designed to resolve urban-water scarcity, disregarding the impact

of desalination on irrigation-water salinity. We develop a dynamic hydro-economic

programming model where infrastructure capacities and allocations of water quantities

and salinities in a regional water-distribution network are endogenous. We show that

subsidizing desalination is socially warranted because the associated reduction in

irrigation-water salinity is an external effect of water consumption by all water users.

Empirical application to the entire state of Israel indicates that large-scale desalination of

seawater and treated wastewater for irrigation is optimal. This result stems from the large

share of irrigation-intensive salinity-sensitive high-value crops, motivated by Israel’s

policies to support local agriculture. Ignoring salinity results in a 45% reduction in

desalinated irrigation water, a 29% reduction in farming profits, a 250% increase in

water-suppliers’ profits, and an average deadweight loss of $1,200 a year per hectare of

arable land.

Keywords: Desalination, Irrigation, Salinity, Economics, Agriculture, Water,

Externality, Policy, Model, Natural Resource

JEL Classification: Q15, Q25, Q28

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1. Introduction

Salts already affect about a third of the world’s arable areas, and a fifth of the world’s

irrigated lands (Nellemann et al., 2009; Qadir et al., 2014). Salinization is expected to

expand further through a range of processes driven by population growth; these include a

rise in irrigation with brackish water as a substitute for the freshwater amounts diverted to

domestic use, agricultural reuse of the growing treated wastewater (TWW) volumes

discharged from urban areas (Jimenez & Asano, 2008; Qadir et al., 2007), and

salinization of freshwater sources due to seawater intrusion and deep percolation of salts

from irrigated lands (Assouline et al., 2015). The integrative nature of these spatially and

intertemporally linked processes implies that salinity damage should be considered

intrinsic to the design of agricultural and water policies, as well as to the long-run

development of water infrastructures at the regional and state levels, in particular

desalination.

Worldwide desalination capacity is continuously growing, and is expected to be

nearly double by 2050 relative to the 2015 level of 97 × 106 (m3 day-1) (Darre & Toor,

2018). Nevertheless, due to high supply costs, adverse environmental effects, and

agronomic constraints, large-scale desalination is generally perceived as a technology for

relieving urban-water scarcity rather than agricultural water shortages and salinity

damage (Burn et al., 2015; Martínez-Alvarez et al, 2016; Sepehr et al., 2017). However,

recent field- and farm-level analyses have indicated that desalination can provide an

economically viable water source for irrigating high-value crops in water-scarce countries

such as Spain (Reca et al., 2018; Zarzo et al., 2013), Australia (Barron et al., 2015), Saudi

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Arabia (Multsch et al., 2017), and Israel (Hadas et al., 2016; Kaner et al., 2017). Thus, the

tendency to overlook the potential contribution of desalination to agricultural productivity

in the design of policies and water infrastructures may entail suboptimal water

management and deadweight loss.

Water economies at the basin, regional or state levels may comprise multiple water

sources with diverse qualities and supply costs (e.g., naturally recharged surface water

and groundwater, brackish water, desalinated seawater, and TWW), various consumers

(e.g., domestic, industrial, and agricultural users) with different demands for water

quantity and quality, and an ensemble of infrastructures that constitute a complex water-

distribution network to treat and convey water from sources to consumers, separated or

blended. Efficient management of such networks should account for the linkage of

scarcities across points in time and space, meaning that water use at a particular place and

time may have opportunity costs with respect to its usage for various purposes at

alternative locales and times (Fisher et al., 2005). Moreover, population growth, climate

change, and the long construction period for water infrastructures imply that water-

system designers should foresee scarcities and decide ahead of time which, when, where,

and to what extent infrastructural elements should be installed or extended.

Hydro-economic models are an efficient tool for integrating the economic,

hydrological, engineering, agronomic, and environmental aspects associated with water

policies and water-infrastructure blueprints of large-scale water systems (Booker et al.,

2012; Harou et al., 2009). However, despite the vast economic literature on irrigation-

water salinity (Connor et al., 2012; Feinerman & Yaron, 1983; Knapp, 1992; Letty &

Dinar, 1986; and Schwabe et al., 2006 are but a few examples for topics and modeling

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methods developed in the last decades), to date, the incorporation of salinity in hydro-

economic models has been limited. For example, Housh et al. (2011), Lavee et al. (2011),

Reznik et al. (2016), Saglam (2013) and Tanaka et al. (2006) refer to desalination as a

means of resolving water-quantity scarcities, overlooking the benefits of reducing

irrigation-water salinity. Howitt et al. (2010) and Welle et al. (2017) employed the van

Genuchten and Hoffman (1984) production function to internalize salinity’s agronomic

impact into a static analysis of agricultural irrigation-water management in the Central

Valley of California. However, that framework considered agriculture as a single water

consumer, and therefore did not capture interlinks with domestic and industrial water

users, for example, when agriculture consumes the TWW produced by urban regions. In

addition, economies of scale associated with water conveyance warrant a mixture of

water sources with different qualities for long-distance delivery. The economics of

blending irrigation-water sources with diverse salinities has been studied at the field and

regional levels (Dinar et al., 1986; Kan, 2008; Kan & Rapaport-Rom, 2012; Kan et al.,

2002); however, to our knowledge, less attention has been given to the policy and welfare

implications of salinity in spatially widespread water-distribution networks that supply

mixed water to both agricultural and urban sectors.

The objective of this paper is to assess the welfare contribution of large-scale

desalination through its impact on irrigation-water salinity. Specifically, we compare

optimal water management at the regional scale under two scenarios: in the first, termed

Salinity Internalized (SI), the salinity effects are considered in the design of water

infrastructures, whereas the second, Salinity Externalized (SE), presumes that temporal

and spatial changes in salinity are disregarded.

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The following section presents a general dynamic hydro-economic model that

optimizes water allocations and infrastructure development while accounting for water

salinity and its agricultural damage. Based on an analytical solution, we show that the

salinity reduction following desalination is an external effect of water consumption by all

sectors, which can be internalized by subsidizing the supplied water. Otherwise,

disregarding salinity leads to higher-than-optimal water prices and welfare loss, where

water suppliers benefit at the expense of urban and agricultural water users.

In Section 3 we develop an empirical version of the model based on the Israeli water

system. The case of Israel seems to correspond to the assertion that: “…for water-scarce

countries that already implement all other measures for freshwater generation,

desalination may serve as the only viable means to provide the water supply necessary to

sustain agriculture, support population, and promote economic development” (Elimelech

& Phillip, 2011, p. 717). Indeed, to cope with its growing water scarcity, Israel has

established a complex water-supply system, incorporating extraction of freshwater,

agricultural reuse of TWW, and extensive desalination of brackish water and seawater.

The empirical model tracks the dynamics of water salinity throughout the water-delivery

system, and controls the supplied water salinity by both the allocation and mixture of

water from different sources and the establishment of plants for the desalination of

seawater, brackish water and TWW. The model also comprises the farmers’ adaptation to

irrigation-water salinity through land allocation across crops in relation to the crops’ salt

tolerance.

Section 4 presents the empirical results. For the SI scenario, we obtain that the

negative effect of irrigation-water salinity on agricultural production in Israel warrants

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large-scale desalination of seawater and TWW for irrigation. We attribute this result to

the large share of high-value, salinity-sensitive fruit and vegetables in Israel’s vegetative

agriculture, where the Israeli farmers’ specialization in the production of these crops is

motivated by supporting regulations. We then show that disregarding the salinity effects

in the design of water infrastructures yields a considerable deadweight loss, evaluated at

$1,200 per average hectare of cultivable land. This estimate, which accounts for the

indirect salinity effects on domestic water supply and agricultural output prices, is nearly

three times larger than the direct salinity damage to agriculture of $440 ha-1 year-1

reported by Qadir et al. (2014). Section 5 summarizes with a discussion of the model’s

limitations and extensions.

2. General Framework

We first present a general dynamic hydro-economic model; then, to obtain theoretical

insights, we solve the optimization problem of a simplified static version analytically.

2.1. Hydro-economic Model

Consider a water-distribution network that is centrally managed by a water master whose

objective is to maximize welfare throughout a planning horizon of 𝑇 discrete periods by

setting efficient prices and developing infrastructures. Let 𝕂 be a set of nodes

representing spatially linked water sources, treatment infrastructures, and water-use

regions, and 𝐪𝑡𝑘 = (𝑤𝑡

𝑘 , 𝑠𝑡𝑘) denote the pair of quantity (𝑤𝑡

𝑘) and salinity (𝑠𝑡𝑘) of the water

flowing through node 𝑘 ∈ 𝕂 during period 𝑡 (𝑡 = 1,… , 𝑇). The elements in 𝐪𝑡𝑘 are

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constrained by the vector of exogenous factors 𝐛𝑡𝑘 (i.e., a volumetric balance constraint in

a pipeline junction, the water salinity in groundwater sources, etc.), 𝐪𝑡𝑘 ≤ 𝐛𝑡

𝑘, where 𝐛𝑡𝑘 =

𝑓𝑡𝑘(𝐛𝑡−1

𝑘 , 𝐪𝑡−1𝑘 ) represents the intertemporal dependence between water flows and

constraints (e.g., the extractable aquifer stock depends on the initial stock and extraction

during the previous period). A related set of constraints, 𝐛𝑇+1𝑘 ≥ 𝐛𝑘, represents end

conditions; for example, minimum extractable stocks in an aquifer.

The vector 𝐪𝑡𝑘 is also constrained by the node’s capacity attributes 𝐳𝑡

𝑘 (e.g., the

maximum annual volume and minimum salinity level of a desalination plant’s outflow),

which are endogenous. We denote by Δ𝐳𝑡𝑘 the change in the capacity features of node 𝑘

during period 𝑡, such that, given the initial capacity 𝐳0𝑘, 𝐳𝑡

𝑘 = 𝐳0𝑘 + ∑ Δ𝐳𝜏

𝑘𝑡−1𝜏=1 . The total

per-period costs associated with the capacities incorporated in 𝐳𝑡𝑘 (i.e., maintenance and

capital costs) are denoted 𝐶𝑡𝑘(𝐳𝑡

𝑘).

We denote by 𝑉𝑡𝑘(𝐪𝑡

𝑘, 𝐱𝑡𝑘) the value associated with water flow through node 𝑘 ∈ 𝕂

during period 𝑡, where 𝐱𝑡𝑘 is a vector of non-water input variables (e.g., land allocation to

crops) which may be constrained from above by �̅�𝑡𝑘 (e.g., regional agricultural land). The

value function 𝑉𝑡𝑘(∙) may vary in time (e.g., due to population growth or climate change),

and it is negative when node 𝑘 is a water-treatment infrastructure (e.g., the variable costs

of a groundwater-pumping station, or a desalination or wastewater-treatment plant), and

positive if the node is an urban or agricultural water-consumption region.

Let 𝐐, 𝐗, 𝐁 and 𝐙 be the vectors incorporating 𝐪𝑡𝑘, 𝐱𝑡

𝑘, 𝐛𝑡𝑘 and 𝐳𝑡

𝑘 for all 𝑘 ∈ 𝕂 at all

the 𝑇 periods, respectively, and the vector 𝚫𝐙 represent all the capacity changes

throughout the planning horizon. Given the initial levels of the exogenous and capacity

constraints for all 𝑘 ∈ 𝕂, 𝐁0 and 𝐙0, the planner’s objective is to solve the problem

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max𝐐,𝚫𝐙,𝐗

𝑊 = ∑ (1 + 𝑟)−𝑡 ∑ [𝑉𝑡𝑘(𝐪𝑡

𝑘, 𝐱𝑡𝑘) − 𝐶𝑡

𝑘(𝐳𝑡𝑘)]𝑘∈𝕂

𝑇𝑡=1

𝑠. 𝑡. 𝐛𝑡𝑘 = 𝑓𝑡

𝑘(𝐛𝑡−1𝑘 , 𝐪𝑡−1

𝑘 ) ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,

𝐳𝑡𝑘 = 𝐳0

𝑘 + ∑ Δ𝐳𝜏𝑘𝑡−1

𝜏=1 ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,

𝐱𝑡𝑘 ≤ �̅�𝑡

𝑘 ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,

𝐐 ≤ min(𝐁, 𝐙), 𝐁𝑇+1 ≥ 𝐁, 𝐐, 𝚫𝐙, 𝐗 ≥ 𝟎

(1)

where 𝑊 denotes welfare and 𝑟 is the discount rate. The solution defines the optimal

infrastructure-development plan and allocation of water throughout the distribution

network, induced by water quotas or prices. In the SI scenario, the water master accounts

for the impact of salinity changes embedded in the value function 𝑉𝑡𝑘(𝐪𝑡

𝑘, 𝐱𝑡𝑘) for all 𝑘 ∈

𝕂 and 𝑡 = 1, … , 𝑇, whereas the SE case implies 𝑠𝑡𝑘 = 𝑠0

𝑘 for all 𝑘 ∈ 𝕂 and 𝑡 = 1, … , 𝑇.

2.2. Theoretical Insights

To obtain an analytical solution, we consider a simplified static version of the

optimization problem expressed in equation (1). Figure 1 depicts a water economy in

which groundwater and desalinated seawater are two water sources with different

salinities, which are mixed and then delivered to two water-consumption zones—urban

and agricultural.

Figure 1 about here

We denote by 𝑠𝑔 and 𝑠𝑑 the salinities of the groundwater and desalinated water,

respectively, where 𝑠𝑔 > 𝑠𝑑. These salinity levels constitute minimum constraints for the

salinities of the water supplied by the respective sources: 𝑠𝑔 ≥ 𝑠𝑔 and 𝑠𝑑 ≥ 𝑠𝑑. The

extracted groundwater quantity, 𝑤𝑔, is limited by the availability constraint �̅�𝑔, whereas

the delivery of desalinated water, 𝑤𝑑, is unlimited. The total water supply, 𝑤 ≡ 𝑤𝑑 +

𝑤𝑔, is a mixture of the two sources with a salinity that is the volumetric weighted average

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𝑠 =𝑤𝑑𝑠𝑑+𝑤𝑔𝑠𝑔

𝑤. The blended water is split such that the urban and agricultural sectors

obtain amounts 𝑤𝑢 and 𝑤𝑎, respectively, and 𝑤𝑢 + 𝑤𝑎 = 𝑤.

We assume constant per-water-unit marginal costs, where the marginal cost of

desalination, 𝑐𝑑, exceeds that of the groundwater, 𝑐𝑔. Unlike groundwater, desalination is

also associated with fixed cost 𝐶𝑑, contingent on the supply of desalinated water. The

functions 𝑉𝑢(𝑤𝑢) and 𝑉𝑎(𝑤𝑎, 𝑠) are, respectively, the value of water consumed by

agents in the urban and agricultural zones (gross of water-purchasing expenses), where

water quantity is beneficial to both sectors (i.e., 𝑉𝑤𝑢(𝑤𝑢) > 0 and 𝑉𝑤

𝑎(𝑤𝑎, 𝑠) > 0),

whereas water salinity is harmful only to agriculture (𝑉𝑠𝑢(𝑤𝑢) = 0 and 𝑉𝑠

𝑎(𝑤𝑎, 𝑠) < 0).

A benevolent water authority manages water centrally by setting the capacities of

groundwater extraction and desalination, as well as the administrative water prices at the

consumption zones. As already noted, under the SI scenario, the planner solves the

problem in equation (1) which, with simplifying specifications, becomes

max𝑤𝑑,𝑤𝑔,𝑤𝑢,𝑤𝑎,𝑠𝑑,𝑠𝑔

𝑊 = 𝑉𝑢(𝑤𝑢) + 𝑉𝑎(𝑤𝑎, 𝑠) − 𝑐𝑑𝑤𝑑 − 𝑐𝑔𝑤𝑔 − 𝐶𝑑

𝑠. 𝑡. 𝑤 = 𝑤𝑢 + 𝑤𝑎 = 𝑤𝑑 + 𝑤𝑔, 𝑤𝑔 ≤ �̅�𝑔,

𝑠𝑑 ≥ 𝑠𝑑, 𝑠𝑔 ≥ 𝑠𝑔, 𝑠 =𝑤𝑑𝑠𝑑+𝑤𝑔𝑠𝑔

𝑤

𝑤𝑑, 𝑤𝑔, 𝑤𝑢, 𝑤𝑎, 𝑠𝑑, 𝑠𝑔 ≥ 0

(2)

By substituting the balance constraint 𝑤𝑢 = 𝑤𝑑 + 𝑤𝑔 − 𝑤𝑎 into 𝑉𝑢(𝑤𝑢) and optimizing

with respect to 𝑤𝑎 (assuming that the second-order conditions prevail), we get

𝑝SI = 𝑉𝑤𝑢(𝑤𝑢) = 𝑉𝑤

𝑎(𝑤𝑎, 𝑠) (3)

implying that a single optimal administrative water price (denoted 𝑝SI to indicate the SI

scenario) should be set for both consumption sectors. Optimization with respect to 𝑤𝑔

and 𝑤𝑑 subject to the condition in equation (3) yields

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𝑝SI = 𝑐𝑑 − 𝑉𝑠𝑎(𝑤𝑎, 𝑠)

𝑤𝑔(𝑠𝑑−𝑠𝑔)

(𝑤SC)2 (4)

𝑝SI = 𝑐𝑔 + 𝑉𝑠𝑎(𝑤𝑎, 𝑠)

𝑤𝑑(𝑠𝑑−𝑠𝑔)

(𝑤SI)2 + 𝜆𝑔 (5)

where 𝑤SI denotes the total water consumption under price 𝑝SI, and 𝜆𝑔 is the shadow

value of the groundwater constraint 𝑤𝑔 ≤ �̅�𝑔. Taken together, equations (4) and (5) yield

the efficiency condition underlying the price 𝑝SI

𝑉𝑠𝑎(𝑤𝑎,𝑠)

𝑤SI(𝑠𝑑 − 𝑠𝑔) = 𝑐𝑑 − (𝑐𝑔 + 𝜆𝑔) (6)

which requires the (left-hand-side) per-water-unit agricultural benefits associated with

reducing salinity from 𝑠𝑔 to 𝑠𝑑 to be equal to the (right-hand-side) difference between the

per-water-unit supply (plus scarcity) costs of the two sources.

Equations (4) and (5) imply 𝑐𝑑 ≥ 𝑝SI ≥ 𝑐𝑔. Equation (4) expresses the price of the

supplied blended water in relation to the supply of desalinated water. The term

𝑉𝑠𝑎(𝑤𝑎, 𝑠)


(𝑤SI)2 in equation (4) reflects the marginal benefits accrued to the

agricultural sector by the decline in salinity of the mixed water due to the last unit of

desalinated water. However, from the perspective of any urban or agricultural water

consumer, this is an external effect, as she or he overlooks the salinity reduction

associated with the consumption of an additional unit of desalinated water. Therefore,

efficiency requires internalizing this external effect as a subsidy for the desalinated water

incorporated in the supplied blended water. The subsidy incentivizes the consumption of

desalinated-water quantities beyond the level equating the water price to the marginal

desalination cost 𝑐𝑑. Clearly, supplying the water quantity demanded under price 𝑝SI

requires the establishment of a sufficiently large desalination capacity.

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The optimal price 𝑝SI is also obtained in equation (5) by inspecting the effect of the

groundwater incorporated in the supplied blended water. The term 𝑉𝑠𝑎(𝑤𝑎, 𝑠)

𝑤𝑑(𝑠𝑔−𝑠𝑑)

(𝑤SI)2

in equation (5) represents the marginal damage caused to agriculture by an additional unit

of groundwater due to the increased salinity of the mixed water. This is a negative

external effect, which should be introduced as a tax to all water consumers in order to

render the optimal groundwater supply lower than that equating the water price to 𝑐𝑔

(even under an ineffective groundwater constraint; i.e., 𝜆𝑔 = 0).

The optimal solution is illustrated schematically in Figure 2a. It is assumed that

groundwater is supplied first at the marginal cost 𝑐𝑔, and water deliveries beyond the

groundwater constraint �̅�𝑔 require desalination at the marginal cost 𝑐𝑑. The brown

dashed curve denoted 𝑉𝑤𝑢(𝑤𝑢) is the inverse urban-water demand. The solid pink curve

marked by 𝑉𝑤(𝑤, 𝑠) represents the inverse aggregate demands of the urban and

agricultural sectors. At �̅�𝑔, the curve 𝑉𝑤(𝑤, 𝑠) kinks upward due to the increase in

agricultural produce resulting from the reduction in the blended water’s average salinity

𝑠, which occurs under positive supplies of desalinated water. The solid green curve

𝑉𝑤(𝑤, 𝑠𝑔) illustrates the inverse aggregate demand for the (hypothetical) case in which

the salinity of the blended water is unaffected by desalination, and remains similar to that

of the groundwater. The optimal conditions in equations (3), (4), and (5) imply that the

optimal water supply, 𝑤SI, is set such that 𝑉𝑤(𝑤SI, 𝑠) = 𝑐𝑑. Then, the water price can be

computed based on the equality 𝑝SI = 𝑉𝑤(𝑤SI, 𝑠𝑔).

Figure 2 about here

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Are the variable water-supply costs covered under the SI optimal price 𝑝SI? Based on

equation (5), the cost-recovery condition with respect to the variable costs, 𝑝SI𝑤SI ≥

𝑐𝑑𝑤𝑑 + 𝑐𝑔𝑤𝑔, becomes

𝑉𝑠𝑎(𝑤𝑎,𝑠)

𝑤SI(𝑠𝑑 − 𝑠𝑔) ≥ 𝑐𝑑 − (𝑐𝑔 + 𝜆𝑔 + 𝜆𝑔

𝑤𝑔

𝑤𝑑) (7)

which, in view of equation (6), indicates that the surplus of water suppliers is positive

provided that 𝜆𝑔𝑤𝑔

𝑤𝑑> 0; that is, provided that 𝑤𝑔 = �̅�𝑔 > 0.

The economic implications of changes in the salinities of the water sources can be

learned from the shadow values of the respective desalination and groundwater salinity

constraints 𝑠𝑑 ≥ 𝑠𝑑 and 𝑠𝑔 ≥ 𝑠𝑔, which are defined by 𝜆𝑠𝑑 = 𝑉𝑠𝑎(𝑤𝑎, 𝑠)

𝑤𝑑

𝑤SI and 𝜆𝑠𝑔 =


𝑤𝑔

𝑤SI, respectively. Thus, the larger the share of a water source in the total water

supply, the larger the negative agricultural impact associated with a marginal increase in

the salinity of that source.

Turning to the SE scenario, suppose that the groundwater source is exhausted (i.e.,

𝑤𝑔 = �̅�𝑔), and desalinated water is supplied (𝑤𝑑 > 0); alas, the water master refers to

desalination as an instrument for resolving water-quantity scarcity while ignoring its

impact on salinity; that is, she or he erroneously assumes that the salinity of the supplied

blended water is fixed at 𝑠𝑔. Consequently, when determining the administrative water

price (denoted 𝑝SE for the SE case) according to equations (4) and (5), the terms



(𝑤𝑑+𝑤𝑔)2 and 𝑉𝑠

𝑎(𝑤𝑎, 𝑠)𝑤𝑑(𝑠𝑑−𝑠𝑔)

(𝑤𝑑+𝑤𝑔)2 , respectively, are dropped; hence, 𝑝SE =

𝑐𝑑, and equation (5) implies 𝜆𝑔 = 𝑐𝑑 − 𝑐𝑔. Nevertheless, the actual salinity of the mixed

14

water, 𝑠, will be lower than 𝑠𝑔 when desalinated water is supplied, and the actual levels

of 𝑤𝑑 and 𝑤𝑎 can be computed by the conditions

𝑐𝑑 = 𝑉𝑤𝑢(𝑤𝑑 + �̅�𝑔 − 𝑤𝑎) = 𝑉𝑤

𝑎(𝑤𝑎, 𝑠) + 𝑉𝑠𝑎(𝑤𝑎, 𝑠)

�̅�𝑔(𝑠𝑑−𝑠𝑔)

(𝑤𝑑+�̅�𝑔)2 (8)

which follow from equations (3) and (4), together with the water-balance constraint 𝑤𝑢 =

𝑤𝑑 + �̅�𝑔 −𝑤𝑎.

Figure 2b illustrates the SE solution. The policy maker mistakenly refers to the

(green) curve 𝑉𝑤(𝑤, 𝑠𝑔) as the inverse aggregate demand, and therefore sets 𝑝SE =

𝑉𝑤(𝑤, 𝑠𝑔) = 𝑐𝑑. Since 𝑝SE > 𝑝SI, the desalination capacity and the surpluses of the urban

and agricultural consumers are lower than their SI counterparts, whereas the surplus of

the water suppliers is positive, and equals (𝑐𝑑 − 𝑐𝑔)�̅�𝑔. The area marked F indicates the

deadweight loss associated with ignoring the desalination impact on salinity.

So far, we have assumed that desalination is warranted under both scenarios; that is,

the welfare with desalination exceeds the welfare without it. It may well be that this

condition holds under the SI scenario, but not under that of SE, as illustrated in Figure 2c.

The total water-consumption value associated with desalination under the SI scenario

(i.e., the area of the dashed-yellow-line trapezoid underneath the (pink) inverse aggregate

demand curve 𝑉𝑤(𝑤, 𝑠) in the segment 𝑤 ∈ [�̅�𝑔, 𝑤SI]) exceeds the total desalination cost

(the area of the pink rectangle, 𝑐𝑑(𝑤SI − �̅�𝑔) + 𝐶𝑑). In the SE case, however, the total

consumption value erroneously perceived by the water master (the area of the dashed-

brown-line trapezoid below the (green) inverse aggregate demand curve 𝑉𝑤(𝑤, 𝑠𝑔) in the

segment 𝑤 ∈ [�̅�𝑔, 𝑤SE]) is smaller than the respective desalination costs (the area of the

green rectangle, 𝑐𝑑(𝑤SE − �̅�𝑔) + 𝐶𝑑). Therefore, in the SE case, the water master

would reject desalination altogether, and may set a market-clearing water price according

15

to 𝑝SE = 𝑉𝑤(�̅�𝑔, 𝑠𝑔). The deadweight loss under SE increases relative to the case in

which the desalination infrastructure is warranted or already in place, as assumed in

Figure 2b.

To conclude, we show that overlooking the effect of desalination on the supplied-

water salinity leads to higher water prices, lower desalination, and lower consumer

surplus, whereas the water suppliers’ profits increase. Moreover, the establishment of

desalination infrastructures may be wrongly perceived as economically unwarranted.

Thus, in a dynamic framework, where water demands increase over time, the

development rate of desalination capacities will be slower under SE than under SI.

3. Empirical Model of Israel’s Water Economy

Our objective is to evaluate empirically the economic implications of ignoring the salinity

impact of large-scale desalination in the design of Israel’s water economy.

3.1. Israel’s Water Economy

Israel faces three water-management challenges: first, while precipitation is relatively

abundant in the north, the population is concentrated in the center, and most of the

agricultural lands are located in the south; second, whereas rainfall events occur only in

winter, summer is the main irrigation season; third, natural freshwater is scarce,

successive drought years are common, and water scarcity is steadily increasing due to

rapid population growth (Kislev, 2011).

16

Israel has confronted these challenges by establishing a complex water-distribution

network that spans most of the country’s regions, in particular based on a national water

carrier that essentially turns almost the entire state into a single basin in terms of water

management. Severe water scarcity motivated the exploitation of brackish water and

TWW for irrigation, and in recent years, extensive seawater desalination has been

employed (Burn et al., 2015; Martínez-Alvarez et al., 2016) (see Appendix A). However,

desalination capacities were primarily designed to meet the growing water demand for

domestic uses, whereas the impact of desalination on irrigation-water salinity was not

considered explicitly (see Israel Water Authority, 2012a).

3.2. Empirical Model

By virtue of the Israeli Water Law (Israel Ministry of National Infrastructures, 1959),

water is a public property that is centrally managed by the government, which designs

water-supply infrastructures and sets administrative water prices and quotas to control

consumption; accordingly, the model’s objective is to characterize the optimal levels of

these policy instruments from the point of view of a welfare-maximizing benevolent

government.

Our model is based on a partial-equilibrium setup, integrating a water-distribution

module and an agriculture module, as depicted schematically in Figure 3. Adopting a

holistic approach (Brouwer & Hofkes, 2008), the variables of both modules are solved

simultaneously. The water-distribution module determines the allocation of water from

sources to regions of urban and agricultural consumers, sets the development trajectories

of infrastructure capacities, and computes the salinities, the shadow values of constraints,

17

and (assuming price-based water allocations) the efficient water prices throughout the

water-distribution network during the simulated period. The agriculture module

characterizes the optimal allocation of agricultural land across crops in each of the

agricultural regions subject to constrained regional land, foreign-labor quotas, and the

quantity and salinity of the water allocated to that region by the water-distribution

module. The irrigation water’s salinity affects crop yields in relation to crops’ tolerance

to salinity. In addition, the agricultural module includes demand functions for vegetative

agricultural products, such that the prices of those products constitute equilibria in the

local markets for fresh fruit and vegetables—the latter protected by import tariffs.

Figure 3 about here

We calibrate the model to a base year (2015) and run it for a 30-year period. The

demands for urban water and agricultural products shift along the years in relation to a

projected population growth—this incentivizes the extension of water-supply

infrastructures, particularly the supply of desalinated water, which affects the irrigation-

water salinity and thereby yields optimal agricultural land allocation, equilibrium prices

and quantities in the different markets for vegetative agricultural products, and the

allocation of surpluses among the urban-water users, farmers, consumers of agricultural

products, and water suppliers.

The model is programmed in GAMS (General Algebraic Modeling System), with

links to input-data and output-data Excel files (see supplemental materials), and solves

simultaneously for all variables throughout the entire planning horizon. The GAMS code

describes the model components in detail; here, we outline the main empirical elements.

18

3.2.1. Water-Distribution Module

The water-distribution module extends the hydro-economic model MYWAS (Multi-Year

Water Allocation System) (Fisher & Huber-Lee, 2011; Reznik et al., 2017), which is an

Israeli multiyear version of the one-period WAS (Water Allocation System) model

developed in the 1990s for the areas of Israel, Jordan and the Palestinian Authority

(Fisher et al., 2005). Appendix B presents schemes of the water network embedded in

MYWAS. There are 19 naturally enriched freshwater stocks (15 aquifers, the Sea of

Galilee, and 3 regional arrays of artificial reservoirs), 5 seawater-desalination plants in

the center of the country, 4 non-enriched brackish-water aquifers which are connected to

desalination plants, 18 wastewater-treatment plants (WWTPs) that apply secondary

treatment, and 1 which applies tertiary treatment to the sewage of the Tel Aviv

metropolis. Water users include 21 urban regions and 18 agricultural zones. Urban zones

obtain freshwater for domestic and industrial uses from natural freshwater sources,

desalinated seawater and desalinated brackish water, and generate sewage outflows that

undergo mandatory treatment at the WWTPs. The agricultural zones can consume

irrigation water from all sources. The prevailing base-year water system includes 163

freshwater pipelines and 74 pipelines for wastewater and brackish water.

We introduce infrastructures that are nonexistent in the base year, the timing and

extent of which can be set as determined endogenously; these include an optional

desalination plant in the northwest region of Acre, 12 pipelines that connect seawater-

desalination plants directly to agricultural areas located close to the Mediterranean

shoreline, and deliveries of desalinated TWW to agricultural zones (which necessitates

tertiary wastewater pretreatment). For the wastewater-desalination activities we introduce

19

an output/input rate parameter of 0.85, meaning that the brine needed to be disposed of

constitutes 15% (Pérez-González et al., 2012). We also allow discharge of TWW from

WWTPs to the environment (at zero cost or benefit), conditional on being reclaimed to

the level of tertiary treatment to meet regulated quality standards. Together with these

potential activities, the water network includes 118 nodes, connected by 289 pipelines.

The extractions from naturally enriched freshwater sources are limited by stock

constraints. Let (𝑗 = 1,… ,19) denote a freshwater-source node, and 𝑤𝑡𝑗 (m3 year-1) be the

extraction from source 𝑗 during year 𝑡. The amount 𝑤𝑡𝑗 is limited by the extractable stock

�̅�𝑡𝑗 (m3 year-1), which is a state variable defined by �̅�𝑡

𝑗= max(0, 𝑅𝑡−1

𝑗− �̅�𝑡−1

𝑗− 𝑒𝑡−1

𝑗),

where 𝑅𝑡−1𝑗

(m3 year-1) is the previous year’s recharge, and 𝑒𝑡−1𝑗= max(0, �̅�𝑡−1

𝑗+ 𝑅𝑡−1

𝑗−

𝑤𝑡−1𝑗− �̅�𝑗) (m3 year-1) is the spillover from the source to the environment when the stock

exceeds its maximum extractable content �̅�𝑗 (m3 year-1). In addition, we set a minimum

extractable stock for the last period, 𝑏𝑇+1𝑗

, such that �̅�𝑇+1𝑗≥ 𝑏𝑇+1

𝑗.

The water salinity is defined for each pipeline as the average salinities of the inflows

into the pipe, weighted by the respective inflow volumes. The source salinities are 1 dS

m-1 for freshwater from naturally enriched sources, 0.25 dS m-1 for desalinated water

(Yermiyahu et al., 2007), and 4 dS m-1 for brackish water. The salinity of freshwater

pumped from the Sea of Galilee decreases linearly with the lake's water stock. Pursuant

to regulations, the salinity of urban inflows is constrained to not exceed 1.4 dS m-1. The

salinity of the sewage produced in any urban region is 0.7 dS m-1 higher than the salinity

of the inflow into that region (Israel Water Authority, 2012b).

Variable and fixed water-supply costs of all infrastructural elements are taken from

Reznik et al. (2017). Note that the desalination cost of TWW ($0.63 m-3 on average) is

20

higher than that of seawater ($0.56 m-3) due to the multiple TWW-desalination

pretreatments and the need to dispose of the brine produced by plants located away from

the seacoast. To define the benefits of urban-water users we denote by 𝑖 (𝑖 = 1,… ,21) an

urban-region node, and by 𝑤𝑡𝑖 (m3 year-1), the respective water consumption. The total

benefits associated with 𝑤𝑡𝑖 equal the integrated inverse constant-elasticity demand

function 𝑉𝑡𝑖(𝑤𝑡

𝑖) = (𝜂 + 1)−1𝜐𝑡𝑖(𝑤𝑡

𝑖)𝜂+1

($ year-1), where 𝜂−1 is the demand elasticity

and 𝜐𝑡𝑖 is computed for any year 𝑡 by 𝜐𝑡

𝑖 = 𝑝0𝑖 (𝑤0

𝑖(1 + 𝜌)𝑡)−𝜂

, wherein 𝜌 is the

population-growth rate and 𝑝0𝑖 ($ m-3) is the observed base year (𝑡 = 0) urban-water

price. The parameter 𝜂 = −0.1 is taken from Bar-Shira et al. (2007).

3.2.2. Agriculture Module

Our analysis incorporates the 55 main crops grown by the Israeli agricultural sector on

about 300,000 ha, supplying vegetative products to the processing industry, export, and

the local fresh-produce markets. Nearly 60% of the arable area is devoted to high-value

fruit and vegetable crops (Israel Central Bureau of Statistics, 2019), requiring intensive

irrigation and a large labor force; the latter is highly dependent on foreign workers

(Kemp, 2010), who are allocated to farmers based on cropping-acreage declarations.

Whereas most of the field-crop outputs (particularly grains) are exempted from import

tariffs, the production of fruit and vegetables is protected by import tariff-rate quotas

(Finkelshtain & Kachel, 2009; Finkelshtain et al., 2011); we assume that the local-market

prices and quantities of fruit and vegetables constitute a competitive equilibrium.

Figure 4 about here

21

Apparently, the fresh-product crops grown in Israel are also relatively sensitive to

salinity. Figure 4 presents the aggregate agricultural land, water use, and production value

of the 55 crops in the base year, categorized into production to the local market,

processing industry, and export. In addition, each value is separated into four crop

bundles that classify the crops according to their salinity tolerance (Maas & Hoffman,

1977). Consider the salinity-sensitive and moderately sensitive crop bundles delivered to

the local market, where the demand is steadily growing due to population growth, and

where prices may rise due to the presence of import tariffs: while only 20% of the total

arable land in the country is allocated to these two bundles (Figure 4a), their water

consumption constitutes 46% of the total irrigation-water use (Figure 4b), and their

production value amounts to 59% (Figure 4c). These patterns can potentially incentivize

large allocations of desalinated water to the agricultural sector to reduce irrigation-water

salinity, increase the yields and per-hectare profits of these crops, and in turn, the land

allocated to them and their total production value. To capture these effects, we base the

agriculture module on the VALUE (Vegetative Agriculture Land-Use Economics) model.

VALUE is a positive mathematical programming (PMP) partial-equilibrium model

of Israel’s agriculture, used to analyze rural landscape amenities (Kan et al., 2009),

organic-waste policies (Kan et al., 2010; Raviv et al., 2017), climate change (Palatnik et

al., 2011; Zelingher et al., 2019), and water management (Baum et al., 2016; Kan &

Rapaport-Rom, 2012). The decision variables in VALUE are the cultivated lands

allocated to the 55 crops in each of the 18 nodes specified in MYWAS as agricultural

water-consumption regions. We denote by 𝑥𝑜𝑡𝑎 (ha) the land assigned in year 𝑡 to crop 𝑜

22

(𝑜 = 1, … ,55) in agricultural region 𝑎 (𝑎 = 1, … ,18). The output 𝑦𝑜𝑡𝑎 (ton ha-1 year-1) is

given by the production function

𝑦𝑜𝑡𝑎 (𝑤𝑜

𝑎, 𝑠𝑜𝑡𝑎 ) =

�̅�𝑜𝑎

1+𝛼𝑜1𝑎 (𝛼𝑜5

𝑎 𝑠𝑜𝑡𝑎 +𝛼𝑜2

𝑎 (𝑤𝑜𝑎)𝛼𝑜3

𝑎)𝛼𝑜4𝑎 (9)

where 𝑤𝑜𝑎 (m3 ha-1 year-1) is the total water available to the crop, including irrigation

water and rainfall during the crop’s growing season, both of which are assumed constant;

𝑠𝑜𝑡𝑎 (dS m-1) is the salinity of 𝑤𝑜

𝑎, which is a weighted average of the salinities of the

water supply set by MYWAS for irrigation in region 𝑎 and the rainfall salinity (assumed

to be 0.1 (dS m-1)); �̅�𝑜𝑎 (ton ha-1 year-1) is the maximum potential yield obtainable under

zero salinity and no water deficit; 𝛼𝑜1𝑎 through 𝛼𝑜5

𝑎 are crop- and region-specific

parameters.

We develop the production functions by a four-stage meta-analysis procedure. First,

we use the yield–water salinity model developed by Shani et al. (2007) to generate a

dataset of plant-level relative yields (i.e., relative to �̅�𝑜𝑎) under different combinations of

water and salinity levels, adopting crop salinity-tolerance parameters from Tanji and

Kielen (2002), and region-specific soil and climate parameters from Kan and Rapaport-

Rom (2012); second, to account for intra-field spatial irrigation heterogeneity, we

calculate field-level relative-yield levels by applying the log-normal distribution function

(Knapp, 1992), calibrated for a Christiansen uniformity coefficient of 85; third, we apply

a nonlinear regression to the generated dataset to estimate the parameters 𝛼𝑜1𝑎 through

𝛼𝑜5𝑎 ; finally, we calibrate �̅�𝑜

𝑎 using the observed base-year yield 𝑦𝑜0𝑎 and salinity 𝑠𝑜0

𝑎 :

�̅�𝑜𝑎 = 𝑦𝑜0

𝑎 (1 + 𝛼𝑜1𝑎 (𝛼𝑜5

𝑎 𝑠𝑜0𝑎 + 𝛼𝑜2

𝑎 (𝑤𝑜𝑎)𝛼𝑜3

𝑎)𝛼𝑜4𝑎

). The resultant functions exhibit the

23

expected properties of 𝜕𝑦

𝜕𝑤> 0 and

𝜕𝑦

𝜕𝑠< 0. In addition,

𝜕2𝑦

𝜕𝑠2> 0, meaning that the higher

the salinity of the water applied to a crop, the lower the salinity’s marginal damage.

The statewide production of each crop 𝑜 in year 𝑡, 𝑌𝑜𝑡 = ∑ 𝑥𝑜𝑡𝑎 𝑦𝑜𝑡

𝑎18𝑎=1 (ton year-1), is

allocated to the local food-processing industry and export markets based on the respective

constant market shares 𝜇𝑜𝐿, 𝜇𝑜

𝐼𝑛 and 𝜇𝑜𝐸𝑥, where 𝜇𝑜

𝐿 + 𝜇𝑜𝐼𝑛 + 𝜇𝑜

𝐸𝑥 = 1. The prices of crop

𝑜’s outputs supplied to the industry and to export, denoted, respectively, 𝑝𝑜𝐼𝑛 and 𝑝𝑜

𝐸𝑥 ($

ton-1), equal their corresponding (exogenous) import prices, whereas the price of the

local-market product, 𝑝𝑜𝑡𝐿 , is determined in equilibrium subject to the import-tariff-rate

quotas. We use a constant-elasticity demand function to represent the benefits to local

consumers of crop 𝑜’s products, 𝑉𝑜𝑡(𝑌𝑜𝑡, 𝐼𝑚𝑜𝑡) = 𝐴𝑜𝑡(𝜇𝑜𝐿𝑌𝑜𝑡+𝐼𝑚𝑜𝑡)

𝜗𝑜+1

𝜗𝑜+1 ($ year-1), in which

𝐼𝑚𝑜𝑡 (ton year-1) is import, 𝜗𝑜−1 is the demand elasticity, and 𝐴𝑜𝑡 = 𝑝𝑜0

𝐿 ((𝜇𝑜𝐿𝑌𝑜𝑡 +

𝐼𝑚𝑜𝑡)(1 + 𝜌)𝑡)−𝜗𝑜

($ year-1) is an inverse-demand-function parameter, calibrated for the

base year based on the observed local price 𝑝𝑜0𝐿 and output 𝑌𝑜𝑡. The total import is given

by 𝐼𝑚𝑜𝑡 = 𝐼𝑚𝑜𝑡0 + 𝐼𝑚𝑜𝑡

1 , with 𝐼𝑚𝑜𝑡0 and 𝐼𝑚𝑜𝑡

1 denoting the amounts imported free of

tariff and with the tariff, respectively, where 𝐼𝑚𝑜𝑡0 cannot exceed the free-of-tariff quota

𝐼𝑚̅̅̅̅ 𝑜0. For the import price of each crop, we select the country from which the import cost

(including transportation to Israel) is the lowest. The cropping acreage, per-hectare

yields, imports, prices and tariffs are from the Israel Ministry of Agriculture and Rural

Development, and the crop-specific output-demand elasticities (𝜗𝑜) are adopted from

Fuchs (2014).

Following the PMP approach, we assume a quadratic regional profit function, 𝜋𝑜𝑡𝑎 =

𝑥𝑜𝑡𝑎 (𝑝𝑜𝑡𝑦𝑜𝑡

𝑎 − 𝛄𝑜𝑎 − 𝜙𝑜

𝑎 − 𝛿𝑜𝑎𝑥𝑜𝑡𝑎 ) ($ year-1), where 𝑝𝑜𝑡 = 𝜇𝑜

𝐿𝑝𝑜𝑡𝐿 + 𝜇𝑜

𝐼𝑛𝑝𝑜𝐼𝑛 + 𝜇𝑜

𝐸𝑥𝑝𝑜𝐸𝑥 ($

24

ton-1) is the average price of crop o, 𝛄𝑜𝑎 ($ ha-1 year-1) is a vector of input costs, and 𝜙𝑜

𝑎 ($

ha-1 year-1) and 𝛿𝑜𝑎 ($ ha-2 year-1) are parameters representing unobservable costs,

calibrated by the two-stage procedure proposed by Howitt (1995). The calibration

accounts for the base-year constraints of regional agricultural land, foreign labor, and

water: ∑ 𝑥𝑜0𝑎55

𝑜=1 ≤ 𝑥𝑎, ∑ 𝑥𝑜0𝑎 𝑓𝑙𝑜

𝑎55𝑜=1 ≤ 𝑓𝑙𝑎, and ∑ 𝑥𝑜0

𝑎 𝑤𝑜𝑎55

𝑜=1 ≤ 𝑤0𝑎, respectively, where

𝑥𝑎 (ha) is region 𝑎’s total arable land, 𝑓𝑙𝑜𝑎 (day ha-1 year-1) and 𝑓𝑙𝑎 (day year-1) are,

respectively, crop 𝑜’s consumption and regional aggregate quota of foreign labor, and 𝑤0𝑎

is the base-year total irrigation water allocated to the region.

3.2.3. Integrated Model

The integrated MYWAS–VALUE model solves the problem expressed in equation (1),

the elements of which incorporate the empirical specifications of benefits, costs, and

constraints described above. We employ a social discount rate (𝑟) of 3.5%, as suggested

by Nordhaus (2007), and adopt the Israel Central Bureau of Statistics (2014) prediction of

1.8% annual population growth rate (𝜌). As an end condition, we mandate retaining a

minimum of 5% of the extractable stock from each naturally enriched freshwater source.

The historical average annual precipitation and enrichment of natural freshwater sources

(taken from Weinberger et al., 2012) are assumed for every year during the simulated

period. Monetary values are in 2015 US dollars, discounted to the 15th year (2030).

Note that while the demands for urban water and agricultural products are calibrated

for 2015 based on the assumption of market-clearing prices, the observed base-year water

prices and the associated water distributions and infrastructures are not optimal! This is

because of the Israeli Balanced Budget Water Economy legislation (Reznik et al., 2016);

25

therefore, as shown in Appendix C, the model does not reproduce the observed values of

the decision variables in the base year. Thus, the base-year conditions do not serve as a

reference in our analyses. Instead, we compare the optimal solutions under the SI and SE

scenarios.

While the solution for the SI case is obtained by solving the problem in equation (1),

the SE scenario requires a two-stage procedure: first, we run the model with the water

salinity in each agricultural region fixed at its base-year level (i.e., in equation 9, 𝑠𝑜𝑡𝑎 =

𝑠𝑜0𝑎 for all 𝑡 = 1,…30); the output of this simulation is an infrastructure-development

plan that the planner erroneously considers optimal given her or his presumption of

nonresponsive irrigation-water salinity. However, as already noted in the theoretical

analysis, salinity will change, and in turn affect crop production, agricultural output

prices, farming profitability, land use, and surpluses of producers and consumers in the

agricultural sector. Therefore, in the second stage, we rerun the model while allowing

salinity to change, but at the same time forcing the development of infrastructures to

follow the infrastructure plan that resulted from the first stage. Thus, the SE scenario

represents the expected evolution of the water and vegetative-agriculture sectors under

efficient prices, given a non-optimal water-infrastructure blueprint.

4. Economic Implications of Externalizing Salinity

We first evaluate the differences between the SI and SE scenarios with respect to water

supplies, salinities, prices, and surplus allocation across sectors. Then, we assess how

these differences are affected by changes in precipitation and in the agricultural product

26

import tariffs and foreign-worker quotas. Appendix D provides detailed results tables;

here, we present the main findings.

Figure 5 about here

4.1. Internalized versus Externalized Salinity

Figure 5 presents optimal trajectories of statewide water supply to the agricultural regions

and discharge of tertiary-TWW to natural waterways under the two scenarios. The SI

optimal solution suggests massive delivery of desalinated water to the agricultural zones,

mostly from seawater-desalination plants, and to a lower extent by desalinating TWW

(Figure 5a). It is found optimal to install 8 out of the 12 optional pipelines connecting

seawater-desalination plants directly to agricultural regions, as well as the optional

seawater-desalination plant in the north of the country. Irrigation with natural freshwater

and secondary-TWW is stable throughout the period, seawater desalination for irrigation

increases slightly with time, and most of the growing amount of sewage produced by the

urban zones (not shown) is discharged to nature after tertiary wastewater treatment.

Compared to the SI scenario, the total irrigation water under the SE scenario is 45%

lower (Figure 5b), particularly because of the lower capacity of the infrastructures

supplying desalinated seawater to the agricultural zones, and because desalination of

TWW becomes unwarranted due to the higher costs relative to that of seawater

desalination. Concomitantly, a larger share of the TWW is used for irrigation, such that

lower amounts are discharged to nature. Moreover, the water-supply trends differ from

the SI solution: seawater desalination for agriculture declines over time, continuously

27

replaced by the growing amounts of TWW produced in the urban zones and by

freshwater from natural sources.

Figure 6 presents per-annum statewide averages of water supply, use and salinity

under the two scenarios. Clearly, the total water deliveries (Figure 6b) are lower under

SE, and the average irrigation-water salinity (Figure 6c) is 0.2 (dS m-1) higher due to the

larger shares of natural freshwater and TWW in the supplied water (Figures 5a, 5b, and

6a).

Figure 6 about here

Figure 7 reports average shadow values of water availability at the sources (Figure

7a), infrastructure-capacity constraints (Figure 7b), water prices in the urban and

agricultural zones (Figure 7c), and shadow values of the salinity of the water sources

(Figure 7d). In the SE case, water is scarcer due to the lower water-infrastructure

capacity; hence, the higher water prices compared to SI. Notice the switch in sign of the

shadow value of the inflow–outflow balance constraint imposed on the WWTP (Figure

7a), meaning that instead of subsidizing TWW to encourage farmers to consume it under

SI, farmers are willing to pay for TWW in the SE case. In addition, while irrigation

salinity is higher under SE (Figure 6c), the shadow value of the salinity in the irrigation

water is slightly lower (Figure 7d), which is attributed to the aforementioned positive sign

of the second derivative of the production function with respect to salinity (𝜕2𝑦

𝜕𝑠2> 0).

Also notable is the relatively large negative shadow value of the salinity of the

desalinated TWW under SI, which can be explained by the fact that this water source

supplies low-salinity water only for agricultural irrigation, whereas the salinity of the

TWW supplied to agricultural regions is high, and desalinated brackish water and

28

seawater are also supplied to the urban users who are assumed immune to salinity

changes (up to the maximum urban-water salinity limit of 1.4 (dS m-1)). Thus, as TWW

desalination vanishes under the SE scenario, the share of the other sources rises and

therefore, their salinity shadow values become higher.

Figure 7 about here

As already noted, we assume that prices are set efficiently, and use the demand

functions and shadow values to compute the water and agriculture-product prices, and the

corresponding allocation of surpluses across sectors. Figure 8a presents average yearly

surplus allocations under the SI and SE scenarios (consumer surpluses are normalized to

0 under the SI scenario). As shown analytically, all sectors except for water suppliers face

a welfare loss under the SE vs. SI scenario, where the overall annual deadweight loss is

$366 million. On average, this damage amounts to about $1,200 per hectare of arable

land, caused by the salinity rise (of 0.2 (dS m-1) on average, Figure 6c), of which farming

losses are $1,087 ha-1 year-1 (29% of farmers’ profit under the SI scenario).

Figure 8 about here

4.2. Sensitivity Analyses

We commence by analyzing a change in precipitation. On a per-annum average, Israel’s

arable lands obtain 375 mm and 333 mm of water from naturally enriched freshwater

sources and direct rainfall, respectively. However, climatological studies (Bentsen et al.,

2013; Gent et al., 2011; Watanabe et al., 2010) predict a precipitation reduction of 10–

30% throughout Israel in the coming decades. In Figure 8b, we present the impact of a

20% reduction in precipitation for every year of the 30-year period on the allocation of

29

surpluses under the SI and SE scenarios. All sectors except for the water suppliers lose

from the change, farmers in particular. The overall deadweight loss is 37% and 38%

under the SI and SE scenarios, respectively. Regarding water management (not shown),

in both scenarios, increasing seawater desalination is the main means of offsetting the

reduction in availability of natural freshwater sources, as well as cuts in agricultural

irrigation.

As already noted, Israel employs import tariffs to support local agriculture and

controls the allocation of foreign labor. In Figures 8c and 8d we present, respectively, the

surplus change caused by the abolishment of import tariffs on vegetative products and

dismissing the control of foreign labor by quotas (for the latter, we assume no change in

the regulated minimum wage of the foreign workers or in the crop-specific per-hectare

employment of foreign and local workers). Both policy changes effectively transfer

surpluses from farmers to consumers of agricultural products in both the SI and SE cases,

raising the overall welfare, with a larger effect under the SE scenario.

The agricultural intervention policies employed in Israel are continuously criticized

economically (Organization for Economic Co-operation and Development [OECD],

2018), and are the subject of public and political debate (Hendel et al., 2017). The overall

producer-support estimate for Israel is 17.7%, slightly below the OECD average of 19.2%

(OECD, 2019). However, the share of domestic price support, border measures, and other

market-distorting interventions is relatively high (91%); therefore, the effect of changes

in such policies is expected to be larger than in other countries with similar semiarid

conditions (e.g., Australia, Spain, and California).

30

5. Limitations and Extensions

This study shows that, under the specific circumstances of Israel, large-scale supply of

desalinated water for irrigation is economically warranted, and overlooking the impact of

desalination on irrigation-water salinity entails significant deadweight loss. Nevertheless,

“no model solves all problems” (Draper et al., 2003, p. 156), and the economic valuations

provided herein may vary with the inclusion of a range of exempted factors; a few

examples follow.

Our ability to introduce salinity impacts on agricultural outputs into our hydro-

economic model builds on decades of theoretical and experimental agronomic research.

However, aside from irrigation, salinity has additional economic implications, such as

health effects associated with drinking water (Dasgupta et al., 2016). Moreover, salinity

is but one of a large set of water-quality measures that determine the economic value of

water in various water uses. For example, the contents of Mg2+ and SO42– in desalinated

seawater are lower than recommended for drinking and irrigation water (Yermiyahu et

al., 2007), and desalination removes nutrients that might otherwise save on fertilization

expenses (Ben-Gal et al., 2009; Dawson & Hilton, 2011). On the other hand, TWW

desalination also eliminates various contaminants (Gur-Reznik & Dosoretz, 2015) that

damage irrigation systems (Tarchitzky et al., 2013) and cause environmental and health

risks (Fatta-Kassinos et al., 2011; Kasprzyk-Hordern et al., 2009) which, in turn, may

affect the demand for agricultural products (Messer et al., 2017). In addition, while our

model allows for environmental discharge of tertiary-TWW and spillovers from

31

freshwater aquifers, we do not assign values to these flows because there are as yet no

monetary valuations of the associated impacts on ecosystem services (Tsur, 2020).

Our modeling approach is suited to centrally managed water systems, as in Israel.

We assume benevolent policy makers; however, centralization attracts political pressure

to bend policies in favor of interest groups. Such distortions can be captured in a

political-equilibrium analytical framework (Finkelshtain & Kislev, 1997). For the case of

decentralized water systems, one should account for imperfections of water markets and

water-right allocations, asymmetric information, and transition and transaction costs

(Garrick et al., 2013; Richter et al., 2013).

Finally, our model does not explicitly incorporate uncertainty with respect to key

factors, such as population growth, climate conditions, and environmental effects, some

of which may be associated with deep uncertainty. Moreover, we maximize a single

objective, whereas water systems may involve multiple objectives. The analysis provided

here may be extended by employing many objective robust decision-making procedures

(e.g., Kasprzyk et al., 2013; Moallemi et al., 2020; Trindade et al., 2017).

Acknowledgments

This study was partly funded by the Israel Ministry of Agriculture and Rural

Development (grant number 12-04-0011) and the Center for Agricultural Economics

Research at the Hebrew University of Jerusalem. The authors thank the Editor, Associate

Editor, and three anonymous reviewers for valuable comments, and to Yael Kachel from

the Israel Ministry of Agriculture and Rural Development for providing data. The

32

empirical hydro-economic model developed in this study (entitled MYWAS-VALUE) is

available at: 10.5281/zenodo.3702053.

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39

Figure 1. A water economy with urban and agricultural zones in which water consumers

obtain a mixture of groundwater and desalinated water.

Groundwater

Desalination

Urban Zone

Agriculture Zone

�̅�𝑔, 𝑠𝑔, 𝑐𝑔

𝑤𝑔, 𝑠𝑔

𝑠𝑑 , 𝑐𝑑 , 𝐶𝑑𝑤𝑑 , 𝑠𝑑

𝑤𝑢, 𝑠

𝑤𝑎, 𝑠

𝑉𝑢 𝑤𝑢

𝑉𝑎 𝑤𝑎, 𝑠

40

𝑉𝑤𝑢 𝑤𝑢 - Inverse urban demand

𝑉𝑤 𝑤, 𝑠 - Inverse aggregate demand under average salinity 𝑠

𝑉𝑤 𝑤, 𝑠𝑔 - Inverse aggregate demand under groundwater salinity 𝑠𝑔

𝑉𝑤 𝑤, 𝑠𝑔

𝑉𝑤𝑢 𝑤𝑢

�̅�𝑔𝑤 = 𝑤𝑔 +𝑤𝑑

𝑐𝑑

𝑐𝑔

𝑝SI

𝑝

𝑤SI

𝑉𝑤 𝑤, 𝑠

𝑤𝑔 𝑤𝑑 0

Salinity Internalized

B

C

𝑉𝑠𝑎 𝑤𝑎, 𝑠

�̅�𝑔 𝑠𝑑 − 𝑠𝑔

𝑤SI 2

(a)

𝑉𝑠𝑎 𝑤𝑎, 𝑠

𝑤𝑑 𝑠𝑑 − 𝑠𝑔

𝑤SI 2+ 𝜆𝑔

A

Consumer surplus = A+B

Producer surplus = C-B

Welfare = A+C

Consumer surplus = D

Producer surplus = E

Welfare = D+E

Deadweight loss due to disregarding salinity = F



𝑐𝑑

𝑐𝑔

𝑝

𝑤SE

𝑉𝑤 𝑤, 𝑠

𝑤𝑔 𝑤𝑑 0

Salinity Externalized

E

(b)

𝑝SE=

D

F


41

Figure 2. Schematic illustration of water prices, quantities and surplus allocations under

(a) the Salinity-Internalized scenario, (b) the Salinity-Externalized scenario, and (c)

where water-use benefits from desalinated water exceed the desalination variable and

fixed costs under the Salinity-Internalized scenario, but not under the Salinity-

Externalized scenario.



𝑐𝑑

𝑐𝑔

𝑝

𝑤SE

𝑉𝑤 𝑤, 𝑠

𝑤𝑔 𝑤𝑑 0

Desalination Fixed Cost Effect

H

(c)

𝑝SEG


𝑤SI

Consumer surplus = G

Producer surplus = H

Welfare = G+H

42

Figure 3. Scheme of the integrated water and agriculture modules of the hydro-

economic model.

Seawater

Brackish

Water

Aquifers

Natural

Freshwater

Sources

Water Module

Agriculture Module

Labor

Land

Local Market

Export

Industry

Agricultural Zones

Import

Urban ZonesWater flow

Agriculture output

Agriculture input

TWW

Desalination

Wastewater Secondary Treatment

Precipitation

Environment

Desalination Wastewater Tertiary Treatment

43

Figure 4. Base-year statewide allocation of (a) land use, (b) water consumption, and (c) production value across four crop bundles

with different salinity-tolerance levels, separated into production for the local fresh-produce, industry and export markets.

0

20

40

60

80

100

120

140

160

180

200

Lo

cal

Indu

stry

Ex

port

10

3h

ecta

re

Land

Tolerant

Moderately Tolerant

Moderately Sensitive

Sensitive

(a)

0

100

200

300

400

500

600

700

Lo

cal

Indu

stry

Ex

port

10

3m

3year

-1

Water(b)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Lo

cal

Indu

stry

Ex

port

10

6$

year

-1

Production Value(c)

44

Figure 5. Optimal trajectories of statewide annual water supplies to agriculture and

discharges of tertiary-TWW to nature under (a) the Salinity-Internalized and (b) the

Salinity-Externalized scenarios.

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

(10

6m

3year

-1)

Year

Salinity Internalized(a)

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

(10

6m

3 y

ear

-1)

Year

Salinity Externalized (b)

Fresh Groundwater Seawater Desalinated

Brackish Water Desalinated TWW Desalinated

Secondary TWW to Agriculture Tertiary TWW to Nature

Total Agriculture Total Urban

45

Figure 6. Optimal average (a) annual water supplies, (b) annual water uses, and (c)

supplied-water salinities under the Salinity-Internalized and Salinity-Externalized

scenarios.

0

200

400

600

800

1000

1200

Natu

ral F

resh

water

Tre

ated W

astew

ater

Desa

linated

Seaw

ate

r

Desa

linated

Brac

kish

Desa

linated

TW

W

10

6m

3year-1

Water Supply


Salinity Externilized

(a)

0

200

400

600

800

1000

1200

Urb

an

Agric

ultu

re

Natu

re

10

6m

3year-1

Water Use(b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Urb

an

Agric

ultu

re

Natu

re

dS

m-1

Water Salinity(c)

46

Figure 7. Average (a) water-source shadow values, (b) shadow values of infrastructures,

(c) water prices at consumption points, and (c) shadow values of water-source salinity

(per supplied cubic meter of water) under the Salinity-Internalized and Salinity-

Externalized scenarios.

-0.2

0

0.2

0.4

0.6

0.8

1

Natu

ral F

resh

water

Tre

ated W

astew

ater

Desa

linated

Seaw

ate

r

Desa

linated

Brac

kish

Desa

linated

TW

W

$ m

-3

Water Shadow

Value



(a)

0

0.1

0.2

0.3

0.4

0.5

Natu

ral F

resh

water

Tre

ated W

astew

ater

Desa

linated

Seaw

ate

r

Desa

linated

Brac

kish

Desa

linated

TW

W

$ m

-3

Infastructure

Shadow Value(b)

0

0.3

0.6

0.9

1.2

1.5

1.8

Urb

an

Agric

ultu

re

$ m

-3

Water

Price(c)

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Natu

ral F

resh

water

Tre

ated W

astew

ater

Desa

linated

Seaw

ate

r

Desa

linated

Brac

kish

Desa

linated

TW

W

Agric

ultu

re

$ (

dS

m-1

)-1m

-3

Salinity Shadow

Value

(d)

47

Figure 8. (a) Average annual surplus allocation under the Salinity-Internalized and

Salinity-Externalized scenarios. Surplus change caused by (b) 20% reduction in

precipitation, and (c) and (d) policy reforms in which agricultural import tariffs and

foreign-labor quotas, respectively, are abolished.

-600

-300

0

300

600

900

1200

1500

Urb

an W

ate

r Con

sum

ers

Agri. P

rodu

ct Co

nsu

mers

Farm

ing

Pro

fits

Wate

r Sup

pliers

So

cial W

elfa

re

10

6$ y

ear-1

Surplus



(a)

-600

-500

-400

-300

-200

-100

0

100

200

Urb

an W

ate

r Con

sum

ers

Agri. P

rodu

ct Co

nsu

mers

Farm

ing

Pro

fits

Wate

r Sup

pliers

So

cial W

elfa

re

10

6$ y

ear-1

Surplus Change Due to

Precipitation Reduction(b)

-600

-400

-200

0

200

400

600

800

1000

1200

Urb

an W

ate

r Con

sum

ers

Agri. P

rodu

ct Co

nsu

mers

Farm

ing

Pro

fits

Wate

r Sup

pliers

So

cial W

elfa

re

10

6$ y

ear-1

Surplus Change Due to

Import Tariff Abolishment(c)

-400

-300

-200

-100

0

100

200

300

400

500

600

Urb

an W

ate

r Con

sum

ers

Agri. P

rodu

ct Co

nsu

mers

Farm

ing

Pro

fits

Wate

r Sup

pliers

So

cial W

elfa

re

10

6$ y

ear-1

Surplus Change due to Foreign-

Labor Quota Abolishment(d)

48

Appendix A. Water and Agricultural Production in Israel

Figure A1 presents the evolution of water sources and uses (Israel Water Authority,

2016), population growth and vegetative agricultural production (Israel Central Bureau of

Statistics, 2017) in Israel during the period 1996–2016. Fresh groundwater extractions

declined dramatically, and were partly substituted by seawater desalination (Figure A1a).

At the same time, the population increased by 50% (Figure A1c), generating larger

amounts of sewage, which was reclaimed (Figure A1a) and reused by irrigation (Figure

A1b). The population growth also increased the demand for food; however, while the

index of local vegetative agricultural production increased until 2010, it stabilized

thereafter.

49

.

Figure A1. Trends of (a) water sources, (b) water uses, and (c) population growth and vegetative agricultural production in Israel

during 1996–2016.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

10

9m

3yea

r-1

Water Sources

Agri. Brackish Water

Agri. Treated Wastewater

Seawater Desalination

Natural Freshwater

(a)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

10

9m

3 y

ear-1

Water Uses

Agri. Brackish Water

Agri. Treated Wastewater

Agri. Freshwater

Urban Freshwater

(b)

80

90

100

110

120

130

140

150

160

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

Veg

. Agri. P

rod

uctio

n In

dex

Po

pu

lati

on

(10

6)

Population & Agri. Production

Population

Veg. Agri. Prod. Index

(c)

50

Appendix B. Schemes of the MYWAS Model

5000Zalmon

5001Menashe

5002 Metzer

5003 Rosh Haain

5004 Achisemech

5005 Holda

5006 Zohar

Natural Fresh

Water Sources

Urban

Demand

Nodes

Agricultural

Demand Nodes

Waste Water

Treatment

Plants

Sea Water and

Ground Water

Desalination

Plants

1101Hadera

1102Palmachim

1103Ashkelon

1100Carmel Coast

1105Negav

1104Southern

Coast

Model TopologyNational

Carrier

Junctions

1000Sea of Galilee

1002Western Kineret

GW

1003Western Galilee

1008Northern Coast

1009Central Coast

1006North Mountain

1010Central Mountain

1011Southern Coast

1012Negev Coastal GW

1013Southern Mountain

1001Golan

1004Lower Galilee

1005Eastern Aquifers

1015Arava

1014Negev Aquifer

1106Arava

1107Eilat

1007Carmel Coast

3114Jerusalem

3101Tzfat

3102Kineret

3105Jeezrael Valley

3100Golan

3104Haifa

3108Hadera

3109Sharon

3110Petah Tikva

3112Ramle

3113Rehovot

3111Tel Aviv

3115Ashkelon

3107Judea and Samaria

3116Negev

3106Jordan Valley

3103Acco

3117Arava

1212Southern

Coast

1216Negev

1218Arava

1211Shafdan

1215Negev Coast

1200Golan

1206Jordan Valley

1217Dead Sea

1205Western Galilee

1204Kishon

1207North Coast

1208Central Coast

1202Kineret

1201Tzfat

1203Beit Shean

1209Yarkon

1210Nesher


1214Shfela

3001Eastern Galilee

3015Western

Negev

3016Lachish

3014Granot

3013Adolam

3012Modieen

3009Tel Aviv

3011Jerusalem

3007Sharon South

3010Lod

3006Hadera

3002Western Galilee

3005Carmel Coast

3003Lower Jordan

River

3004Jordan Valley


3018Dead Sea

3019Arava

3017Ramat Negev

3000Golan

3020Eilat

Brackish and

Surface Water

Sources

Golan Local

WG Local

Eastern Local

Southern Coast

Brackish

Carmel Coast

Brackish

Negav Brackish

Arava Brackish

51

Rosh Haain

Achisemech

Holda

Zohar

Zalmon

Menashe

Metzer

Sea of GalileeWestern Kineret

GW

Hadera SWD

Northern Coast

Northern Mountain

Central Coast

Central Mountain

Ashkelon SWD

Negev Coastal GW

Southern Mountain

Palmachim SWD

Southern Coast GWD

Southern Coast

3001Eastern Galilee

3016Western Negev

3018Lachish

3015Granot

3014Adolam

3013Modieen

3010Tel Aviv

3012Jerusalem

3008Sharon South

3011Lod

3007Hadera

3002Western Galilee

3006Carmel Coast 3003

Lower Jordan River

3004Jordan Valley


3005Dead Sea

3020Arava

3019Ramat Negev

3000Golan

3021Eilat

Golan GWGolan Local

Western GalileeWG Local

Lower Galilee

Eastern Aquifers

Eastern Local

Fresh water system

Carmel Coast

Arava

Negev Aquifer

Carmel Coast GWD

Negav GWD

Arava GWD Eilat S/GWD

52

Fresh and Brackish water for

Agriculture

3114Jerusalem

3101Tzfat

3102Kineret

3105Jeezrael Valley

3100Golan

3104Haifa

3108Hadera

3109Sharon

3110Petah Tikva

3112Ramle

3113Rehovot

3111Tel Aviv

3115Ashkelon


3117Negev

3106Jordan Valley

Rosh Haain

Achisemech

Holda

Zohar

Zalmon

Menashe

Metzer

Sea of GalileeWestern Kineret

GW

Northern Coast

Northern Mountain

Central Coast

Central Mountain

Negev Coastal GW

Southern Mountain

Southern Coast

Brackish

Southern Coast

Golan GWGolan LocalWestern GalileeWG Local

Lower Galilee

Eastern Local

Carmel Coast

Arava

Negev Aquifer

Carmel Coast

Brackish

Negav Brackish

Arava Brackish

3103Acco

Eastern Aquifers

3118Arava

53

1200Golan

1206Jordan Valley

1214Dead Sea

1205Western Galilee

1204Kishon

1207North Coast

1208Central Coast

1212Southern Coast

1216Negev

1218Arava

Waste water system

3001Eastern Galilee

3016Western Negev

3018Lachish

3015Granot

3014Adolam

3013Modieen

3010Tel Aviv

3012Jerusalem

3008Sharon South

3011Lod

3007Hadera

3002Western Galilee

3006Carmel Coast

3003Lower Jordan

River

3004Jordan Valley


3005Dead Sea

3020Arava

3019Ramat Negev

1211Shafdan

3000Golan

3021Eilat

1202Kineret

1201Tzfat

1203Beit Shean

1209Yarkon

1210Nesher


1214Shfela

1215Negev Coast

3114Jerusalem

3101Tzfat

3102Kineret

3105Jeezrael Valley

3103Acco

3100Golan

3104Haifa

3108Hadera

3109Sharon

3110Petah Tikva

3112Ramle

3113Rehovot

3111Tel Aviv

3115Ashkelon


3117Negev

3118Arava

3106Jordan Valley

54

Water-Distribution Network

55

Appendix C. Calibration Data vs. Optimization Results

Figure C1 presents the statewide patterns of Israel’s water economy for the first year of

the optimal solution under the Salinity-Internalized scenario in comparison to the

observed base-year calibration data.

Figure C1. (a) Water supplies, (b) water uses, (c) water prices, and (d) salinities of the

supplied water in the first year of the Salinity-Internalized scenario and the base-year

calibration data.

As already shown by Reznik et al. (2016), the water supply costs in Israel are

characterized by economies of scale. Since water prices are set subject to a regulatory

requirement to recover variable and fixed costs, water prices in the urban sector are higher

than their optimal counterparts (Figure C1c), and hence the larger water supply in the

Salinity-Internalized case relative to that of the base year (Figure C1a). The larger share

0

100

200

300

400

500

600

700

800

900

1000

Natu

ral F

resh

wate

r

Tre

ated

Waste

wate

r

Desa

linate

d S

eaw

ate

r

Desa

linate

d B

rack

ish

Desa

linate

d T

WW

10

6m

3year-1

Water Supply


Calibration

(a)

0

200

400

600

800

1000

1200

1400

Urb

an

Agric

ultu

re

Natu

re

10

6m

3year-1

Water Use(b)

0

0.5

1

1.5

2

2.5

3

3.5

Urb

an

Agric

ultu

re

$ m

-3

Water Price(c)

0

0.5

1

1.5

2

Urb

an

Agric

ultu

re

Natu

re

dS

m-1

Water Salinity(d)

56

of desalinated water in the total water supply causes the lower salinity under the Salinity-

Internalized scenario (Figure B1d).

57

Appendix D. Results of the Salinity-Internalized and Salinity-Externalized Scenarios

Table D1

Per-Annum Statewide Average Water Volumes

Salinity

Internalized

Salinity

Externalized

All Water Consumers

Water Supply (106 m3 year-1)

Natural Freshwater 1,124 1,153

Brackish Groundwater 0 0

Brackish Groundwater Desalinated 106 63

Treated Wastewater 626 714

Treated Wastewater Desalinated 81 0

Seawater Desalinated 865 652

All 2,802 2,582

Water Consumption (106 m3 year-1)

Urban 1,263 1,242

Agriculture 1,149 9 8

Nature 390 3 2

All 2,802 2,5 2

Agricultural Sector

Water Supply (106 m3 year-1)

Natural Freshwater 262 270

Brackish Groundwater 0

Brackish Groundwater Desalinated 0 0

Treated Wastewater 236 373

Treated Wastewater Desalinated 81 0

Seawater Desalinated 569 355

All 1,149 9 8

Agricultural Labor (106 day year-1)

Foreign 9.5 9.4

Local 5.1 5.0

58

Table D2

Per-Annum Statewide Average Shadow Values of Water-Quantity and Water-

Infrastructure-Capacity Constraints at Supply Points; Water Prices at the Consumption

Points ($ m-3); Shadow Values of Land and Foreign Labora

Salinity

Internalized

Salinity

Externalized

Water Supply Constraint ($ m-3)

Natural Freshwater 0.27 0.87

Brackish Groundwater

0.11 0.00

Brackish Groundwater Desalinated

0.10 0.75

Treated Wastewater

-0.09 0.14

Treated Wastewater Desalinated

0.38 0.82

Seawater Desalinated

0.00 0.00

Consumption Price ($ m-3)

Urban

1.54 1.77

Agriculture

0.41 0.72

All

0.86 1.13

Capacity Constraint ($ m-3)



0.01 0.00


0.47 0.25

Treated Wastewater

0.05 0.15


0.27 0.10


0.05 0.38

Water Conveyance

0.00 0.01

Non-Water Agricultural Production Factors

Agricultural Land ($ ha-1) 5.12 2.49

Foreign Labor ($ day-1)

59.3 45.7

a Shadow values and prices were discounted to the 15th year, and then averaged.

59

Table D3

Per-Annum Statewide Average Salinity Levels and Salinity Shadow Values at the Water

Supply and Consumption Points

Salinity

Internalized

Salinity

Externalized

Salinity (dS m-1)

Supplya


Treated Wastewater

1.46 1.49

All

0.83 0.95

Consumption

Urban

0.82 0.84

Agriculture

0.60 0.82

Nature

1.55 1.73

All

0.83 0.95

Shadow Value ($106 (dS/m)-1 year-1)b

Supply

Natural Freshwater -19.3 -31.3


0.0 0.0


-6.6 -8.6

Treated Wastewater

-17.5 -43.1


-33.5 0.0


-95.5 -98.0

Consumption

Agriculture

-77.4 -68.1

a The salinity of brackish water and desalinated water is 4 and 0.25 dS m-1, respectively.

b Shadow values were discounted to the 15th year, and then averaged.

60

Table D4

Per-Annum Statewide Average Welfare Elements ($106 year-1)a

Salinity

Internalized

Salinity

Externalized

Agricultural Products

Production Value 5,577 5,229

Import Valueb 662 724

Variable Costs 3,999 3,765

Capital Costs 336 322

Water-Supply Costs

Variable Costs 1,432 1,291

Capital and Operation Costs 472 421

Total 1,903 1,712

Water Purchase Expenses

Urban 1,855 2,100

Agriculture 442 655

Water to Nature 131 115

Total 2,297 2,755

Surpluses

Urban Water Consumersc 0 -465

Agricultural Product Consumersc 0 -241

Farming Profits 1,136 810

Water Suppliers 263 929

Social Welfare 1399 1032

a Annual welfare-element values were discounted to the 15th year, and then averaged.

b The import value includes only imports of products associated with the 55 crops incorporated in the

model.

c Since the computation of the areas beneath the calibrated constant-elasticity demand functions of urban

water and agricultural products involves extrapolations, we normalize the surpluses of urban-water and

agricultural-product consumers to 0 under the Salinity-Internalized scenario, and report their changes

under the Salinity-Externalized scenario in comparison to the Salinity-Internalized one.

61

Table D5

Laspeyres Quantity and Price Indices, and Value Index, of Agricultural Production by

Salinity-Tolerance Crop Bundles, under the Salinity Externalized Scenario Relative to the

Salinity-Internalized Scenario (i.e., Salinity Internalized = 100)

Crop Bundle Sensitivity to Salinitya Quantity Price Value

Sensitive (36%) 92 104 95

Moderately Sensitive (47%) 94 102 97

Moderately Tolerant (14%) 95 100 95

Tolerant (3%) 64 102 66

All crops 92 102 94

a Values in parentheses indicate the share of the crop bundle in the production value under the Salinity-

Internalized scenario.

large-scale desalination and the external impact on

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