Download Global change and the management of water

Economic modelling for water quantity and quality management:
a welfare program approach
Abstract
In the literature on economic analysis of water issues, there exists a class of the so-called
integrated hydro-economic models, which aim to capture the complexity of interactions
between water and the economy. The progress is, however, hampered by the lack of sound
theoretical framework(s). We develop a theoretical model framework to (i) deal with the
interactions between the economic and water system, (ii) cope with the economic functions of
water, and (iii) consider both the water quantity (scarcity) and the water quality (pollution)
problems. Particularly, we use a welfare program to maximize the social welfare subject to
the economic and ecological constraints, where interactions, emissions and environmental
impacts are incorporated. Such a welfare program can provide the marginal values of the
commodities and therefore can price water (i.e. shadow pricing). The optimal solution to a
specified welfare program provides the optimal response strategies, i.e. the efficient allocation
of the economy including water use and the efficient level of water quality. We illustrated the
mechanism in a numerical example and showed that we can invest on water reservation in
high season for high demand in low season and introduce low-high prices for high and low
seasons to achieve efficiency.
Keywords: water management, economic models, welfare program, water pricing, water
reservation, efficiency
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Economic modelling for water quantity and quality management:
a welfare program approach
1 Introduction
The world is facing serious water shortages and millions in the world are suffering from water
pollution with large health risk, particularly for the poor and for children. In the future these
problems will be aggravated by population growth, increases in economic activity and
increasing demand for water. The problems will become even more serious due to the global
change, including deterioration of ecosystems and climatic change.
To solve these water problems, different options have been identified. Among all,
Integrated Water Resources Management (IWRM) proposed by the Technical Advisory
Committee of Global Water Partnership has became the most cited option, which promotes
the co-ordinated development and management of water, land and related resources in order
to maximize the resultant economic and social welfare in an equitable manner without
compromising the sustainability of vital ecosystems (GWP-TEC, 2000).
Integrated resources management implies that we should take into account the
complexity of human-environment systems and understand the feedback effects, nonlinearities, time delays and changes in human behaviour as a consequence of policy
interventions (Pahl-Wostl, 2004). Integrated water management, which aims to maximize
economic and social welfare, is optimal or efficient. However, efficient allocation requires
clear insight in water use rights and proper pricing of water. The amount of water allocated to
meet basic human and environmental needs depends on biological, ecological but also sociopolitical considerations. Hence, we need to understand the functioning of the water system
and the economic context in which water is used. This would enable us to identify solutions
that keep rivers flowing, and prevent deterioration of flora and fauna, i.e. to assure the
functioning and productivity of aquatic and terrestrial ecosystems.
Economic models can support water policies aiming at sustainable allocation and
quality conservation of water (see e.g. Braden and van Ierland, 1999). Europe’s Water
Framework Directive (WFD) recommends applying economic methods to support the
identification of measures to achieve the environmental objectives. It calls for a wider
consideration of economic instruments (e.g. water pricing, charges and taxes) to provide
adequate incentives for reducing pressures exerted on water resources. In the literature of
economic analysis of water issues, there are at least four strands of economic models or
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methods: i) game theoretical models (see Ansink and Ruijs, 2008); ii) valuation methods
(Viscusi et al., 2008); iii) integrated hydro-economic models (Rosegrant et al., 2000; Cai et al.
2003; Heinz et al. 2007); and iv) optimization models (e.g. Fisher, 2008). These models deal
with water issues from different perspectives. Game theoretical approaches are mainly used
for establishing inter-regional or international water allocation agreements. Valuation
methods are usually used in cost-benefit analysis of water projects. Integrated hydroeconomic models integrate the economic (agronomic) processes with the hydrological
processes and maximise the economic benefit from water supply and hydroelectricity
generation to examine some specific “what-if” scenarios. Optimization models maximize total
benefits from water and thus allocate the available water efficiently.
Important feedback effects from the water system to the economy and from the
economy to the water system are often missing in existing economic models (Brouwer and
Hofkes, 2008). Batten (2007) identified the following challenges for economists. First,
environmental costs and other externalities must be incorporated into water pricing regimes.
Second, we must develop ecological sustainable water trading regimes that facilitate efficient
allocation of water for all uses (including ecosystem services). Third, we must address the
issue of qualitative changes in the long run. New tools and approaches are therefore needed
(Batten, 2007).
The lack of sound theoretical frameworks hampers the progress of integrated
economic modelling for water resource management. The economic literature provides only
few examples of well-integrated water management models. For example, Keyzer (2000)
developed a theoretical model framework which adapts the capital theory to value the stocks
and flows of water with specific consideration of the water regeneration process in a processbased model and the sustainable use of water in a river basin system. The model is written in a
welfare program with the characteristics of an economic general equilibrium and deals with
water quantity issues. However, water quality issues are not explicitly considered.
Our objective in this paper is to develop an integrated economic model which is able
to address both water quantity and quality explicitly. Particularly, we capture the interactions
between the economic system and the water system considering the feedback effects, and the
economic functions of water as inputs, amenity services and environmental services in a
welfare program. This allows us to explicitly consider water quantity and quality problems in
a general equilibrium setting. The objective function of the welfare program is to maximize
the social welfare subject to the economic and water quality and quantity constraints. Solving
the welfare programme gives the most efficient allocation of water quantity and the efficient
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level of water quality as well as water price (i.e. shadow price). Doing so, we contribute to the
integrated water management literature with a consistent model framework and a tool for
determining water quantity allocation and water pollution concentration, pricing water by
Lagrange multiplier pricing (or shadow pricing) and determining compensation rules for
relevant externalities.
The organization of the paper is as follows. Section 2 discusses the socio-economic
and institutional aspects related to water management, the economic functions of water, and
the special features of water (e.g. rivalry/non-rivalry and excludability/non-excludability).
This prepares us to address the economic mechanisms of dealing with water use efficiency
and water quality in different situations. Section 3 explores the economic mechanisms of
managing water quantity as a rival good (i.e. a private good, or a common-pool resource) and
water quantity as a non-rival good (a public good, or a club good). In section 3 we also
elaborate on the economic instruments of dealing with water quality issues, including how
pollution compensation (or tax) should be determined. Section 4 illustrates how to work with
the model framework in an example, including the model specification and how to solve the
program as well as the discussion of policy implications. Section 5 concludes.
2 Socio-economic and institutional aspects and special features of water
2.1 Socio-economic and institutional aspects
Uses of water can be categorised into three groups: to meet the basic human needs, the
environmental needs and the other water uses by industry, agriculture as well as by
households exceeding basic needs (Kemper, 1996). The first two categories are based on the
basic needs, i.e. they are essential for life and thus non-negotiable, while the third category is
related to uses exceeding the basic needs, i.e. economically and politically articulated
demand, which can be managed by means of various instruments.
Access to sufficient and safe water is essential for human welfare and good health.
With increasing scarcity it seems logic to use a pricing mechanism to allocate resources in an
efficient way. Competing uses in industry, agriculture and tourism call for an efficient
allocation. In some industrialized countries water management has led to institutional
arrangements where water pricing is a common practice. An efficient allocation of water by
means of the market mechanism requires that the use rights be clearly defined. In practice the
use rights of water in rivers or in groundwater are not clearly defined. This often leads to
upstream-downstream controversies, because excessive
use of water by upstream users
reduces the opportunities of downstream users. This requires agreements between upstream
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and downstream users. Similarly, for water quality issues upstream riparians may pollute the
water as such that downstream users suffer. This requires coordination between upstream and
downstream actors to regulate pollutions and to share the costs of abatement for instance
according to the polluter pays principle. For transboundary rivers, international river basin
authorities for managing both water quantity and quality issues are needed.
Water pollution hits all continents. Human access to the safe drinking water and
sanitation (sewage treatment plants) in the world is still not ensured. The World Health
Organization estimated that one billion people are without access to safe drinking water.
Ingesting toxic substances can lead to health problems, even death from cancers, mutations,
blindness, and a host of illness, although it is complicated to know the exact linkages between
ingestion of particular concentrations of pollutants and health consequences, and the latency
period. Besides, infant mortality in developing countries is still largely caused by poor water
quality, or even by no access to the safe drinking water supply (Shaw, 2005). Therefore, we
need legislation, finances and waste water treatment as well as sanitation systems for the poor.
We also need water standards as proposed by the authorities e.g. Europe’s Water Framework
Directive (WFD), World Health Organization (WHO), United Nations Environmental
Programs (UNEP) or United Nations Development Programs (UNDP).
From a socioeconomic point of view the challenge is to develop a sustainable water
system that covers the needs of the population for drinking water, the need of industry and
agriculture and the need of nature for water in an efficient manner. In economic models for
water issues, the basic human needs, the needs of the environment and institutional aspects
cannot be overlooked. This requires a balancing of the various demands and an optimal use of
the opportunities provided by the hydrological cycle, the geographical circumstances and the
accumulated water available in aquifers or reservoirs as well as other resources. In an
interesting paper Hellegers et al. (2008) clearly show that water issues in the world can no
longer be separated from energy, food and environmental issues. The high energy prices drive
up the price of water pumping and water transportation, whereas the increasing demand for
food, biofuels and nature intensify the demand for water and the competing claims on scarce
water resources.
2.2 Economic functions and special features of water
2.2.1 Water as an economic good and a natural resource
Water is part of the environmental resource systems. There are two primary types of fresh
water in the natural environment: surface water consisting of rivers, lakes and oceans and
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underground water beneath the earth’s surface in soils or rocks. In literature, the functions of
water are classified in different ways (see e.g. Briscoe, 2005; Young, 2005). Briscoe (2005)
classified five types of values of water: irrigation of agriculture, hydropower, household
purposes, industrial purposes and environmental purposes. Obviously the first four values are
directly related to the economic activities and therefore can be treated as direct input to
economic system, while the last (environmental purposes) is related to the maintenance of
wetlands, wildlife support and river flows and therefore can be treated as the environmental
services function of water. Water provides environmental services including support of, and
habitat for aquatic life, and riparian area animals and plants, and birds that feed on aquatic
life. Humans sometimes just enjoy simply looking at, or being near, a water body. These
activities are referred to as water’s service flows to humans (due to the amenity value of
water). No matter how they are labelled, water has value to economic activities. Thus, the
economic functions of water can basically be interpreted as the input function (e.g. production
and consumption) and the environmental and human services (e.g. providing regeneration of
the natural resources and amenity to human beings). This is consistent with the Dublin
statement “water has an economic value in all its competing use and should be recognized as
an economic good.”
2.2.2 Rivalry/non-rivalry and excludability/non-excludability
Although water can be treated as an economic good, we have to understand the characteristics
of water in economic sense. Water is different from the goods in standard term because water
is part of the environmental resource systems. Due to the physical attributes, natural water
often has the property related to rivalry/non-rivalry and excludability/non-excludability. Nonrivalry refers to a situation in which the consumption of water by one individual does not
reduce the availability of consumption by another. Non-excludability refers to the property
that it is impossible to exclude people from consumption in a physical and legal sense.
According to the different levels of involvement of non-rivalry and non-excludability, we may
classify water as different types of good (or bad) in economic terms (Grafton et al. 2004):

Water is a private good if it is both rival and excludable,

Water is a public good if it is both non-rival, and non-excludable (or if exclusion costs
are very high),

Water is a common-pool resource (or open access resource) if it is rival but nonexcludable (or if exclusion costs are very high),
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
Water is a club good if it is non-rival but excludable.
According to these classifications, we may find many examples for different types of
water: a private good, a public good, a common-pool resource, or a club good. Firstly, typical
water such as drinking water, agricultural and industrial water is a private good. This kind of
water use is competing; the water used for one purpose makes it unavailable for the other
purposes. It is exclusive because one can exclude the others using water e.g. by piping the
water to his/her own location.
Secondly, flood-control projects are public goods because the benefits of projects can
be enjoyed by anybody without extra costs (they are non-rival and non-excludable). Water
that is causing a flood is a public bad because nobody in the flooding area can be excluded
and that one person suffers from the troubles of flooding does not reduce the suffering of
other people. A beautiful stream for recreation can be viewed as a public good because your
enjoyment of the beauty of the stream does not reduce the possibility of other people enjoying
it (non-rivalry) before congestion occurs, and the exclusion cost (such as building a wall or a
fence around the stream) is too high.
Thirdly, groundwater (or water in a local lake) has been a common-pool resource in
many regions of the world, because its use is rival and the exclusion costs can be very high.
On the one hand, the groundwater is rival, because your extraction will reduce the
groundwater table (there is a limited volume of water under ground or a limited flow of
groundwater) and the extraction possibility of other people will thus be reduced. On the other
hand, the exclusion costs of using groundwater are very high. You can only stop people
extracting water either by physical means such as setting monitoring equipment in many
locations, or by setting up institutions such as laws, which incur high transaction costs or
monitoring costs.
Finally, water for fishing can be a club good if fishermen have to pay for fishing
(using of water for fishing), and if it is to some extent non-rival because many people can go
fishing at the same time and location, as long as no congestion occurs. In this case, the
exclusion costs are low; simply introducing the fishing license or asking fishing men to pay
the membership fee can exclude fishing for free.
2.2.3 Causes of water scarcity and water pollution
Water quantity is closely related to water scarcity. Water scarcity can be caused by the natural
environment or by the human activities. Earth water balance follows the hydrologic cycle.
Precipitation, evaporation and run off determine the water availability in the different seasons
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at various locations of the globe. In some areas water is abundant; while in other regions
absolute water scarcity occurs. The patterns of precipitation and evaporation show huge
variations over the seasons and over the years, which always has led to periods of drought and
incidental floods in many areas.
The issue of water quality issue is closely related to water pollution. Water pollution
can be caused by human activities directly, but the environmental processes can also
contribute to water pollution following the bio-physical laws. For example, climate change
can worsen water quality due to a higher temperature. To manage water quality therefore
starts by understanding the impacts on water quality from both the economic system and the
environmental system.
3 An economic framework for water quantity and quality management
3.1 Theoretical background
Economically, the efficiency of water allocation can be achieved through the first welfare
theorem. The objective of the society according to this theorem is to maximise the social
welfare subject to the economic constraints. It is shown that for given ownership of
endowments, the resulting equilibrium allocation of the welfare program reflecting the social
objective is Pareto-efficient1.
However, the resulting allocation may be considered to be unacceptable from an
equity perspective. A very careful design of the institutions is required to arrive at socially
desirable outcomes that consider both allocative efficiency and distributional aspects. The
potential compensation criterion is useful in separating efficiency and equity. This is
addressed in the second welfare theorem. For the equity concern, the distributional goal can
be achieved through transfer, which is also Pareto-efficient (Ginsburgh and Keyzer, 2002). If
the gains outweigh the losses, it would be possible for the gainers to compensate fully the
losers with money transfers and still be better off with the policy.
The welfare theorems indicate that Pareto-efficiency is achieved when the marginal
benefits of using a good or service (e.g. water) are equal to the marginal costs of supplying the
good. In welfare economics, (shadow) prices are determined by the marginal value of the
resources (e.g. water).
The welfare economic theory provides a basis for economic valuations of water use
because water is an input (to production and consumption) to economic activities. The value
1
A resource allocation is Pareto-efficient when it is impossible to reallocate resources to make an economic
agent better off without making at least one economic agent worse off.
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of water reflects its contribution to the objectives, which is called the shadow price of water.
The way of determining the value of water in a welfare program is called shadow pricing.
Because of the economic value of water to water users, shadow pricing of water can
determine the willingness to pay of users. A shadow price, as the accounting price, therefore
reflects the economic value of water.
3.2 Economic models for water
In economic analysis, we distinguish two characterisitcis of water in terms of its economic
functions and special features, i.e. water quantity as a rival good, and water quality
considering pollution as a non-rival good. They are represented in two types of models. The
first type of model considers the input function of water in the production process thus it is
rival. The second type considers both input and amenity function, where water quality is
influenced by the emissions from economic activities and it has impacts on the utility of
consumer utility and the production of producers. Thus feedback effects, both of water
quantity and water quality are basically captured.
3.2.1 Rival water as an input to economic activities
If water is a private good (rival and excludable), the efficient allocation can be realized by a
welfare program with a water market. If water is a common-pool resource, it is rival but nonexcludable. The non-excludability of water is caused by the fact that there are no clearly
defined property rights. To achieve the optimal allocation of a common-pool resource, we can
define a property right and establish a (pseudo-)market for it. Particularly, in a welfare
program we can determine the optimal allocation of a rival good (private or common-pool
water resource) and the shadow price of water.
Let us consider an economy with r commodities indexed by k =1, 2, … , r. The
commodity space is an r-dimensional space, denoted by Rr. There are two types of agents who
make decisions: producers (firms) and consumers. There are n producers, indexed by j =1, 2,
…, n. Each producer j is endowed with a technology, represented by a set Yj, which belongs to
Rr. Let yj be the production plan with a vector of outputs and inputs of producer j, and the
outputs of production carry a positive sign and inputs a negative sign. The feasible production
plan is expressed as: y j  Y j . The producer chooses from the set of feasible production plans
such that it maximises his profit, defined as py j , where p is the price vector. The problem of
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the producers can be described as:  j ( p)  max y j { py j y j  Y j } , where  j ( p ) is the resulting
maximal profit.
There are m consumers, indexed by i =1, 2, …, m. Every consumer is endowed with
commodity endowments  i for sale and sets his or her consumption plan. The consumption
of any commodity cannot be negative: x  Rr . Each consumer is also faced with a budget
constraint: pxi  hi , where hi is the income of consumer i. The income consists of two parts:
the proceeds pi of selling the endowment  i and the distributed profits

j
ij
 j ( p) ,
expressed as: hi  pi   j  ij  j ( p ) , where  ij is consumer i’s non-negative share in firm j.
All profits are distributed so that

i
ij
 1 for producer j. The welfare program where water
is a rival good or common-pool resource reads:
W ( )  max  i  i ui ( xi )
xi  0, all i, y j , all j
,
(1)
subject to
 x 
i
i
j
y j   i i ,
(p)
y j  Yj ,
where xi is the vector of consumption goods (including water), yj is the vector of net output
including water,  is the vector of initial endowments. Parameter in bracket (p) gives the
vector of shadow prices of the rival goods (including water), αi is the welfare weight of
consumer i and is chosen such that his/her budget constraint holds,
pxi  pi   j  ij  j ( p ) .
By solving such a welfare program, the resulting solution shows the optimal allocation of
goods including water with rivalry in production or consumption and their optimal shadow
prices (p).
For dealing with the competing use of water, the social objective is to achieve
efficiency and equity of water allocation. The input function of water is valued by shadow
prices in a market or pseudo-market in a welfare context. This welfare program sets up the
mechanism of water quantity management based on economic efficiency. For the concern of
equity, direct transfers can be made e.g. from the rich to the poor, which can be incorporated
in the budget constraints. The framework proposed here is consistent with the hydro-
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economic modelling framework, because the process of water production (part of yj) follows
the hydrological process model.
3.2.2 Non-rival water quality as a public good
Many environmental and human service flows of water can be disrupted by pollution of the
groundwater or the surface water. Water pollution is the contamination of water bodies such
as lakes, rivers, oceans, and groundwater caused by human activities. Pollutants can be toxic
or non-toxic, and toxic ones may impair the environmental and human services that water
provides.
Water pollution is to a large extent non-rival because the negative impacts on one part
of the environmental and economic system does not reduce the negative impacts on the other
parts. For water quality management, we need to reduce its negative impacts on the
environment and humans. Poor water quality has negative impacts on the economic activities
of human beings because of the decreased capacity for life support and reduced water quantity
caused by the regeneration process following hydrological processes. For example, lower
quality water can have negative effects on crop growth or fish production.
Economically how can we solve or improve the water quality efficiently? Water
quality has impacts on utility because of the health effects and amenity services. Water quality
has impacts on production because of its input function. Therefore, it is necessary to include
water quality, which has impact on utility and production function, in an economic model.
Since water pollution is caused by emissions, we also consider the compensation by the
‘polluters pay principle’ in the welfare program. The welfare program which includes the
water quality impacts on utility and production and compensation for pollution reads:
max  i i ui ( xi , gi )
(3)
xi  0, gi  0 all i, y j all j, y w  0 ,
subject to
 x 
e e
i
i
j
j
y j   i i
j
g i  y w
( p) ,
( )
(i ) ,
Fj ( y j , g j , e j )  0 ,
Fg ( y w , e)  0
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where gi is water quality indicator for consumer i, y w is water quality indicator which is
“produced” according to a transformation function Fg(.), where total emissions (e) from the
production processes have impacts on the water quality. This transformation function will
mainly be determined by the hydrological process and the biogeochemical circumstances. yj is
the vector of inputs and outputs following a certain production technology according to a
transformation function Fj(), where water quality g plays a role in the production process and
there are also emissions ej. Since the total emissions are the sum of emissions from individual
producers, the compensation that the polluter has to pay can be based on the shadow price of
emission . This  can also be used as the tax rate for emissions (or emission tax).
Parameter (  i ) indicates the shadow price of water quality, implying the costs of increasing
the water quality by one unit. αi is the welfare weight of consumer i and is chosen such that
the budget constraint holds,
pxi  pi   j  ij  j ( p ) .
This welfare program can be applied for dealing with the industrial pollution problem, transboundary water management, upstream and downstream interaction and pollution
compensation and charges.
The framework proposed here is different from the hydro-economic modelling
framework, because the process of water quality transformation is a biophysical process
model instead of the hydrological process model.
4 Illustration for water management in a numerical example
The economic principles discussed in Sections 3 can be applied to real world cases. By
specifying the welfare programs we may discuss how water systems in specific settings can
be managed in economically efficient way. Policy insights may be obtained from the results
of well-designed integrated models. In this section we illustrate how to manage water by
applying a welfare program and find the policy implications of water management in the case
of a local water system.
4.1 Specification of the welfare program
Consider an economy, whose water use relies on a local water system (e.g. river). In the
economic system, the economic process follows a certain production technology for
production or consumer preference for consumption. In this system, there is water demand.
Different users use water as a consumption good (e.g. drinking water and bathing water for
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households) or an intermediate input e.g. irrigation for agricultural production, or cooling for
industrial production. In the water system, water is supplied according to the hydrological
cycle with precipitation and evaporation and runoff. Following this cycle, water quantity (i.e.
availability) fluctuates over seasons. For simplicity, we distinguish a high and a low season in
a year according to the hydrological cycle. In the high season, there is higher precipitation,
while in the low season, there is lower precipitation and possibly droughts. Water quality is
determined, following the biophysical process, by the total emissions from production which
are released into water. The higher the emission level, the lower the water quality.
A planner wants to make the best use of the water system in order to achieve the
sustainable economic development in the local economy. Particularly, the water manager aims
to provide sufficient water for economic activity in the low season and sufficient water quality
for sustaining the economy. This can be achieved by reserving water in high season for use in
low season. Because the different demand for water, different prices should be introduced as
well. This can be determined by a welfare program. Solving the welfare program, the water
manager can determine the water use or the allocation of water over two seasons among
different users, and the different prices in different seasons, as well as the corresponding
emission charges for those who release emissions into the water body.
For this problem, we need to specify the number of consumers and producers involved
in this economy. We consider one aggregate representative consumer, and two production
sectors that produce agricultural and industrial goods in this model economy. The utility of the
consumer depends on the consumption of agricultural and industrial goods, water
consumption and water quality. Water is an input for both sectors and two sectors also pollute
the river with different levels of emissions. Agricultural production is influenced not only by
the quantity of water as input, but also by the water quality. We specify the welfare program
(2), which is presented in Appendix.
4.2 Solution to the model and policy implications
This is an optimization model with equality and inequality constraints. Obviously it is very
difficult to solve this model analytically, although it is a small-scale model with only limited
number of commodities and simplified hydrological process for water quantity and
biophysical process for water quality. Nevertheless, with the parameter values for the
production and utility functions, hydrological cycles and biophysical process from empirics
we can solve the model numerically using optimization algorithms from the help of powerful
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computer softwares. We use the given parameters and exogenous variable in Table 1 to solve
the model in GAMS as an illustration.
Table 1 Exogenous variables and given parameters
K
L
H
L
e
W
H
L
σ
ζ
δ
σ1
σ2
ck
cl
100
150
600
150
400
50
0.2
0.25
0.1
0.4
0.05
0.85
0.5
0.02
0.04
From this model, variables such as production ( y1, y2 ) and consumption ( x1 , x2 ) of
agricultural and industrial goods, water use of consumer and producers ( xwH , xwL , W1 and W2)
and water reservation (CR), factor use ( L1, L2 ,LR and K1, K2 ,KR), emissions ( e1,e2 , e), and
water quality level ( y w , g) can be determined numerically, and shadow prices (p1, p2, pwH ,
pwL , w, r,  ,  ) are determined as the Lagrange multipliers during the optimization process.
Since the model outcome is the solution to a planner’s problem whose objective is to
maximize the social welfare, it is efficient. Table 2 provides the model results on the
allocation of water among different users over two seasons and the prices of water in high and
low season, the emission charges and so on.
Table 2 Commodity balance for production, consumption, water and prices
Producers
Agri.
Producers
Agri.
3.4
Indus.
Water
Emissions
Consump.
Reserve
Environ.
Prices
Endowm.
3.4
71.1
33.2
33.2
10.8
High
1.7
16.7
249
600
282.6
50
0.24
Low
1.7
16.7
364.2
150
-282.6
50
0.32
100
1.63
Water quality
Factors
Indus.
Consumer
100
100
Capital
55.3
39.1
100
5.7
1.72
Labour
87.5
51.2
150
11.5
1.0
34.3
165.7
200
200
0.59
Table 2 shows that 282.6 units of water will be reserved in the high season for use in
the low season. The economy will allocate 5.7% of their capital (i.e. 5.7 from 100 units) and
7.6% of the labour sources (11.5 from 150 units) for reserving water in order to meet the
higher demand in low season. The prices differ in the two seasons, namely 0.32 € /unit in low
14
season but 0.24€/unit in high season to achieve the best use of water. This is 29% more
expensive in the low season than in the high season. The consumers have the incentive to pay
such a higher price because they value the water higher in their utility in low season (for
example, they prefer to use more water in the summer). The total consumption of water in the
low season (e.g. summer) is 364.2, while in the high season (e.g. winter) is 249.
As for the water quality, it is determined by the total emission level and the local
ecological condition. The emission permit is set according to the ecological bound. In this
example, the total emission permit is 200 unit. The agricultural producer emits 34.3 units and
industrial producer 165.7 unit. If an emission tax is levied, a producer should pay 0.59€ for
each unit of emissions.
In order to obtain the insights of seasonal water pricing and water allocation by water
reservation (scenario1), we compare the consumer welfare level with that in the no-waterreservation case (which we call scenario 0). The same model is applied to scenario 0. The
comparison show that if we invest some capital and labour for water reservation and introduce
the low-high season prices for water use, the total welfare of the consumer is increased from
15.9 (scenario 0) to 16.9 (scenario1). This result indicates that proper water management can
achieve a higher welfare level, and low-high season water pricing makes water use more
efficiently.
We have shown from this example that we can achieve an efficient allocation of water
through water reservation and water pricing. The important policy implication is how to
achieve the decentralization of the efficient allocation and implementation of water pricing.
As long as relevant institutions are provided (water markets are established and every water
user agrees to pay for the use of water), an efficient allocation can be achieved in a
decentralized manner. Therefore, the policy implication is to ensure such an institutional
arrangement.
5 Conclusions
The objective of this study is to elaborate an integrated model which can deal with efficient
allocation and management of
water quantity and water quality. We start with the
background of the socio-economic and institutional aspects related to water management. The
special features of water regarding the rivalry/non-rivalry and excludability/non-excludability
of water resources are also discussed. This helps us to address the economic mechanisms of
dealing with water use efficiency and water quality in economic models. We explore the
economic mechanisms of managing the water quantity as a rival good (i.e. a private good or a
15
common-pool resource) and water quality as a non-rival good (a public good or a club good)
in welfare programs.
Quantity management is closely related to water scarcity. Water is a basic need to
human life. For dealing with the competing use of water, the social objective is to achieve
efficiency and equity of water allocation. The economic approach to the allocation of water is
a way towards the efficient use of water, and it can also help decision-makers to achieve the
distributional goal if equity is considered in the social objective.
We elaborate on the economic instruments of dealing with water quantity and quality
issues, including how and to what extent we can reserve water and how pollution
compensation (or tax) should be determined. We illustrate how to manage water using the
theoretical framework in a numerical example and discuss the policy implications. By solving
the model, we show that we can invest on water reservation because there are seasonal
differences in water availability and we can introduce different prices based on the concept of
shadow pricing because of different demands in different seasons. Pricing for water in
different seasons can achieve a higher total welfare, thus it is a parato-improvement.
Management of water quantity requires us to understand the causes of the scarcity and
the involved property such as rivalry. Scarcity can be linked to the rivalry property of water,
because rivalry causes the competing use of water. Particularly, for rival water (i.e. a private
good and a common-pool resource) such as drinking water, agricultural and industrial water,
we may use the existing markets to achieve the economic efficiency. For example, households
pay the water bill to the water company for the consumption of the drinking water in a price
which in most cases is supposed to reflect the market price. In the case of different seasonal
water availability and demand, we may introduce high-low prices, for example, using higher
price in low season than in high season as shown in our numerical example. But if water is
un-priced or underpriced, for instance, in agriculture due to undefined property rights (e.g.
common-pool water resources such as groundwater), we may define the water rights first and
then price water properly according to its scarcity or marginal value (i.e. shadow pricing). If
water is a non-rival good (i.e. a public good such as a beautiful water resort), the policy
requirement is to exclude the “free-riders” by institutional arrangements (e.g. by law) or by
physical exclusion or simply decide to provide the non-rival good by a public authority for the
sake of the public. In the latter case the costs need to be covered by tax payments.
As far as water quality is concerned, it is important to improve the water quality
because of its impact on economic activities and environmental services. The causes of water
pollution are mainly the emissions from economic activities. From the perspective of policy
16
making, it is thus important to implement proper measures particularly the economic
instruments to reduce the emissions, such as the polluters pay principle. Institutional
arrangement such as levying pollution taxes may be needed for implementing such policies.
Similarly, the pollution tax can be determined by the marginal value of the emission permit
(i.e. shadow pricing in a welfare program). Besides, a decrease in water quality also
contributes to the reduction of water quantity because less clean water is available in the case
of lower water quality. In this case, we may consider, for example, the reuse of ‘waste’ water.
The important tasks for modelling water resource problems are to improve the
representation of the hydrological cycle of water quantity and the biophysical process of water
quality in the economic models. In the case of environmental change, we should pay attention
to the interaction between the economic and the environmental system and the related
environmental processes. In the perspective of climate change, economic modelling should
consider the impacts of climate change on the hydrological cycle, which affects the
quantitative and qualitative status of the water resources. Feedbacks and interactions between
the economic system and the water system should be carefully incorporated in the model,
which help identify the ‘best’ policy options.
17
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19
Appendix Model specification
Utility functions and objective function
Since there are seasonal differences in consumer’s water consumption, the consumer has
different expenditure shares of water consumption and therefore different parameter values in
utility functions for different seasons. For example, in the low season, water is more
demanded due to hot weather (e.g. watering gardens and bathing), so there is a higher
expenditure share than in the high season. The utility function for high and low season can be
written as:


1 1 1  H
uH  xwH H {g  [ x1 x 2


] }
1 1 1  L
uL  xwL L {g  [ x1 x 2
] }
,
(A1)
(A2)
where  H ,  L is the expenditure share of water in the high season and low season
respectively, but  H   L because in the low season the consumer uses more water than in
high season because of e.g. a higher temperature.
For allocating water in high and low season in a year, the objective of the water
manager is to maximize the total sum of the utility in high and low season because this leads
to the highest welfare in the year. This is:
max (uL  uH ) ,
(A3)
subject to the transformation functions and balance equations of commodities such that the
budget constraints of the consumer are fulfilled.
Transformation functions of agricultural good, industrial good and water quality
Transformation function of agricultural and industrial goods can be written as Leontief form
due to the water use and factor inputs.
F1  y1  min{ W1 , Ag  [CES ( K1 , L1 ,  1 ]1 } ,
(A4)
F2  y2  min{ W2 , CES( K2 , L2 ,  2 )} ,
(A5)
where y1, y2 are the production quantity for agricultural and industrial goods respectively, K,
L are the production factors for capital and labour used in production, σ is the substitution
parameter, and W is the water input. Subscripts 1 and 2 refer to agricultural and industrial
production. Water quality g influences the agricultural production but not on industrial
production, and parameter δ is the Cobb-Douglas exponent for water quality.
Emissions from the agricultural and industrial production are e1,e2 , which are the
calculated by the emission coefficients of the particular production., i.e.
20
e1  c1 y1 and e2  c2 y2 . The total emissions to water is thus: e  e1  e2 .
Transformation function of water quality following the biophysical process, we use
the following relationship:
e
Fg  y w  100(1  ) ,
e
(A6)
where y w is the water quality indicator, e is the total emissions from the economic system and
e is the threshold of water contamination reflecting the ecological limit, which depends on the
local circumstances.
Balance functions of commodities (agricultural and industrial good, water quantity, water
quality and emissions)
Agricultural and industrial goods are subject to:
x j  y j  0,
( p j ),
(A7)
where j= 1 and 2 refer to the agricultural and industrial good respectively, with x for the
consumption and y for the production.
For representing the balance function of water quantity, we define the water demand,
supply, and the balance equation step-by-step. Water uses by the water users (consumer and
producers) in the two seasons are the water quantity used in consumption and in production.
We only consider that the consumer uses different amount of water in the different seasons
but there are no seasonal differences for the producers in this model. Thus the total levels of
water consumption (demand) in high and low season are respectively:
WH 
1
(W1  W2 )  xwH
2
(A8)
WL 
1
(W1  W2 )  xwL ,
2
(A9)
where W1 and W2 are the water quantity used for agricultural and industrial production, xwH
and xwL are the water quantity used directly by the consumer. To ensure that there is
sufficient water in the river in both seasons, the water balance should be fulfilled:
WH  W  CR  H
( pwH )
(A10)
WL  W  L  CR
( pwL ) ,
(A11)
where W is the minimum amount of water in the river, which are determined by the
ecological requirement (i.e. for fish), and C R is the amount of water that can be stored in a
21
reservoir (i.e. water reservation) in high season ( CR  0) , which can be used in the low season
if there is not enough water in the low season. The reservation of water for low season uses
capital and labour. Assuming that reserving one unit of water needs ck of capital and cl of
labour, the labour and capital used for water reservation C R is: K R  ck CR , and LR  cl CR .
As we have mentioned above, water supply (i.e. endowment) in the river in high and
low season follows the hydrological cycle:
H  PRH  EVH  RFH
(A12)
L  PRL  EVL  RFL ,
(A13)
where H , L is the water endowment,
PRH , PRL , EVH , EVL
and RFH , RFL
are the
precipitation, evaporation and run off in the local river, with subscripts H and L for high and
low season respectively. And we also have the following relations: PRH  PRL , EVH  EVL
and RFH  RFL . That is, we have: H  L . For simplicity, in the numerical example we
assume H  600 , and L  150 .
Labour and capital used in the production should not exceed the initial endowments:
L1  L2  LR  L
(w)
(A14)
K1  K 2  K R  K
(r ) ,
(A15)
where L1, L2 is the labour input and K1, K2 is the capital input for agricultural and industrial
production, L , K is the labour and capital endowment, w is the wage for labour and r is the
rent for capital.
Total emissions is the sum of emissions from the two producers: e  e1  e2 . The total
emission level should not exceed the ecological constraint. With the threshold of e , we
restrict the emission to the half of threshold.
e
1
e
2
( )
(A16)
Water quality is non-rival for consumer and producer who use water, so an equality is used:
g  yw
( )
(A17)
In this model, all parameters in brackets of the commodity balances are the Lagrange
multipliers, which are the shadow prices of the corresponding commodities. They can be
determined in the numerical solution. The price of water is determined by pwH and pwL in
high and low season. In high season, there is abundant water, pwH  pwL . It is also easy to see
that the producer has to pay the emission charge of  for per unit of emissions. The shadow
22
price of water quality (  ) reflects the willingness to pay of the consumer or producer if water
quality is improved by every unit.
Now everything is priced, so the consumer has to pay for the consumption of
agricultural and industrial goods, water quantity and the enjoyment of water quality. Thus the
following budget constraints for the consumer in both seasons can be formulated:
p1 x1  p2 x2  pwH xwH  g  I H
(A18)
p1 x1  p2 x2  pwL xwL  g  I L
(A19)
where I H and I L are the consumer income in the high and low season when water is priced.
Using the standard economic mechanism, all the revenues are attributed to the consumer. The
consumer will receive the remuneration of labour and capital, the water revenue, the
remuneration of water quality used by the consumer and the agricultural producer as well as
the revenue of emission permits sold to the producers (or tax revenue paid by producers who
produce emissions). The following two formula give the income in high and low season
respectively.
I H  rK  wL  pwH H  yw  e ,
(A20)
I L  rK  wL  pwLL  yw  e .
(A21)
This completes the whole model, which consists of one objective function (A3) and 20
constraints (A1, A2, A4-A21).
23