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Cleaning of Eutrophic Inland Waters for Fishery and Amenities_

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									How to Improve Soils Affected by Salinity Using Mandatory Tree Planting:
   Dynamics in Political Economy Models of Common Pool Management:
                                       Ernst-August Nuppenau*

                                               Abstract:
Many farming areas in the tropics and subtropics are characterized by increasing salinity.
These areas include traditional, poorly managed, rain fed dry land farming areas as well as
modern, extensively and intensively used irrigation schemes. In particular, intensification of
agriculture due to human population pressure or increased economic incentives for land
development have contributed to salinity. Salinity nowadays stretches over large landscapes
in tropical and subtropical countries. Surface and ground water systems as well as deeper
aquifers are heavily infiltrated, i.e. polluted with salt. Being largely uncontrolled externalities
of plant production under less appropriate technology, high salt contents reduce productivity,
noticeable only as a common-pool externality. In particular, small-holder communities with
low technological levels, short term needs for agricultural produce, and strong capital
constraints have the tendency to overexploit water. Moreover, the potential of soils to
regenerate from the tendency for salinity, declines with time.
Due to the immanent common property problems of the media, water, as well as high trans-
action costs in soil protection and non-point-pollution problems, salinity is the common fea-
ture of poorly managed irrigation schemes. Salinity levels of small-holder areas are alarming-
ly high. High salinity levels, for instance, - recognizable as reduced short term resistance to
water stress and long term development of high pH-values - are negatively effecting the
security of small-holders’ food. Concerning causes of pollution, overuse of water subject to
high evaporation and no abatement, are regarded as the main causes of continuing problems.
Environmental regulations governing water use and farm practices, such as limitations in
water dosage, specific plants mixes etc., but also regeneration of soils, by methods such as
land set-aside, tree planting etc., are normally not in the direct interest of small-holders, since
these measures reduce current income and resulting in benefits having to be shared. In parti-
cular, tree planting to extract salt and minimize shocks caused by droughts, has recently
gained the interest of scheme management as a low cost and appropriate technological
solution. However, an area covered by tree reduces cropping area. This paper presents a
model that accounts for salinity in the short and long run, attributes levels of mandatory tree
planting to farmers for salinity reduction as well as recognizes short term income waivers
from reduced crop land. A dynamic framework is used to control farm activities and cater for
a reduction of salinity in a community.
The paper applies a combination of a dynamic control model with the optimization of a
common property by a manager. He/she seeks to achieve an agreed level of cleanliness or sa-
linity on behalf of the community. A political economy model depicts the bargaining process
for the establishment of an objective function which includes the manager's own objective.
The manager is a partial manager, not a benevolent dictator, but has the statutory power to re-
gulate tree planting for the extraction of salt. Farmers can cut organic matter from plants
grown on land set-aside, and benefit from use or sales. Benefits are derived from better quali-
ty soil which uniformly helps all members. As institutions, the approach investigates the
tragedy of the common and statutory regulations. Financial innovations for compensation are
also possible .
*Department of Agricultural Policy and Market Research, University of Giessen, Germany
Mail Address: Senckenbergstrasse 3, D-35390 Giessen Germany
E-mail: Ernst-August.Nuppenau@agrar.uni-giessen.de
                                                                                                     1


1 Introduction
The salinity of soil is a serious and complex problem in resource, environmental, and
ecological economics as well as in the related policy debates (Singh and Singh,1995 and
Wichelns, 1999). Salinity threatens agricultural production in many areas of the tropics and
subtropics. These areas are primarily characterized by uneven rainfall patterns, combined with
irrigation and high evaporation. Farmers are particularly criticized for contaminating their
own soils, since they do not invest in the abatement of salinity or apply available techniques
such as drip irrigation, leaching technologies, etc.; even more pronounced farmers
simultaneously pollute soils of neighbors. Somehow non-point pollution (resource
economics), common property management (environmental economics), and ecosystem
problems (ecological economics) are involved and unsolved in the context of salinization.
Soils in arid and ecologically fragile farming regions especially become degraded already in
the short run. Since salinity is normally not a feature confined to a single field, common pool
property management problems and institutional deficits emerge fairly rapid. Consequently,
farmers are even criticized for contributing to greater regional ecological problems and
likewise ecological disasters, such as desertification; in extreme cases a result of salinization.
Processes of salinization may threaten the livelihood of entire communities that are dependent
on irrigation. The observation is not confined to countries with outdated technology. Instead,
the problem also seems to be prevalent in modern irrigation schemes of arid zones in
developed countries or countries with more advanced technologies. Salinity, for instance,
poses the threat of very serious degradation of soils and negative impacts on farming in
complete irrigation schemes of large watersheds (Gretton and Salma, 1997). While treatment
methods seem to be expensive and go beyond single farm abatement (Qadir et al. 2001),
farmers may need help from public management.
It is the objective of this paper to show how tree planting can be an alternative to econo-
mically unsustainable methods. We put an emphasis on the common property management
aspect of tree planting in small-holder communities. The method used is a mix of dynamic
modeling and a political economy bargaining model which caters for several small-scale
farmers. The paper is organized into four chapters. Firstly we will look at the dynamics of
salinity. Secondly, we will state farmers' objective functions with regard to waivers on land
use. Thirdly, we will use this information to explore the dynamic behavior of tree growth.
Fourthly, we will show how the tragedy of the common situation can be modeled and why
limited improvement prevails. Fifthly, a political economy model will show how a particular
improvement can occur using a given interest and power structure in a community which is
                                                                                               2


now managed by a partial manager. Finally, suggestions for application will provide ideas for
empirical research.


2 Problem Statement
2.1 Confronting the problem
Two major arguments are normally put forward to explain individual behavior resulting in
salinization and low interest in abatement. The first argument is that individual rationality of
the balancing of short term and long term benefits is in favor of an increase of salinity.
Farmers deliberately accept salinization in exchange for short term profits whereas the
creation of salinity only results in a decline of soil fertility in the long run. Acceptance of
higher salinity and productivity decline of soils in future periods is congruent with the private
interest argument of those doing so. Irrespective of sustainability considerations put forward
in policy debate, farmers may act rationally when depleting soils and contributing to salinity
of watersheds. In particular, this argument includes a positive discount rate as the driving
force; "comparatively high discount rates determine the speed of salinization!", so the
argument goes. Normatively speaking, the theory of discounting tells farmers to reap short
term benefits and disregard long term negative externalities from increase in salinity. The
behavior apparently depends on the option to substitute soil fertility with other inputs (Knapp
and Olsen, 1996). This is especially the case if costs for abatement today compared to yield
losses tomorrow are high, farmers will make only limited efforts to combat salinity. However,
this creates the question of whether individual time preference (discount rates) and social time
preference (discount rates) are compatible. (Even if Pigouvian taxes are involved, for
instance, see the similar case of peat, Goetz, 1997 and Goetz and Zilberman, 1995, private
and public discount rates become distinct). Note: further time preferences are invariant (Barry
et al. 1996). From observations that poor farmers have higher discount rates, it is concluded
that soil degradation (as escalation: reversible damage by low salinity, irreversible
salinization, desertification, abandonment of farming) is a social phenomena of low income
groups and perhaps justified by unequal distribution of resources. It is hoped that in future the
discount rate may decrease with increases in welfare acquired by soil exploitation. Neverthe-
less, improved individual rationality might just extend the time horizon for degradation, not
halt it, and sustainability seems also to be a rather weak concept (Conrad, 1999). While
effects are related to constant discount rates used in models, models of the optimal decrease of
soil fertility can be misleading in policy debates.
Secondly, common-pool property-rights problems can create an open access situation
(Bromley, 1992) which discourages individuals to move in the direction of soil conservation,
                                                                                               3


and diverge farmers' interest from fighting against salinity as the single, most superior,
strategy of soil conservation. This aspect is a standard argument. It means that an individual
rationality does not include behavior of neighbors who are defecting in cooperation (Hanna et
al. 1996). As a by-product of intensive cropping, excessive water use, and enabled salt
penetration the top soil accumulates salt due to high evaporation rates and salinity becomes a
serious problem for the preservation of fresh water, notably of extended areas (Singh and
Singh, 1995). Sometimes farmers, as a community, are evenly blamed for ecological
disasters; in particular, disasters that occur when farming areas are losing the natural capacity
to recover from salinity. An increase of salt contents can sometimes go beyond a certain
threshold, which makes the loss of farming area irreversible or re-cultivation expensive (i.e.
desertification). Moreover, salinity is not only threatening the future but also the present.
Many ecosystems are nowadays already characterized by high salt loads and have become
increasingly negatively affected and endangered in their natural status. For instance,
regeneration whilst the inflow of salt is ongoing and agricultural use is continuous are both
challenges for public management of irrigation schemes. Generally, salty water and near
surface levels of salt-infiltrated groundwater are immediate threats, and successes in improve-
ment can be labeled as a research priority in achieving sustainability, i.e. economic, ecological
and social sustainability. In the worst cases marginal inflows of salt have ended up in what is
called an ecological collapse or radical change of the soil (environment) for agriculture; then,
it is not only the economic, ecological and social sustainability which are threatened, but live-
lihoods. Typically, farmland becomes converted into a desert, for instance, with a salt crust.
The enrichment of salt and consecutive building up of salt layers on the surface and highly
infected ground water can decrease or even nullify the chances of reasonable crops.
However, there seems to be some type of treatment which is associated with tree or shrub
planting. Tree planting for the extraction of salt out of contaminated soils has gained
considerable attention (Barrett-Lennard, 2002). The questions that are yet to be explored are:
1) Is there a problem in competition between tree planting and agricultural land use (which is
foreseeable in terms of competition for land, but that might not occur, if trees have annual
commercial produce)? 2) Is there a coordination problem that requires public management? 3)
4) What is the assurance of commitment in small-holder communities? 5) What is the adult
life span of a tree and what is the level of remaining salinity in a steady state? 6) How can
sustainability be reached? 7) What roles do tree planting and cutting play, as trees do not live
forever? 8) What is the commercial and what the common interest? etc.


2.1 Economizing the problem
                                                                                                4


However, salinity change and soil improvement are non-point pollution problems of com-
munities that share a common-pool property, soil. Hence, a common property management
problem emerges. Reduction in salinity is the technical problem and tree planting is the
measure. Both should be regarded as a common management problem. The task is to extract
salt from infected soils so that improvement occurs and costs of improvement are minimized.
The management of cleaning an infected area, as understood in this paper, is a co-manage-
ment problem consisting of benefits from reduced salt inflows, delineated as higher pro-
ductivity of farm land, and costs from restrictions in land use, detected as strips planted with
trees and shrubs (Tanji and Karajeh, 1993). Costs also include tree planting, and cutting of
trees and water evaporated by trees. Benefits include fire wood and perhaps annual fruits from
trees. The question is how soils improve, if a political will exists to organize public action and
impose public management, but free-riding is a pertinent strategy. What are the ecological
prerequisites, the economic incentives and the institutions needed to achieve improvement.
First we assume that an irrigation scheme given a certain tree cover, has the potential to
reduce salt, though, only to a certain extent. Secondly, we assume that farmers have an
interest in better soil quality. Thirdly, we assume that an institutional setting has been agreed
upon which the problem of non-point pollution and common property will be overcome. In
principle, we will hand over the task of improving soils to a common-pool property manager,
whose task is to reduce the negative externality of salinity. The manager will be given the
right to allocate tree planting which could be of public interest to individual farmers. How-
ever, we will not naively presume that the manager is maximizing social welfare, i.e. being a
benevolent dictator. Instead, we presume that he is a partial manager. A partial manager is a
manager who reacts to political power. Common property management maybe exposed to po-
litical economy influence; or as a role, the interest and the political power of interest groups
will determine the outcome of a negotiated and environmentally motivated measure such as
tree planting. Though this situation could also possibly be welfare improving, since we have
the open access or tragedy of the common situation, and not the benevolent manager as a
reference situation in reality.
Included in the argumentation concerning common-pool property management we will further
follow the trails of thought concerning political economy modeling of environmental policy
that have been developed in political bargaining models (Harsanyi, 1963). On the basis of the
design of statutory regulations in communities of common property users (Rausser and Zus-
man, 1996) we will derive rules regarding land use to combat salinity. The size of land set
aside for tree strips are under strict rules of planting, but cutting trees is not forbidden. The
                                                                                                                5


waiver on use of certain farm land is specified as distances in a rectangular field system. The
soil improvement aspects are treated dynamically, and a dynamic optimization model is pre-
sented. Dynamic optimization is understood as the optimization task of a manager that is
subject to the political pressure of interest groups, i.e. he lives within the farming community!


3 Dynamics of soil quality and land set-aside in small-holder agriculture
The soil quality of a farming or irrigation district shall be described by an index that measures
negative productivity impacts from salinity. As discussed elsewhere (Gretton and Salma,
1997), a decline in soil quality, as associated with salinity in irrigation schemes, has several
implications for the productivity of soils as a public good. Soils no longer service different
farm types with fresh water, and limitations in application rates of fertilizer reveal soil stress.
As a measurable variable of salinity (an index), concentration of sodium - in principle - is ac-
cepted as the major quantitative contributor to soil quality decline. Sodium can change, and is
subject to accumulation. The accumulation is stimulated by water use, the rise of water tables,
and the fertilization of watersheds. Beside natural increases in salinity, artificial or unintended
enrichment of salt is nowadays a big threat. Mostly imposed by farmers or households as an
non-point pollution phenomena, salinization is not only a by-product of irrigation, but it has
also become a serious problem of its own. Apparently, there might have been other sources of
salt infiltration, notably historically, and soils find a steady state themselves in the long run,
since they have natural processes of enrichment and improvement from salty conditions.
To present the dynamics of soil salinity in conjunction with farm activities and deduction of
salty nutrients by explicitly recognizing land allocation for tree and shrub land, which is set-a-
side by farms, we use a first order differential equation for movements of soil quality such as

S( t )    0S( t )  1[  ( A 0  A j )]   2 [O 0  O( t )]                                           (1)
                               j


The equation caters for land allocation "A" and organic matter "0", where a first part describes
farming activity by area under crops (A-Aj), and a second part area under land set-aside A.

  
 S( t )    0S( t )  1[ ( A  A j )]   2 [ F  A  F( t )  A ( t )] (1')
                                 0                  0   0
                                                                                                           (1')
                                   j
where:         S(t)      : soil quality index (primarily based on salinity) at time t
               A-Aj(t)   : polluting acreage of individual farmer under given technology, i.e. irrigation use
               O(t)      : organic matter by growth in organic matter per hectare on communal land set-aside
               Aj(t)     : area under land set-aside of farmer j,
               F(t)      : organic matter per hectare
                0
               A         : total area or steady state land set-aside stand to offset salinity

First and foremost, the equation describes a natural treatment system, whereby salinity is
reduced by the natural leaching of soils due to rainfall, natural water flows, etc. The
                                                                                                  6


vegetation set up on land set-aside is an amplifying measure. Soils would show decline in
salinity after years. The equation (1') also models the change in soil quality at given areas
under agricultural use in such a way that upper and lower boundaries are specified. Presuming
that salinity is associated with increasing or declining prevalence of trees in the area, a first
order differential equation with a coefficient of "" below 1 implies the area is still capable of
purifying itself over time, with shrub and tree cover strongly contributing to the improvement.
However, the size of "" determines the time period needed for the improvement; values close
to 1 mean very long periods of salinity, while values close to zero mean strong improvement.
The size of land set-aside plays a major role. For instance, presuming an approachable
constant level of salinity at a certain size of natural vegetation or shrub vegetation, the value
of "A0" can specify the steady state situation, with the system moving to different steady
states at different land set-aside levels. Zero salinity, from a modeling point of view is the
steady state under the condition "2(A0-A(T))/0" without agricultural use. Hence, if A(T) is
approaching A0 and the improvement took place, S(t) becomes zero. Natural tree cover ,"A0"
as a benchmark, can be used for calibration of the lower bound of no salinity (upper end of
soil quality). The different levels in land set-aside and agricultural area change the steady
states and improvement capacity. Special cases can be distinguished beside the natural
situation! In the case of no land set-aside in the model "A=0", agricultural land is maximized,
and the second part equals A0, apparently the model would move to an upper point of
salinity"(1[ΣA*j-A0]+2A0)/0" from which A0 can be determined. Notice, on the other
extreme lies A(T)=A0. The latter implies an ideal situation without human influence. Hence
A0 is a matter of definition of S and calibration. Defined as a positive variable per se, salinity
of zero means no agricultural additives. In contrast, the highest salinity means a collapse due
to human inflow that allows no more farming. As a state variable salt content is subject to
additions and subtractions regulating the salinity in various periods.
Organic matter inventories, that catch salt, are also dynamic processes. The catching of salt by
trees and shrubs shall be associated with the volume of organic matter standing on land set-
aside. Organic matter supports desalinization of soils by filtering salt out of the soil. The filter
potential is determined by the size of the organic mass. Hence, the bio-mass enters the
                                                                        
dynamic function (1'). However, loss or enrichment (change) of bio-mass O (equation 2) due
to the cutting down of trees by farmer j on land set-aside area "aj(t)" and vice versa, building
up organic matter on land set-aside "uj(t)" shall also be described by a differential equation,
whereas the coefficients measure the proportional annual decline due to the cutting of mature
shrubs and trees, and the periodical contribution by virgin planting in the first instance:
                                                                                                                 7


O(t )   0 O(t )  1  a j (t )   2  u j (t )
                                                                                                            (2)

As stated the organic matter "O" is qualified as land set-aside multiplied by stands of organic
matter per hectare F and area measured as number of hectare A, i.e. FA. Hence, it follows:
[ F (t )  A(t )]   0 [ F (t )  A(t )]  1  a j (t )   2  u j (t )
                                                                                                            (2')

where additionally: F(t) : organic matter at time t
                   aj (t) : individual cutting of bush and tree land set-aside: optimized
                   uj (t) : individual new set aside of small-holders to shrub and bush land: mandatory regulated


After some manipulations intended to reduce the complexity and focus on the area in land set-
aside; in particular, that we assume a constant growth of the existing area
F (t )  A(t )  F (t )  A(t )   0 [ F  A(t )]  1  a j (t )   2  u j (t )
                                                                                                          (2'')

and
A(t )  [ 0   ] A(t )   2  a j (t )   2  u j (t )  1 F 0 e  t
                                             *
                                                                                                            (2''')

given in equation (2''') an expression of the dynamic equation (2) as a collective action of
communities: collective bush and tree land on set-aside farm land. Equation (2''') shows how
the aggregated change of farmers’ decision making materializes into partial restoration of the
ecosystem. In the initial equation (2') the change of tree and bush on land set-aside, i.e. its or-
             
ganic mass " O(t ) " and hence the need for remedies, depend on the previous years level of or-
ganic mass O(t) (i.e. 0>1 reflects natural growth), individual cleaning of land aj(t) of trees,
and annual intake of land from various farmers uj(t). The total level of individual newly con-
tributed land as movement of organic matter (uj; sum of all farmers' provision) is collective-
ly determined. Every farmer bases his/her decisions - regarding the status of the common pool
property from which the negative externality, i.e. salinity, is derived as a stock variable - on
their farming methods (setting aside of land, cutting of trees, and contribution of arable and ir-
rigated land in production to salinity). If the community wants to decrease salinity, tree cover
on land set-aside has to be increased, i.e. land planted with trees has to become an interest.


3 The farmers' objective function
Allocation of land with different use options has to be seen in conjunction with the overall use
of agricultural land and the farmers' objective function. The applied micro-theory (Varian,
1994) used in this paper is similar to the one of Nuppenau and Slangen (1998). It focuses on
constrained profit functions. In the case of increased salinity, we distinguish between farming
on a remaining field and afforested land dedicated to the improvement of soils. Given
                                                                                                                                          8


minimum requirements for tree planting, farmers loose profits as negative effects of
regulating land use. Positive effects of land set-aside (e.g. higher local humidity on fields
adjacent to forests and higher yields due to cooling evaporation) from common property
management should be differentiated as short term public goods "Aj" from long term salinity
reduction "S". The adjusted total profit is recalculated using crop yields and gross margins on
farm “j”. Profits are essentially determined by land allocation the patterns of farmers and the
dedication of land for recreation (as strips of land set-aside, Nuppenau, 1999). The policy
variable is stretched over the strip "uj". Theoretically, the objective function of a
representative farmer in the provision of land for recreational purposes corresponds to a
constrained profit optimization on farm land (Chambers, 1988). In the case of combating
salinity a farmer, j, shall recognize salinity in the aquifer as a public good in a given utility
function of profits "P=P(Aj,aj,uj,S)". Salinity "S" is common property. Land set-aside appears
because this land cover already improves the micro-climate on the farm. In addition,
individual farmers work with a time horizon "T" and discount "".
           T
Pj,[0,T]=  e  t {P( A j (t ), a j (t ), u j (t ), S (t ))}dt                                                           (3)
           o

where additionally :             P(t) : profit at time t

The profit function needs explicit specification in terms of land allocation, gross margins, wa-
iver on land use, and the recognition of profits from collectively-managed common property.
The cost function is adjusted according to the impacts of land set-aside and salinity.
           T
Pj,[0,T]=  e t {p a d * [A 0  A j ( t )]  p fj a j ( t )  C(d j [A 0  A j ( t )], a j ( t ), S( t ), A( t ), u j ( t ), r j )}dt (3')
                     j j      j                                          j
           o

where: increase: “” and decrease “” :
pa       = gross margins per ton and hectare according to yields per hectare in agriculture, (profit )
pf       = gross margins per ton in sales of land set-aside products from tree cutting, (profit )
dj       = yields per hectare including size of the field, (profit )
(A-Aj) = acreage as area cropped, (profit );
Aj       = acreage under land set-aside, not cropped, (profit );
aj       = acreage where trees are cut, newly cropped next period, (profit );
C(.)     = cost function on quantity of q j at fields with the yield a=q ij/lij, (cost=>profit)
         (A-Aj) = production effect on unit costs (ambiguous)
         aj        = land set-aside land, individual cost reducing effect by biological activity (cost=>profit)
         uj        = cut shrub land, individual cost increasing (cost=>profit)
         rj        = input costs, farm specific (cost=>profit)
         S         = soil quality index (profit), exogenous to farmer


3.1 Farm behavior
Assuming that there is homogeneity in land with respect to the cost function, equal time
horizons for all farmers, and interaction of profits with land quality, i.e. substitution between
other inputs and soil quality, derived from salinity (2), the specification of profits in (3') can
                                                                                                                                                          9


be used for optimization in the traditional sense of individual behavior. Notice: we still have
to elaborate on the distinction between the sector approach and a sum of farm approach in
management. So far only individual farmers are recognized. Even more pronounced (and
from an institutional point of view), the above specified objective function could only be
applied in a straight forward manner if one looks at cropped land and land set-aside - at a
given time - from the perspective of an individual farmer. Note: farmers are faced with the
dynamics of their own land use. Equation (4) qualifies land use in terms of fertility of
soil/land and set-aside by having an option to cut trees "a" and plant trees "u":

Aj (t )   0 F  Aj (t )  1 a j (t )   2 u j (t )  1 F 0 e t
            *
                                                                                                                                                      (4)

Using individual land allocation as a constraint for farm behavior, the intention of the follow-
ing analysis is to explain the cutting- and land-clearing-behavior of individual farms which
are primarily interested in crop land and not forest land; though considering the taking
advantage of firewood if prevalent. The clearing of land for cropping is an instantaneous exer-
cise, since it provides land for obtaining farm surpluses. In order to make the analysis further
operational, we will now introduce a quadratic cost function. Applying the cost function (5):
C(d *j (A o  A j ), S( t ), a j , u j , r j )   10 A j   20 S   30 a j   40 u j  0.5 11 A 2  0.5 22 S 2  0.5 33 a 2  0.5 44 u 2
          j                                                                                          j                           j             j

                                     12 A j S   13 j A j a j   14 j A j u j   23S u j   24 S a j   34 j a j u j                                    (5)

Inserting it in the profit function (3) and following conditions (6) that are corresponding to a

H (t ) A (t )  l(t )           H (t ) a (t )  0                           
                                                            H (t ) l (t )   A j (t )           (6)
        j                                 j



temporal optimization of a Hamilton function (7) in dynamic optimization (Tu, 1992)

we encounter an individual rationality: this is intended to optimize the Hamilton function

H j ( S , A, a, t )  e  t { p a d *j [1  A j (t )]  p jf a j (t )  [ 10 A j   20 S   30 a j   40 u j  0.5 11 A 2  0.5 22 S 2  0.5 33 a 2
                                 j                                                                                            j                           j

 0.5 44 , u 2   12 A j S   13 A j a j   14 j A j u j   23 S u j   24 S a j   34 j a j u j ]}  L1 (t )[ 0 A(t )   1 a(t )   2 u (t )]( 7)
              j


It provides us with three conditions of dynamic behavior towards arable and land set-aside:

  11 Aj (t )   13 a j (t )  [    ]  L(t )  L(t )   10  d * p a   12 S (t )   14 j u j (t )
                                                      
                                                                       j   j                                                                     (8a)

 13 A j   33 a j   1 L(t )  p jf   24 S (t )   34 j u j                                                                                (8b)

0 Aj (t )  1 a j (t )   2 u j (t )  1 F 0 e t   Aj (t )
                                                                                                                                                (8c)

Condition (8) expresses the dynamic behavior of farms with regard to the use of land for im-
mediate cash (to derive short term benefits) or investment into land set-aside for salinity
control (to derive long term benefits). Presumably, land set-aside exists already, but it will be
                                                                                                          10


rather quickly cut or vice versa the intention to build up land set-aside is very meager, given
the individual interest depend on collective "A". Note that the salinity is endogenous to "A".
Unless a farm is very large and comprises the whole area of a watershed, it makes no sense to
optimize "A" for minimal "S". The individual rise of land set-aside on agricultural land will
not occur. Nevertheless, the functions in equation (8) serve as constraints in the optimization
of the manager of the common property, agro-forest. Comparable to incentive constraints con-
ditions (8) depict farm behavior given "S". The interesting feature of the equations in (8) is
the dependency between land set-aside and salinity. Given different stages of salinity – guar-
anteed by an authority - the farmer has different incentives to invest in land set-aside. Vice
versa, the equations reflect the hesitation of farmers to invest if "S" is high. From the point of
view of controlling salinity, a manager of the common property "unsalted soils" can observe
the resistance of farmers to treatment by tree planting from (8). In more general terms, the
functions can be considered as behavioral constraints in a principal agent framework, whereby
farmers are agents and the manager of the common pool property is the principal.
Simplifying (8) by eliminating the instrument variable – cutting - of farms which is "a", we
also get a dynamic constraint for the manager as additional differential equations:
L j (t )   10  11 L j (t )  12 Aj (t )  13 S (t )  15 j u j (t )  15e t
            *     *              *             *            *                *
                                                                                                        (9a)

Where L(t) is the shadow price and "A" is the area under land set-aside (opposite to cropping)

Aj (t )   20   21l j (t )   22 Aj (t )   23 S (t )   25u j (t )   25e t
            *      *              *              *             *              *
                                                                                                        (9b)

These equations apply to all farmers, individually with different coefficients. As a group, if
horizontally summed up, we receive, on area basis, the total land set-aside in the community.
For interpretation purposes: the area under cropping, subject to salt injection, and simul-
taneously the size of land set-aside, covered by shrubs and trees for extraction, is individually
decided. However, a collective action on behalf of the common property manager is possible
and necessary in order to introduce a will for common property. In equation (11) individual
farmers are recognized. Summing up farmers' profits provides an aggregated perception of the
inclusion of preferences and information to the cost functions. Whereas A=aj.

A(t )   20   21 L(t )   22 A(t )   23 S (t )   24 F (t )   25 j u j (t )   26 j e t
         *      *            *            *             *              *                  *
                                                                                                       (10a)
                                                                         j               j


Simultaneously, a vertical summing up of shadow prices gives the second conditions: L=Lj
L(t )   10   11 L(t )   12 A(t )   13 S (t )   15 j u j (t )   16 j e t
         *      *            *            *              *                  *
                                                                                                       (10b)
                                                         j                   j


Presumably, this type of aggregation perceives opportunity costs of land set-aside as
individual functions of the micro-behavior of farms. It caters for variations in the degree of
                                                                                               11


interest for setting aside land from the perspective of individual farmers. Equations (10) are
derived and aggregated positions for public good managers who want to infer the tendency to
cut wood and convert land set-aside back into arable land. Moreover, the identification of
profits from communally assured soil quality needs further explanation. First, the above speci-
fied profit function which is a temporally changing profit function can be most generally
applied to all farmers that are linked to the watershed. But, since every farmer is affected
differently, the gap between micro and macro behavior has to be closed. Secondly, the farm
behavior in equation (11) models situations where farmers contribute to improvement by fol-
lowing regulations on pollution control but also pursue private interests.
Next, in its initial version, the model focuses on mandatory tree planting to regulate salt in-
flows caused by farmers. Institutional amendments to other rights, and eventual payments for
special improvement services, could be analyzed. In the present model, the community is so-
lely engaged in common management according to statutory regulations. This can be justified
by several reasons. Landowners can reap benefits from public good properties of soil quality
by offering public services to neighbors, most noticeable in trees. Landowners living as
residents in a watershed are very often also interested in firewood. Hence a profit derived
from the soil quality (salinity, trees) is not only an indirect profit but commercial interests or
even extra profits derived from the woods are sa good background for the above specification.


3.2 Social welfare function and optimization
In the case of a benevolent manager that maximizes social welfare, welfare is the sum of indi-
vidual welfare (Bentham's utilitarian perspective). A benevolent manager should look for long
term profitability (sustainability), i.e. optimal utility of clients who depend on water quality.
He/she should seek, to maximize benefits for his/her clients, regardless of distribution conse-
quences; not only maximize short term benefits, but also balance them with long term impacts
from sustaining soil quality (apparently, a norm to be justified). From the perspective of the
management of soil quality, the task is to create a temporal welfare function which includes
all members of the community. We may formally represent the problem of the manager as:
W[0,T ]   Pj ,[0,T ]                                                                       (11)
            j

Drawing on the above representation of individual profit functions, we can further establish
the problem as a temporal optimization problem of the manager. It is easiest if we start with
identical farmers and later extend the problem to a bargaining model. Presuming "n" farmers
and optimizing over a time horizon from 0 to T, we get the objective function (8) without
immediate benefits from temporal cutting (5):
                                                                                                                                                   12


          1
aj             [ p jf   24 S (t )   34 j u j (t )  1 L j (t )   13 A j (t )]                                                          (12)
          33
Next, for the conditions of soil quality we use again our treatable linear differential equation
S (t )   0 S (t )   1[[ A0  Aj ]   2 [ A0  A(t )]


Using similar arguments, as given above for gross margins (3') and cost functions (5), and
given an agreed time horizon ("T") in terms of integrating long term welfare arguments,
uniform time preference ("et"), and recognizing the temporal development of fertility from
equation (1), we receive an optimal control problem for a benevolent dictator:
              T
                                                       1 f
W  e t  { {p *j d j [A 0  A j ( t )]  p fj          [p j   24 S( t )   34 j u j ( t )  1 L j ( t )   13 A j ( t )]  C(d j [1
                                                      33
                            j
              o       j
                             1
               A j ( t )], [p fj   24 S( t )   34 j u j ( t )  1 L j ( t )   13 A j ( t )],S( t ), A( t ), u j ( t ), r j )}  P je ]}}dt
                            33
   s.t         ( t )    S( t )   [ [A 0  A ]   [A 0  F( t )  F 0  A( t )]
              S                                                                                                                                    (13)
                           0          1               j          2

           
           A( t )   *   * L( t )   * A( t )   * S( t )    * j u j ( t )    * j e t
                      20    21           22           23             24                  25
                                                                           j                       j
     
 and L( t )   10   11 L( t )   12 A( t )   * S( t )    14 j u j ( t )    15 j e t
                *      *             *                            *                    *
                                                   32
                                                                       j                   j


This specification of the temporal management problem of a benevolent dictator includes area
of land in non-agricultural use "A" (land constraint "A" is under land set-aside and "A0-A" as
cropped land) as state variable. Further state variables are salinity "S" and "L". Newly as-
signed land to be set-aside as afforestation " uj", is the control variable. Note also "uj" is in
the above profit delineation. It contains costs for planting tress. From an institutional point of
view, some rights on land set-aside land are still with farmers; so they can cut trees and bring
land set-aside land into cultivation after some years. This is crucial for individual, agricultural
practices. However, trees are only cut after a certain amount of salt has been extracted.
The management problem is technically solved by control theory (Tu, 1991) as function (13):
H ( A, S , F , u j , t )  e  t {P, * D[1  A(t )]  [[ 10  Pj f ][ 01 A(t )   02 S (t )   03 L(t )]  0.5 11 A 2 (t )
                                                           *             *            *             *                *



                    0.5 11 S 2 (t )  0.5  44 j u 2 (t )   12 A(t ) S (t )    14 j A(t )u j (t )    23 S (t )u j (t )}}dt 
                          *
                                                      j
                                                                 *                     *

                                                 j                                             j                        j


                    1 (t )[ 0 S (t )   1 [ [ A 0  A j ]   2 [ A 0  A(t )] 

                    2 (t )[ 20   21 L(t )   22 A(t )   23 S (t )   24 j u j (t )   25 j e t 
                              *      *            *            *              *                  *

                                                                                      j                    j


                    3 (t )[ 10   11 L(t )   12 A(t )   32 S (t )   14 j u j (t )   15 j e t ]
                              *      *            *            *              *                  *
                                                                                                                                                (13' )
                                                                                  j                    j

Using standard mathematical approaches to solve dynamic optimization problems (Tu, 1992),
a control theory problem has to fulfil three conditions for a maximum: (14)
                                                                                                                                                                 13



                                                                                                                                                            
H (t ) A(t )  1(t ), H (t )S (t )  2 (t ), H (t )L(t )  3 (t ), H (t )u j (t )  0, H (t )1 (t )   A(t ), H (t ) 2 (t )  S (t ), H (t )3 (t )  L(t ),

To simplify, we now take a sector- or watershed-wide approach with "n" identical farmers,
which implies: Conditions (14) are applied to the stated function (13'), we resume a non-
varying cost function (a quadratic function provides linear derivatives, with similar
coefficients see Nuppenau and Slangen, 1998), and the cost function of (9) rechecks cross
effects (note: the size of land set-aside in the community improves the micro-climate). With
identical farmers inserted we get a function of three state variables and one control variable:
H ( A, S , L, u j , t )  e  t {P, * D[1  A(t )]  [[ 10  Pj f ] A(t )  [ 20  Pj f ]L(t )  [ 30  Pj f ]S (t )  n[ 40 j  p jf ]u j (t ) 
                                                          *                      *                     *                       *



                0.5 11 A2 (t )  0.5 22 S 2 (t )  0.5n 44u 2 (t )   12 A(t ) S (t )  n 14 A(t )u (t )  n 23S (t )u (t )  Pje ]}}dt 
                     *                 *                                  *                    *



                                               2                 
                1 (t )[ 0 S (t )  [ 1        ] A(t )  [ 1  2 ]1 A0 ]   2 (t )[ 20   21L(t )   22 A(t )   23S (t )  n 24 nu (t )
                                                                                          *      *           *            *             *

                                                                 
                 n 25e t ]   3 (t )[10  11L(t )  12 A(t )   32 S (t )  n14u (t )  n15 j e t ]
                     *                    *     *          *            *             *            *
                                                                                                                                                                  (15)

Formulation (15) includes all behavioral components of farmers expressed in annual incenti-
ves to cut and collect organic matter from land set-aside, and convert land into cropping area,
So to say; the manager controls afforestation, but sees more in terms of system effects. Then,
applying the optimality criteria to the Hamilton equation (15), three equations comprising two
differential equations appear, where A(t), S(t), L(t), u(t), and i(t) are endogenous.
                                                                                    2                                             
 Pa* D  [ 10  P f ]   11 A (t )   12 S (t )  n 14 u (t )  [ 1 
             *              *             *              *
                                                                                       ] 1 (t )   22  2 (t )   12  3 (t )   1 (t )   1 (t ) (16a)
                                                                                                     *               *

                                                                                    
                                               
[ 20  Pjf ]  21  2 (t )  11)  3 (t )   2 (t )   2 (t )
   *             *              *
                                                                                                                                                            (16b)
                                                                             
[ 30  Pjf ]   22 S (t )   12 n 23u(t )   0 1  23  2  32  3   3 (t )   3 (t )
   *              *             *                         *         *
                                                                                                                                                            (16c)

n[ 40 j  p jf ]  n 44 u (t )  n 14 A(t )  n 23 S (t )  n 24n  2  n 14  3  0
    *                                 *                            *            *
                                                                                                                                                            (16d)

  0 S (t )  1 [ A0  A0 (t )]   2 [ F 0  F (t )]  S (t )
                      j    j
                                                                                                                                                           (16e)
  *     *           *           *              *            *        
 20  21 L(t )  22 A(t )  23 S (t )  n 24u(t )  n 25e t  A(t )                                                                                 (16f)

 10  11 L(t )  12 A(t )  32 S (t )  n 14u(t )  n 15 j e t  L(t )
  *     *           *           *              *            *                                                                                            (16g)

The system (16) can be solved for time dependent paths on the stage variable: Firstly on "soil
quality" as an index for salinity: "S(t)"; secondly, on "land set-aside", hence, agricultural area:
"A(t)"; and thirdly, on the "shadow prices" "L(t)" (see Tu, 1991). For pathways to reach
envisaged states, the control variable u(t) provides necessary annual changes in setting land a-
side. Simultaneously the model provides a solution for the cutting of trees on farm land. The
results are watershed related. They are dependent on the composition of the farm sector; i.e.
                                                                                                  14


the system (16a to g), as a corner solution, could be also applied to a large farm which want to
possess land set-aside and good quality soil. So to say, the aspect of many farms being
involved in community common pool property management has so far not really been tackled.
This aspect becomes even more pronounced when the prime or actual objective of the exerci-
se of public management, the control of salinity, becomes reconsidered. In the given frame-
work, "lowest salinity" could be stated as the final goal or a future state. By any economic de-
liberations, that involves discounting and resource depletion will take place; certainly some
salinity in future is "optimal" as dependent on different rates of discounting. Minimal salinity
or hundred percent improvement, as depending on current salinity, is never optimal involving
discounting. Though, theoretically, one can approach final salinity at S(T), i.e. at a predeter-
mined value, whereas changes become zero, shadow prices are 1(T) to 3(T), and land set-a-
side u(T) are to be derived endogenously. In such case a simple transversality condition oc-
curs! More complex end values may be involved. The above system approach only tells plan-
ners which measures they have to take recursively to reach a desired state after a time "T" has
expired. Results are wishful from a societal point of view, but, are they realistic to conduct?
Other questions are: How can a benevolent planner be institutionalized? Why should he pur-
sue public interest or adopt a minimal discount rate? Why should farmers follow him? etc.
Even more prevalent and interesting is the question how can we explain,: what happens
further if no planner is equipped with coercion to enforce mandatory tree planting? Do we ha-
ve a rationale for common-pool property management on the basis of a benevolent dictator?


5 Political economy bargaining model and game solution
In the previous chapters we have assumed that a benevolent or impartial manager inter-
temporally optimizes the set-aside regime. In runs for comparison, we could also model the
tragedy of the commons looking at long run impacts of water quality in order to demonstrate
severity of the problem. In reality the community has not only the choice between the tragedy
of the common or a manager that is impartial, but, can equip a manager with political power
for statutory regulations; i.e. a benevolent manager is fictional, and a partial manger is subject
to political influence. A situation with a partial manager coincides with a political bargaining
game. Our model of bargaining centers around Harsanyi’s (1963) multiple agent model.

L  [ (I j  I 0j )](Im  I 0 )
                             m                                                                (17)
       j

This mathematical presentation of a bargaining solution refers to a situation with lobbying
and interest functions. Technically, it maximizes the product of the differences between the
                                                                                                  15


cooperative value of each participant in a game and their possible disagreement value (Raus-
ser and Zusman (1992). The manager "m" is subject to a lobbying "s" that increases his wel-
fare, while farmers use resource to lobby "c"; in traditional societies to speak of gifts, etc. Ta-
king the logarithm of the above specification, and recognizing the sum of lobbying activities
sj=s(cj,j) as a function, the bargaining can be more explicitly expressed as a joint function:

lnW  ln[Wm   s j (c j , )  I m ]   ln[W j  c j  I j ]                                (18)
                   j                     j

where:    Wm : is the welfare of the community as anticipated by the manager and
          Wj : are individual welfare functions of farmers.
          sj   : "political gifts" by j to the manager
          cj   : "costs of lobby of j

Moreover, an interior solution can be derived that is similar to the one prescribed by Rausser
and Zusman (1992), resulting in a weighted objective function. In that function, individual
weights correspond to the power of a pressure group. Moreover, it has to be noticed, that the
bargaining solution differs from a policy preference function approach. Instead, the authors
show that weights reflect the analytic properties of both aspects: the “production function” as-
pect and the “resources devotion” aspect in political bargaining. "Production function" means
that political power is built up according to efficiency and technologies in bargaining, and
"resource devotion" means that clients have to use resource, "money, bribes, gifts, etc.".
However, the summing up of farmers and integrating over time gives an objective function
that includes "social" welfare only as part of the objective function of a manager. He/she also
follows his/her own objectives. A "social" manager is partial and deviates from social welfare
by giving weights to different farmers, or, on a more aggregated level, to interest groups.
Interest groups may represent farmers with homogeneous interests. In order to capture the
argument of bargaining in the interest function, one has to decide on elements of bargaining,
specific bribing, procedures and eventually on rules, institutions and external forces for regu-
lation, i.e. the institutional economics framework. A detailed analysis on local constellations
in watersheds may reveal complex behavioral patterns of bargaining. For simplification and in
order to keep the model treatable, our analysis is confined to a pattern of bargaining that
entitles the manager of a watershed the right to regulate land brought into land set-aside, i.e.
uj. The manager is charged with power to allocate land to be set aside for controlling salinity.
As a departing institution from free leasehold, farmers are no longer free in allocating land.
The manager bargains with farmers on land set-aside. Consequently, bargaining elements
affect the elements of the managers objective function. He charges farmers with obligations to
                                                                                                                                   16


plant trees on newly set aside land. In doing so we get the following new objective function.
Note that the weights that reflect bargaining are with uj elements in the objective function
              T
W  e  t  { p * D[1  A j (t )]  [[ 10  P f ][ 01 A(t )   02 S (t )   03 L(t )]   (1   j ) 40 j u j (t )]  0.5 11 A 2 (t )
                                         *            *            *             *                                               *

              o                                                                                                    j


      0.5 22 S 2 (t )  0.5 (1   j ) 44 j u 2 (t )   12 A(t ) S (t )   (1   j ) 14 j A(t )u j (t )   (1   j ) 23 S (t )u j (t )}
            *
                                                  j
                                                             *                               *

                                    j                                                      j                               j


       (1   j ) 23 S (t )u j (t )}  Pje ]   0  u j (t )  1  [u j (t )  u (t )]2 }}}dt
          j                                                 j                      j


    s.t           S (t )   0 S (t )   1 [ [ A 0  A j ]   2 [ A 0  F (t )  F 0  A(t )]
                  


              A(t )   20 j   21 L(t )   22 A(t )   23 S (t )   24 j u j (t )   25 j e t
                       *        *            *            *              *                  *

                                                                           j                           j


... and L(t )   10   11 L(t )   12 A(t )   32 S (t )   14 j u j (t )   15 j e t
                 *      *            *            *              *                  *
                                                                                                                                            (19)
                                                                       j                           j

Where [1+wj] reflects the recognition of farmer "j" in the objective function of a partial ma-
nager (i.e. his weight is 1, the reference numeraire); "plus"-weights (w1,...,wm) give the corre-
sponding achievements of farmers in bargaining. The two final parts reflect transaction costs
associated with a variability of regulations (Transaction costs increase with size and
complexity (variability). Weights (20) are calculated as first derivatives of the strength
(attributed to a threat strategy) minus a reference interest in political bargaining: Formally:
                     (Iopt.  I 0 )] s(cj ,  j )
w 1 ...;w j           C        C
                                                  ;...;w n                                                                      (20)
                     (Iopt.  I 0j )]
                       j
                                        c j
Weights in equation (23) can be interpreted as a notification of political power which can also
be inferred using the model for experiments. Vice versa, given weights in underlying profits
functions, i.e. of the manager, control the allocation of land. In order to proceed, we re-specify
the dynamic Hamilton problem of equation (8) making use of multiple control variables u j(t).

H (...)  e  t {{ p * D[1  A(t )]  [[ 10  P f ][ 01 A(t )   02 S (t )   03 L(t )]   (1   j ) 40 j u j (t )]  0.5 11 A 2 (t )
                                           *            *            *             *                                               *

                                                                                                                       j


           0.5 22 S 2 (t )  0.5 (1   * ) 44 j u 2 (t )   12 A(t ) S (t )   (1   * ) 14 j A j (t )u j (t )  Pje ]   0  u j (t )
                 *
                                           j           j
                                                                  *
                                                                                             j
                                                                                                  *

                                         j                                                     j                                        j


           1  [u j (t )  u (t )]2 }}}dt   1 [ 0 S (t )   1 [[ A 0  A(t )]   2 [ A 0  A(t )]] 
                     j


               2 (t )[ 20   21 L(t )   22 j A(t )   23 S (t )   24 j u j (t )   25 j e t ] 
                         *      *            *              *              *                  *

                                                                               j                           j


               3 (t )[ 10   11 L(t )   12 j A j (t )   32 S (t )   14 j u j (t )   15 j e t ]
                         *      *             *                 *              *                  *
                                                                                                                                            (21)
                                                                                       j                       j
                                                                                                                                                     17


Formally equation (21) means, calculating derivatives of "uj(t)", and "A j(t)", "L j(t)" as well as
"S(t)" of a dynamic system. It provides the bargaining solution "W(t)". Mathematically, be-
cause linear supply and factor demand functions correspond to quadratic functions, we get a
treatable expression of the bargaining solution, solvable for uj's (ubj's) that are embedded in
the dynamics of land set-aside A(t) and salinity S(t) of a watershed. The optimal function of
(21) provides an extension of equations (16a to g). It recognizes individual contributions in-
stead of one normalized provision of land set-aside in watersheds. Technically, conditions for
(21) are similar to (16), but with new coefficients and the explicit recognition of individual
regulations on land set-aside uj(t), i.e.: embedded in the dynamics of the salt index "S", com-
munity-wise land set-aside "A", and shadow prices "L", the manager optimizes the objective
function with targeted controls "uj" which gives us a matrix representation of the derivatives.

                                                                                               u b1 (t )  [ 10  p ](1  1 ) 401  0 
                                                                                                                        f
 (1  w1 )  1
           *
           441       ...         1            0 [1  w1 ] *
                                                            141    0     0      *
                                                                                 241    
                                                                                         *
                                                                                         141                                                   
                                                                                             ...  ...                                       
         ...        ...         ...           ...    ...          ... ...                                [  p f ](1   )   
        1          ...  (1  wn ) 44n  1 0 [1  wn ] 14n
                                      *                     *
                                                                   0     0  24n*
                                                                                        14n  u b n (t )   10
                                                                                         *                                      n 40 n    0 
                                                                                                                                            
                                                                                         0  S (t )   1 (t )  [ 10  p ] 02
                                                                                                                                 f *
         0          ...          0            0       0           0 0   0                                                                    
                                                                                                          
        241
           *
                     ...         24n
                                  *
                                               0       0           0  1   2  22
                                                                                 *
                                                                                        21   Ab (t ) =   2 (t )  p*D  [ 10  p f ] 01 
                                                                                          *                                                  *
                                                                                         * 
                                                                                                                                              
       141
           *
                     ...        14n
                                  *
                                               0        0          0      23
                                                                           *
                                                                                 23
                                                                                  *
                                                                                       11   Lb n (t )    (t )  [  p f ] *
                                                                                                                                                
                                                                                            
                                                                                                                    3        10      03
          0          ...          0           0     1   2      0      0      0       0  (t )                                              
                                                                                              1  S (t )                                    
        241
           *
                     ...         24n
                                  *
                                              23
                                                *
                                                        22
                                                         *
                                                                   21
                                                                    *
                                                                          0      0       0    (t )                                         
                                                                                               2   A(t )  e
                                                                                                                          rt
                                                                                                                                                
       141 0
         *
                                14n
                                  *
                                              13n
                                               *
                                                      12n
                                                        *
                                                                  11
                                                                    *
                                                                          0      0       0    (t )                                          
                                                                                                               
                                                                                                               L(t )  ert
                                                                                                                                               
                                                                                                   3
                                                                                               
(22)
The system (22) recognizes farmers individually. It is dynamic and mathematically it can be
solved by firstly eliminating all instrument variables ubj, and secondly solving the dynamic
differential equations. Graphically, solutions can be expressed, for instance, as opposing poor
farmers and powerful farmers. Diagram 1 demonstrates short term commitments to impro-
vement by interest groups. The institutional framework is given as common property of soil
quality, set aside land, and reduction of salt contents, handed to a manager. The land vector
ub’=[ub1,...,ubn] is the control instrument that is negotiated and conducted in the community.
In such solutions, we explicitly represent economic and political components of soil quality as
bargaining. The solution sketches an economically, ecologically and politically feasible
dynamic equilibrium. For numerical solutions, the system needs transitory conditions. In the
case of an agreement on well specified salt content that is given at a given final time of
“planning“ S(T)= Sfix and that has to correspond to a stead state of forest land A(T)= Afix, we
can derive the constants of integration in four differential equation (Tu, 1992).
                                                                                                                                   18


Diagram 1: Bargaining solution and modified willingness to contribute after bargaining

           A: powerful farmer                                                B: other farmer
marginal willingness to con-                                     marginal willingness to con-
tribute to purification                                          tribute to purification




                                                                  p ja * j

p j a *j
            bargain            tragedy          social
                                                                                     tragedy             social bargain

                      d b j d tj         d sj                                 dt j             dsj dbj
                                                   Distance to waters                                     Distance to water
                                                                    dj                                                        dj

7 Application, empirical background and outlook
The analysis, presented so far, puts its main emphasis on a theoretical model that describes a
political economy oriented model of common property management. The ecological context
of soil quality and farmers’ waiver on land for trees is firstly depicted by a two stage model of
salinity and land set aside. The corresponding parameters of the model can be gained from or-
dinary salt dynamics and detection of links between forest stands and salinity. Quantified ex-
amples of ecosystem behavior of watersheds will be the support basis for empirical analysis.
Empirical analysis will include experiments to find power coefficients for interest groups. Na-
tural science can quantify self improvement of soil quality indices with reduced salt inflows
and tree cover on percentages of farm land. The analysis of dynamics has to be supplemented
with the corresponding inflow measurement from agriculture. In small-holder communities,
depending on the intensity of farming, strips of trees are a good agronomic advice for set up.
The last aspect will also be reflected in the economic modeling of interest functions. Surveys
of particular “homogenous” interest groups can be the basis for the estimation of loss
functions due to land and practice restrictions. Much attention has to be devoted to clarifying
the interest in land use and trees as part of intensity in farming. It can be assumed that large
land holdings imply low costs while intensive farming of small scale farms is the major
problem. However, vice versa, the problem of strong non-point pollution of watersheds will
be most prominent in intensively farmed areas. Therefore, the specification of loss functions
is most crucial since farmers mostly object if their income is considerably reduced, and no
alternatives to land markets exist. However, such cases can be handled with comparative ease
within the given theory.
                                                                                              19



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