Nonpoint source pollution and two-part instruments
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Environmental Economics and PolicyStudiesThe Official Journal of the Society forEnvironmental Economics and PolicyStudies / The Official Journal of the EastAsian Association of Environmental andResource Economics ISSN 1432-847XVolume 15Number 3 Environ Econ Policy Stud (2013)15:237-258DOI 10.1007/s10018-012-0052-4
Nonpoint source pollution and two-partinstruments
Renan-Ulrich Goetz & Yolanda Martínez
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RESEARCH ARTICLE
Nonpoint source pollution and two-part instruments
Renan-Ulrich Goetz • Yolanda Martınez
Received: 31 January 2012 / Accepted: 2 October 2012 / Published online: 20 October 2012
� Springer Japan 2012
Abstract As an alternative to the existing environmental policy instruments,
recent literature proposes to combine different policy instruments (two-part
instruments) which have most of the properties of a first-best Pigouvian tax while
minimizing the need for monitoring and enforcement. This article explores the
design and applicability of a policy based on two-part instruments to control non-
point source pollution. Applying this approach, however, leads to a moral hazard
problem, since it is not only the input itself that is responsible for the pollution but
also the way it is applied. The analysis determines the optimal combinations of taxes
and subsidies as a function of the ability to observe the output and the applied
inputs. In an empirical illustration we determine the magnitude of the taxes and
subsidies to establish the socially optimal level of nitrate emissions from livestock
manure for a region in northeast Spain.
Keywords Two-part instruments � Nonpoint pollution � Moral hazard
JEL Classification D62 � Q10 � Q50 � Q53
1 Introduction
Policies makers often face the difficult task to design policies to control
environmental problem which should be effective, efficient, sustainable, politically
feasible, coherent with the existing legal framework and should provide incentive
R.-U. Goetz
Department of Economics, University of Girona, Campus Montilivi, s/n, 17071 Girona, Spain
e-mail: renan.goetz@udg.edu
Y. Martınez (&)
Department of Economic Analysis, University of Zaragoza, Gran Via, 2-4, 50004 Zaragoza, Spain
e-mail: yolandam@unizar.es
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DOI 10.1007/s10018-012-0052-4
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for innovations. Given the large number of disperse criteria the optimal policy has to
meet; it is not surprising that the economic literature has not been able to provide a
clear ranking of the available policies.
Apart form the inherent properties of the different regulatory approaches the
choice of the correct policy instrument is also determined by the specific
characteristic of each environmental problem. Differences in climatic and geomor-
phologic characteristics make certain locations within a catchment more vulnerable
to nonpoint pollution than others and demands that instruments should be designed
site specific (Panagopoulos et al. 2011). This requirement aggravates the major
obstacle for the regulation of nonpoint pollution that emissions are either not
observable or cannot be observed at a reasonable cost. Therefore, it is impossible to
attribute emissions to particular polluters, and the use of first-best instruments like a
Pigouvian tax on the emissions is infeasible.
Alternatively, economists have focused on designing instruments to control
pollution directly, e.g. economic incentives or standards. However, this requires that
the regulated inputs or management practices can be truncated to a subset of choices
that can be observed easily and is highly correlated with the emissions of the
pollutant (Shortle and Abler 1998; Dosi and Tomasi 1994). This restriction limits
these approaches to being second-best. Moreover, enforcing these approaches may
provide a powerful instrument for reducing pollution, but may also induce illegal
elimination of the pollutant, e.g. illegal dumping or burning, or incorrectly applying
the contaminating input in a way that may be less costly but more pollution
intensive (Fullerton and Wolverton 2005).
In the specific case of nonpoint pollution control, due to the lack of powerful
instruments, regulations in EU countries often concentrate on control instruments
like technology-related standards and management rules. However, the scientific
community lacks tools that use readily available data to investigate the relationships
between management rules, site specific characteristics and water quality (Rao et al.
2009). Moreover, these instruments do not involve economic incentives and farmers
do not act voluntarily. Consequently, introducing clean technologies and imple-
menting good codes of environmental practices have often failed to solve nonpoint
source pollution problems (Abdalla et al. 2007).
Palmer and Walls (1997), Walls and Palmer (2001) and Fullerton and Wolverton
(2000) propose alternative incentive-based instruments that maintain most of the
properties of a first-best Pigouvian tax while minimizing the need for monitoring
and enforcement. These are called two-part instruments and consist of a tax on the
contaminating product, or input and either a subsidy for recycling the product at the
end of its lifetime, or for employing a clean technology. Fullerton and Wolverton
(1999) provide a first-best, closed-form solution within a general equilibrium
framework, as do Walls and Palmer (2001) within a partial equilibrium framework.
Two-part instruments can be considered as a generalization of the deposit–refund
system on products such as glass bottles or batteries. However, in contrast to
deposit–refund systems, two-part instruments do not imply that the tax and the
subsidy are identical and they do not relate to the same commodity or the same
agent. Two-part instruments aim to avoid enforceability and control problems
inherent in previous approaches by simultaneously taxing a product and subsidizing
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other market transactions, such as purchasing a clean input or employing a clean
technology. As noted by Fullerton and Wolverton (2005), the two-part instrument
can be employed within a wide variety of contexts. One such context is the control
of nonpoint source pollution; however, this approach has not been explored in the
existing literature. The objective of this article is to design different two-part
instruments that induce the socially optimal level of nonpoint source pollution. The
different instruments are analysed and compared to assess their applicability in
practice. In this respect, designing two-part instruments to control nonpoint source
pollution can be considered as a novel instrument in the economic literature.
The design of these instruments for nonpoint source pollution, however, has to
overcome several problems which have not been considered in the previous
literature. To analyse two-part instruments in a realistic context it is necessary to
specify the production process as precisely as possible and, in particular, to model
different outputs and several inputs as well as their interdependencies. Only in this
way is it possible to define the tax or subsidy base unambiguously so that firms
cannot escape tax payments or receive subsidies in a fraudulent way. In contrast to
the model suggested by Fullerton and Wolverton (2005), the input or technology
cannot be classified as clean or dirty in the context of nonpoint source pollution, but
rather the way the input is applied leads to lower or higher emissions. Therefore,
technical progress is not embodied in capital or in the input, but in management
practices. This leads to the problem that the application of the input itself cannot
form part of a two-part instrument although its purchase constitutes an observable
market transaction. To overcome the problem of being unable to observe
management practices, we have introduced the figure of an accredited firm to
validate that the input is applied in accordance with good environmental practices.
In other words, we create a market for the best management practices, and the
market transactions can be used to design the two-part instruments.
Since the adoption of good environmental practices is often voluntary our
proposal also relates to the literature on voluntary agreements. Segerson and Wu
(2006) for instance combine voluntary and mandatory policies to induce cost
minimizing abatement behaviour for nonpoint source pollution. They show that the
combination of both types of policies is more efficient than each policy on its own if
the tax can be applied retroactively. However, as noted by the authors this condition
is frequently not given in practice. Millock et al. (2002, 2012) also combine a
voluntary policy (installation of a monitoring technology) and a mandatory policy
(emission tax). Lankoski et al. (2010) propose a similar approach. However, instead
of a monitoring technology they propose self reporting. In this respect our proposal
is close to the approaches chosen by Millock et al. (2002, 2012) and Lankoski et al.
(2010). However, their approach is based on the existence of a monitoring
technology or self reporting while our approach relies on an accredited firm that
guarantees compliance. Moreover, their policy design focuses on emissions or input
use while the presented approach here provides not only policy options for the
regulator with respect to emissions (Millock et al. 2002, 2012) or predominately
contaminating inputs (Lankoski et al. 2010) but also with respect to a variety of non-
contaminating inputs and all outputs. The principal difference between the proposal
of this paper and the approaches in the previous literature resides in the fact that it
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considers multiple inputs and outputs. This distinction is important if the firm
produces more than one output and the utilized inputs are complements or
substitutes among each other, or if the production of the different outputs is related.
This later bond may emerge in form of a vertical chain of different outputs, or in
form of byproducts either as a good or a bad. In this situation the presented approach
provides additional policy instruments (taxes, subsidies, rebate on all inputs and
outputs), and it takes account of the distortions of the production process that will
not be considered if the policy makers rely only on input orientated models, or if the
complementary or substitutable relationship between all inputs is not considered.
The analysis in this article leads to a proposal to design economic incentives for
the implementation of good environmental practices by making use of a mix of pure
regulatory approaches. For the sake of better understanding we frame the analysis
within the context of corn and swine production in which the resulting manure
(byproduct of swine production) can be managed according to good or bad
practices. Nevertheless, the analysis is also applicable to other nonpoint source
pollution where the regulator finds it difficult or very costly to monitor good
practices.
2 The model
Given the regional focus of the environmental problem and the limited effect of the
activities studied on the overall economy, we consider a partial equilibrium model
to be an appropriate choice for our analysis. We assume that there is a social planner
who maximizes the social net margin (SNM), which is defined as the incomes from
production minus the sum of the private production costs and the monetary value of
nitrate pollution of surface and ground waters resulting from the application of
mineral or organic fertilizer.
Moreover, we assume that there are a fixed number n of identical and perfectly
competitive firms that engage in swine production and cultivate corn. Swine
production generates manure as a by-product that can be used in a productive
manner as fertilizer on arable land. To produce crops, farmers combine two inputs:
water and nitrogen fertilizer. The second input can be bought in the form of mineral
fertilizer in competitive markets or be substituted by the available livestock manure.
The manure can be applied in a relatively polluting and inexpensive way (bad
practices), or in a low polluting and more expensive way (good practices).1
In our economic analysis we aim to determine the best choice of ‘‘technology’’
from a social point of view. In the case that this does not coincide with the best
choice from a private point of view, we have designed a two-part instrument and
compared its applicability and efficiency with those of a tax on emissions.
Moreover, since two-part instruments are based on taxes and subsidies where some
of the relevant variables are private information, we explore the extent to which they
1 In our case, good practices are related to the use of technologies that burry or inject the manure under
the soil so as to avoid fertilizer losses by volatilization and runoff. In contrast, bad technologies spread the
manure directly over the soil surface, and maybe apply it in excessive amounts, or at an inappropriate
point of time (frozen soil, crops do not require nitrogen) or both.
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comply with the individual rationality constraint, i.e. whether adopting good
practices is also the farmer’s best choice in the presence of taxes and subsidies.
Mathematically, the SNM is given by2:
SNM ¼Zf ðxft;xwÞnxh
0
pcðqcÞdqc þZðxbþxgÞnxh=c
0
psðqsÞdqs
� nxhðpwxw þ pmxm þ pbxb þ pgxg þ phÞ � DðEÞ ð1Þ
where pc(qc) and ps(qs) denote the inverse demand functions for corn and swine,
respectively.3 Variables of the model are xb (nitrogen content of the manure applied
via bad practices in kilograms of nitrogen per hectare, kg N/ha), xg (nitrogen content
of the manure applied via good practices in kg N/ha), xm (nitrogen content of
mineral fertilizer in kg N/ha), xw (irrigation water in m3/ha) and xh (number of
cultivated hectares per farm); parameters pw, pm and ph denote market prices for the
variables xw, xm and xh, respectively.4 The nitrate emissions per hectare generated
from applying mineral fertilizer are given by the function hm(xm), and from organic
fertilizer by the functions hb(xb) and hg(xg) for bad and good practices, respectively.
We assume that all three nitrate emission functions are strictly convex, with first and
second derivatives h0[ 0 and h00[ 0. Since hl(xl), l = b, g, m denotes emissions as
a result of the application of nitrogen xl we have that xl [ hl(xl) for all xl which
implies that 1 [ h0lðxlÞ. The monetary damages from nitrate emissions of all farms E
resulting from the application of mineral or organic fertilizer xft are denoted by the
function D � DðEÞ with (D0[ 0). Total nitrate emissions are E � nxhe, where e is
the sum of nitrate emissions from mineral and organic fertilizers per hectare, i.e.
e ¼ hbðxbÞ þ hgðxgÞ þ hmðxmÞ:Due to the fixed relationship between manure and swine production all the
production costs can be attributed to the amount of manure rather than to the
number of produced swine. The management and application cost for manure
following bad practices can be represented by pb (€/kg N) and following good
practices by pg (€/kg N). In this situation the annual swine production function per
hectare ~qs (number of swine/ha) can be related to the amount of manure generated
by the function ~qs ¼ xbþxg
c where c denotes the amount of manure (in kg N)
generated by one pig. The overall swine production of the region is therefore given
by qS ¼ ~qsnxh. The corn production function ~qC (tons/ha) depends on the amount of
2 Since the presented model does not identify all costs we refer to the term net margin, i.e. the money that
is available to cover the part of the costs of the production which is identical for bad and good
environmental practices.3 The mathematical model has 5 inputs, 2 outputs and the corresponding 7 market prices. To simplify the
notation as much as possible, and to denote the variables in a consistent and intuitive manner, we select
letter x for the inputs of the model, and q for the outputs. Then, we use subscripts to denote the inputs:
water (w), hectares of land (h), mineral nitrogen (m) and nitrogen applied with bad (b) and good
(g) environmental practices. For the outputs we utilize the subscripts c for corn, and s for swine. This
philosophy permits us to use letter p to denote prices and letter t for taxes using the same subscripts
previously defined for inputs and outputs.4 The area below the inverse demand function minus the social cost of production yields the sum of the
consumer and producer rent.
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water applied xw and the amount of overall nitrogen applied xft where xft = [(xm -
hm(xm)) ? (xb - hb(xb)) ? (xg - hg(xg))]. The terms xl - hl(xl), l = b, g, m denote
the amount of nitrogen applied minus nitrogen emissions, i.e. they denote the
effective nitrogen. Hence, the production function can be written as ~qc ¼ f ðxft; xwÞand the regional supply is given by qC ¼ ~qcnxh: We assume that the corn production
function is strictly concave with respect to both inputs xft and xw. Finally, note that
the subscript of a function with respect to a variable indicates the partial derivative
of the function with respect to this variable.
Maximizing expression (1) with respect to xb, xg, xm, xw and xh, and following the
same order of the variables we obtain the first-order conditions for the social problem
pcfxftð1� h0bÞ þ ps
1
c� pb � D0ð�Þh0b ¼ 0 ð2Þ
pcfxftð1� h0gÞ þ ps
1
c� pg � D0ð�Þh0g ¼ 0 ð3Þ
(2) and (3) imply that D0ð�Þ þ pcfxftb cðh0b � h0gÞ ¼ pg � pb
pcfxftð1� h0mÞ � pm � D0ð�Þh0m ¼ 0 ð4Þ
pcfxw� pw ¼ 0 ð5Þ
pcf þ ps
ðxb þ xgÞc
� xwpw � xmpm � ph � pbxb
� pgxg � D0ð�Þe ¼ 0 ð6ÞNecessary conditions (2)–(5) state that, for an interior solution, each input xb, xg,
xm and xw should be employed up to the point where its marginal social margin
equals its marginal social cost. The marginal social margin is the value to a farmer
of the additional output produced with an additional unit of input used, while the
marginal cost is the price of the input in competitive markets including the
application costs in the case of good and bad manure application practices (Eqs. (2)
and (3)), plus each of the marginal environmental damages generated by an
additional unit of the input. The clean input xw does not cause any environmental
damage, and therefore Eq. (5) requires that the marginal net margin of water be
equal to the marginal costs of water. Finally, Eq. (6) states that the marginal social
margin of land (input xh) should equal the marginal social cost of land.
In the following section we solve the private decision problem with alternative
combinations of two-part instruments. All sets of policy instruments can induce the
social optimum.
3 Optimal policies for addressing pollution emissions
We assume that farmers choose inputs and a combination of outputs to maximize
their private profits without considering the environmental damage caused by
agricultural production. Hence, we have calculated the corresponding taxes that
provide incentive for farmers to choose the inputs and outputs that correspond to the
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social optimum. Each of the taxes in the following model is written with the
corresponding subscript, that is tqCfor corn production, tqS
for swine production, tbfor manure applied with bad technology, tg for manure applied with good
technology, tm for mineral fertilizer, tw for water irrigation, th for land use and te for
emissions. These taxes can be positive (tax) or negative (subsidy). We distinguish
between five different situations: in Situation I (the reference point) we solve for the
case in which the regulator can observe emissions; in Situation II we obtain the
social optimum when the regulator has full information about the use of all inputs;
Situation III is like Situation II, but the regulator only has limited information about
the way the inputs are applied; in Situation IV we present the case in which
emissions cannot be monitored, but corn production and some productive inputs can
be monitored; and finally, in Situation V we consider the case in which corn and
swine production and some productive inputs can be observed.
The farmer’s margin function is given by
Y¼ pcf ðxft; xwÞ þ ps
1
cðxb þ xgÞ � tqc
f ðxft; xwÞ � tqs
1
cðxb þ xgÞ
�
�ðpm þ tmÞxm � ðpw þ twÞxw � ðph þ thÞ � ðpb þ tbÞxb
�ðpg þ tgÞxg � tee
�xh: ð7Þ
Maximizing with respect to xb, xg, xm, xw and xh, we obtain the first-order
conditions for the private problem:
ðpc � tqcÞfxftð1� h0bÞ þ ðps � tqs
Þ 1c� ðpb þ tbÞ � teh
0b ¼ 0 ð8Þ
ðpc � tqcÞfxftð1� h0gÞ þ ðps � tqs
Þ 1c� ðpg þ tgÞ � teh
0g ¼ 0 ð9Þ
ðpc � tqcÞfxftð1� h0mÞ � ðpm þ tmÞ � teh
0m ¼ 0 ð10Þ
ðpc � tqcÞfxw� ðpw þ twÞ ¼ 0 ð11Þ
ðpc � tqcÞf þ ðps � tqs
Þ 1cðxb þ xgÞ � ðpb þ tbÞxb � ðpg þ tgÞxg
� ðpw þ twÞxw � ðph þ thÞ � ðpm þ tmÞxm � tee ¼ 0 ð12ÞEquations (8)–(12) state that the firm maximizes the margin by choosing inputs
and outputs such that the marginal revenue products of each input used equal their
full marginal costs, including all taxes.
3.1 Situation I: The regulator can observe the emissions of each firm
(Pigouvian tax)
We still assume that farmers maximize their margin with respect to xb, xg, xm, xw
and xh; however, the regulator is able to monitor emissions. In this situation Eqs.
(8)–(12) yield the social optimum defined by Eqs. (2)–(6) if we set tb ¼ tg ¼ tm ¼ 0
and define the remaining taxes by
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�D0ð�Þh0b ¼ �tqcfxftð1� h0bÞ � tqs
1
c� teh
0b ð13Þ
�D0ð�Þh0g ¼ �tqcfxftð1� h0gÞ � tqs
1
c� teh
0g ð14Þ
�D0ð�Þh0m ¼ �tqcfxftð1� h0mÞ � teh
0m ð15Þ
tw ¼ �tqcfxw
ð16Þ
�D0e ¼ �tqcf � tqs
ðxb þ xgÞc
� twxw � th � tee ð17Þ
From Eqs. (13) and (14) we obtain D0ð�Þ ¼ te � tqcfxft
, which together with (15)
implies that te ¼ D0ð�Þ. Therefore, the remaining taxes tqc; tqs
; tw and th can be
written as
tqc¼ D0ð�Þh0m � teh
0m
fxftð1� h0mÞ
¼ 0 ð18Þ
tqs¼ ½ðD0ð�Þ � teÞh0b�c ¼ 0 ð19Þ
tw ¼ �D0ð�Þh0m � teh
0m
fxftð1� h0mÞ
fxw¼ 0 ð20Þ
th ¼ ðD0 � teÞe ¼ 0: ð21ÞThe usual Pigouvian tax on emissions te is equal to the marginal environmental
damage. If this is the case, then Eqs. (13)–(21) show that there is no need to tax outputs,
inputs or the way the manure is applied to attain the social optimum. Even though the
characteristics of nonpoint source pollution imply that the regulator is not able to
monitor these emissions, we have analysed this case as it provides a reference point for
other policies. In particular, the regulator has to look for other configurations of taxes/
subsidies which can be implemented and that replicate the first-best outcome.
3.2 Situation II The regulator can observe the inputs applied (full information)
In this situation the regulator does not have to be able to observe emissions and the
choice of outputs, i.e. tqc¼ tqs
¼ te ¼ 0. However, the regulator must be able to
monitor the amount of all inputs, more precisely xb, xg, xm, xw and xh, whether they
pollute or not. In this way the substitution processes between all the inputs can be
taken into account. For this reason applying two-part instruments yields the first-
best and not the second-best outcome. In this case the following set of taxes/
subsidies is able to establish the social optimum:
tb ¼ D0h0b [ 0 ð22Þ
tg ¼ D0h0g [ 0 ð23Þ
tm ¼ D0h0m [ 0 ð24Þ
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tw ¼ �tqcfxw¼ 0 ð25Þ
th ¼ D0ðe� h0bxb � h0gxg � h0mxmÞ\0 ð26Þ
Placing these instruments in Eqs. (8)–(12) shows that these equations generate the
necessary conditions for the social optimum described by Eqs. (2)–(6). Hence, the
two-part instruments defined by Eqs. (22)–(26) are able to induce the social optimum.
Expressions (22)–(25) show that three taxes are strictly positive, and one is zero. In
contrast, the sign of expression (26) cannot be assigned in a straightforward way.
Since the functions hl;l ¼ b; g;m are convex on the interval ½0; x�l � and hlð0Þ ¼ 0, we
have that h0lx�l [ hlðx�l Þ. Consequently, the land-use tax th ¼ D0ð�ÞðhmðxmÞ þ hbðxbÞþ
hgðxgÞ � h0mxm � h0bxb � h0gxgÞ is negative, since D0 is strictly positive. In practical
terms it signifies that the land-use tax is a subsidy. If the emission functions were
linear, or strictly concave, we obtain that h0lx�l � hlðx�l Þ; l ¼ b; g;m. Therefore, in the
case of linear or strictly concave emission functions the land-use tax would be zero or
positive, respectively, i.e. a proper tax. The intuition for a negative land-use tax
(subsidy) resides in the fact that the farmer’s tax expenditures per hectare are D0h0lx�l
where l = b, g, m. However, with respect to land use, the farmers’ tax expenditures
should correspond to the environmental damage times the emissions, i.e.
D0hl; l ¼ b; g;m. Since the emission functions are strictly convex, the difference
between the farmer’s actual tax expenditures and the correct tax expenditures per
hectare is positive, i.e. the farmer pays too much. Hence, the land-use tax is a land-use
subsidy which returns the overpayment to the farmer.
3.3 Situation III: The regulator can observe the amount but not the way inputs
are applied (limited information)
In this situation the regulator is able to observe the amount of all applied inputs, but
cannot distinguish between good and bad manure application practices because this
is the farmer’s private information. This leads to asymmetric information between
the regulator and the farmer. Previous literature has considered adverse selection
models to regulate nonpoint source water pollution where the information about the
type of farming (productivity) is private. These models assume that either the input
(Xepapadeas 1997) or the output (Laffont 1994; Clemenz 1999; Bontems et al.
2005) is observable, and emissions are a function of the unobservable farmer type
and the outputs or inputs. The case studied in Situation III, however, is not covered
by the cited literature since emissions vary for the same amount of input and output
according to the way the manure is applied. Alternatively, Innes (1999) and Macho-
Stadler and Perez-Castrillo (2007) analysed a model in which polluters have the
possibility to report high emissions in exchange for lower taxes. However, this
approach requires that the regulator can determine the emission levels after
inspection at any moment in time. Yet, once the manure is applied the regulator
cannot deduce the way the manure was applied and therefore, this approach is also
not applicable in Situation III.
Since the taxes associated with bad practices are higher than those associated
with good practices, tb [ tg, farmers have incentives to report that they use good
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practices even if it is not true. Likewise, since the regulator cannot observe the way
manure is applied, he/she cannot impose a differentiated tax according to the
agronomic practices of the farmer. To overcome this adverse selection problem the
regulator may impose a tax of tb on the entire manure, independently of whether
the farmer uses good or bad practices.5 To obtain information about the practices
employed to apply manure, the regulator can create the figure of an accredited
verifier6 who validates that the manure was applied in accordance with good
environmental practices.7 The farmer decides voluntarily to contract or not the
services of the accredited verifier. It can be a firm that applies manure on behalf of
the farmer or a firm that limits its activity to validating the fact that the farmer has
used good environmental practices. In the later case it is in the own interest of the
farmer that the accredited verifier is in the position to observe the application of
good environmental practices, because only then she/he qualifies for a refund. For
simplicity of the exposition, let the costs of the accredited verifier in either case be
denoted by pv. They reflect the difference between the costs of the commissioned
service of the accredited verifier and the cost to farmers of applying the manure
themselves. Once the manure has been applied, the accredited verifier issues a
certificate that shows the amount of manure that has been applied correctly. Farmers
who present this certificate to the regulator receive a refund given by tb � tg for each
kg of correctly applied manure. The amount of the refund (rebate) is equivalent to
the decrease in the marginal environmental damage resulting from the adoption of
good practices tb � tg ¼ D0ð�Þðh0b � h0gÞ[ 0:
In the absence of asymmetric information, Eqs. (22)–(26) together with tqc¼
tqs¼ te ¼ 0 define the taxes/subsidies that achieve the social optimum. Hence, the
additional cost of eliciting the private information is given by pv and is not borne by
the regulator but by the farmer. If the subsidy received tb - tg compensates the
additional cost pv, the farmer is likely to commission the service of the accredited
verifier. Moreover, the remaining two-part instruments, defined in (22)–(26),
guarantee that farmers generate the socially optimal level of manure. Thus, in the
presence of two-part instruments, the net margin of farmers who follow good
5 This approach has some parallels to the principle of ‘‘guilty until proven innocent’’ embodied in the
concept of ‘‘default values’’ in environmental regulation. For example, the Irish Department of the
Environment Heritage and Local Government established, in the absence of verifiable information,
default values for assessing noise pollution. The same spirit gives rise to performance bonds where fees
are levied upon companies that extract certain natural resources, such as timber, coal, oil, and gas.
Amounts deposited with the performance bond can be refunded when the payer fulfils certain obligations.
In that sense, a performance bond acts like a deposit–refund system.6 For example the figure of an ‘‘accredited verifier’’ or certified pesticide applicator is used by the
California Department of Pesticide Regulation. Its licensing and certification programme is responsible
for examining and licensing pest control dealer designated agents, agricultural pest control advisers; and
for certifying pesticide applicators that use or supervise the use of restricted pesticides. For more
information see http://www.cdpr.ca.gov/docs/license/liccert.htm (accessed 06/09/2012). Similar regula-
tions are in place for instance in New York State http://www.labor.state.ny.us/stats/olcny/commercial-
pesticide-applicator-technician.shtm (accessed 06/09/2012), or in British Columbia, Maine and New
Mexico.7 One may ask who supervises and controls the accredited verifier. However, since this question is also
true for any pollution problem (point or nonpoint), it will not be pursued here.
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practices should be higher than the net margin of those who follow bad practices.
This restriction, as stipulated in the literature on asymmetric information, can be
conceived as an individual rationality constraint. The presence of this constraint is a
clear distinction between traditional economic incentives, such as taxes, subsidies or
tradable permits and two-part instruments. The individual rationality constraint
emerges because the adoption of good practices is completely voluntary and the
reduction in marginal environmental damages (refund/rebate) needs to cover the
costs of the accredited verifier.
If the increase in the SNM resulting from the adoption of good practices does not
cover the costs of the accredited verifier, it is not socially optimal to implement the
proposed two-part instruments, or to introduce the figure of an accredited verifier.
This situation may arise when the reduction in marginal environmental damages is
small, or when the costs of the accredited verifier are high, or both.
It is also possible to relax the assumption that all firms are identical. The Appendix
shows the changes that are necessary to consider heterogeneity of the firms.
3.4 Situation IV: The regulator can observe corn output and some of the inputs
We consider the situation in which the regulator is able to monitor corn production
and some of the inputs, but not all of them, e.g. tqs¼ tm ¼ te ¼ 0. The exclusion of
the tax on mineral fertilizer may be motivated by the fact that although the model
has n identical firms, farms outside the region under consideration probably have
different production functions. It implies that the purchase of mineral fertilizer
would have to be taxed at different rates. But the separation of mineral fertilizer
markets is not recommendable because varying taxes from one region to another
provides incentives for trading of mineral fertilizer on the black market which
undermines the environmental instrument. Along the same lines, the emergence of a
black market for manure is far less likely since the transportation costs are relatively
high. Hence, one can maintain taxes/subsidies on manure following good or bad
practices as an effective instrument. Consequently, the regulator can impose a tax
on corn production, water, land and good and bad practices. Placing these taxes into
the system of Eqs. (8)–(12), the following necessary conditions provide the
equivalence between the private and social outcome.
tb ¼ �D0ð�Þh0mð1� h0mÞ
ð1� h0bÞ þ D0ð�Þh0b 6¼ 0 ð27Þ
tg ¼ �D0ð�Þh0mð1� h0mÞ
ð1� h0gÞ þ D0ð�Þh0g 6¼ 0 ð28Þ
tw ¼ �D0ð�Þh0m
fxftð1� h0mÞ
fxw\0 ð29Þ
tqc¼ D0ð�Þh0m
fxftð1� h0mÞ
[ 0 ð30Þ
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th ¼ D0ð�Þ½e� h0bxb � h0gxg� þD0ð�Þh0mð1� h0mÞ
� f ð�Þfxft
þ ð1� h0bÞxb þ ð1� h0gÞxg þfxw
fxft
xw
� �
ð31ÞThe results show that the tax on water tw is negative while the tax on corn tqc
is
positive. The taxes on manure have to be applied in the same way as in Situation III
where the rebate for the application of good practices is equal to tb � tg. The tax on
land has to be strictly negative if corn production relies entirely on manure, i.e. no
mineral fertilizer is applied, and hm and h0m are equal to zero. Taking account of the
convexity of the emission function equation (31) yields
th ¼ D0ð�Þ½hb � h0bxb þ hg � h0gxg�\0:
These calculations show that corn output is taxed (deposit) while the non-
polluting input receives a subsidy (refund). However, without particular assump-
tions the sign of Eq. (31) cannot be determined unambiguously, and therefore, we
have complemented our theoretical analysis with an empirical illustration presented
in Sect. 4.
3.5 Situation V: The regulator can observe both outputs and some of the inputs
Finally, we look at the situation where the regulator can observe not only corn but
also swine production along with water and good and bad practices, i.e.
tm ¼ th ¼ te ¼ 0. Placing taxes on corn and swine production, water and good and
bad practices into the system of Eqs. (8)–(12) shows that the tax on swine
production cancels out. To see this isolate tb and tg in Eqs. (8) and (9) and
substitute these term in Eq. (12). Hence, the term tqSwill disappear in the first-
order conditions as a consequence of the linearity of the mathematical
specification of swine production and of the tax on the emissions. As a result
we cannot determine the tax on swine production analytically via the first order
conditions. For the indeterminacy of tqSit does not matter whether we try to solve
for tqCand tqS
, or just for tqSon its own. Nevertheless, we can determine the tax
on swine production empirically because the numerical solution of the
corresponding optimization problem is not based on the solution of the first-
order conditions.
Apart from the five situations presented above, it would have been possible to
analyse more situations; however, we have not presented more situations for the
sake of brevity. In general the choice of which instruments to include and which to
eliminate by setting them to zero depends on the availability, or capacity to monitor
the relevant data. However, since the regulator determines the optimal value of five
variables which gives rise to five first-order conditions, it is not possible to include
more than five from the eight available instruments. In other words, three
instruments have to be set equal to zero to ‘‘guarantee’’ a unique solution. In the
case that the regulator cannot monitor whether farmers follow good or bad practices,
the regulator can overcome the asymmetric information problem by creating the
figure of an accredited verifier as described above.
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4 Empirical illustration
In this section, we illustrate the previous theoretical results with data from a region
located in north-east Spain. First, we portray the main agricultural characteristics of
the area studied and describe the data employed in the numerical analysis. We also
present the specification of the parameters and functions of the economic model
described above. Then, we interpret the results of the model solution and conduct a
sensitivity analysis of our results with respect to the magnitude of marginal
monetary damages of the nitrogen emissions considered.
4.1 Data and study area
Our study is based in Aragon, an autonomous community in north-east Spain. This
region is one of the main areas of intensive pig farming in Spain. It accounts for
40 % of the total Spanish swine population.8 In the region, pig production represents
54 % of the total livestock production and 28 % of the final value of agricultural
production (Iguacel 2006).
For our numerical analysis we considered the operational costs of an average
farm located in the study area, which represents the behaviour of a farmer with
swine and corn production.9 The specified farm model reproduces the typical
conditions of the region with respect to the farm size and biophysical data, as corn is
one of the main crops grown (see Martınez 2002).
The numerical solution of the mathematical model (Eq. (1)) requires the
functions and parameters to be specified. Relevant data on nitrogen emissions and
management costs of different practices were collected from Iguacel (2006),
Dauden et al. (2004) and Dauden and Quılez (2004). The corn production as a
function of applied nitrogen requires the estimation of function f ðxft; xwÞ of the
model. In order to simplify the estimation process, we determined a new production
function depending directly on xl, l = b, g, m and xw. This function is given by
1ðxb; xg; xm; xwÞ and was previously estimated by Martınez and Goetz (2007) in the
usual quadratic form:
1ðxb; xg; xm; xwÞ ¼ a0 þ a1xf þ a2x2f þ a3xw þ a4x2
w: ð32ÞIn this way we avoided estimating xft first and thereafter f ðxft; xwÞ. The nitrate
emissions as a function of applied nitrogen were specified in the form of:
hj ¼ b0 þ b1xf þ b2x2f with j ¼ b; g;m: ð33Þ
In order to estimate these functions we calibrated the process-oriented
biophysical model Erosion Productivity Impact Calculator (EPIC, Mitchell et al.
1998) to the local conditions and simulated corn production under varying
8 After Germany, Spain has the second largest swine population in the European Union, representing
18 % of the total production in the European Union with a strongly growing trend over the last 10 years
(Dauden and Quılez 2004).9 We consider the case of a farm in a vertically integrated production system, i.e. the farmers’ services
for the fatting of the hogs are commissioned by another firm. It usually provides the incoming animals
and several other inputs of production.
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conditions. As a result of these simulations we also obtained data about nitrogen
emissions (in the form of nitrate leaching) which allowed us to estimate the
functions hj; j ¼ b; g;m. The simulated data sets obtained with EPIC were validated
by comparing them with crop yields, amounts of inputs applied and nutrient losses
available from an experimental farm of the Department of Soils and Irrigation
(CITA, Aragon Government).10
The results of the estimations of the corn production and nitrate leaching
functions (32 and 33) for mineral fertilizer and good and bad agricultural practices
are presented in Table 1. The parameters of the quadratic functions were estimated
using the nonlinear least-squared regression procedure in SHAZAM (White 2002).
The costs of production and product/input prices were determined based on data
published annually by the Extension Service of the Aragon Government (2005,
2007). The fixed and variable costs of the two ‘‘technologies’’ considered for manure
application, in our example good and bad practices, were obtained from Iguacel and
Yague (2007). The parameter c was assigned a value of 1.57 kg N, based on data
provided by the Extension Service of the Aragon Government (2005, 2007).
Unfortunately, there are no regional data available to estimate the water
treatment costs as a function of nitrate concentration. In accordance with the
literature, the treatment cost function was specified linearly (Tahvonen 1995;
Spraggon 2002). The unitary cost for water treatment is 1.3 €/kg of nitrogen and m3
of water with a targeted concentration below 25 mg of nitrate per litre of water
(Martınez 2002).11 In Table 2 we present the values of the product and input prices
Table 1 Corn production function and nitrate leaching functions
Production
function (~qC)
Nitrate leaching functions
Good
practices (hg)
Bad
practices (hb)
Mineral
fertilizer (hm)
Intercept -2.77 (-6.84)
Lineal water
coefficient (xw)
0.349 9 10-2
(42.90)
Squared water
coefficient (xw2 )
-0.269 9 10-6
(-35.23)
Lineal nitrogen
coefficient (xf)
0.251 9 10-1
(12.21)
0.0344 (6.27) 0.08073 (2.15) 0.0702 (7.21)
Squared nitrogen
coefficient (xf2)
-0.336 9 10-4
(-9.79)
0.113 9 10-3
(5.09)
0.2645 9 10-3
(5.51)
0.23 9 10-3
(4.49)
Adjusted R2 0.86 0.87 0.89 0.85
t statistics are shown in parentheses
10 See Dauden et al. (2004) and Dauden and Quılez (2004) for the physical characteristics of the
experimental farm and details on the conditions of the field trial conducted for the calculation of the
nutrient losses.11 Foess et al. (1998) compared the cost of different processes applied in the USA to remove biological
nutrients from water, and reported water treatment costs that range from 1.4 to 21 US$/m3. The large cost
discrepancy with respect to our cost can be explained in part because the costs considered here are
independent of the pre-treatment nitrate level.
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employed in the numerical study. The prices are identified based on the notation
used in the previous section of the paper.
4.2 Empirical results and interpretation
Applying the economic model requires the demand functions for the two production
activities considered to be specified. If this information is not available it is possible
to solve the problem using the first-order conditions of the model (Eqs. (2)–(6)). In
this case, the only information required is the equilibrium prices of the two
activities, the expression of the first derivative for the crop and swine production
functions with respect to inputs (fxf; fxw
) and the first derivative of the leaching
functions for each fertilizer type. After the functions were specified we first solved
the private problem numerically and then we solved the social problem (2)–(6)
using the CONOPT solver of GAMS (Brooke et al. 1998). To take account of the
current legislation in the EU, we also considered the Nitrate Directive, 91/676/CEE,
which establishes an upper limit for swine manure application of 170 kg N/ha for
vulnerable zones and 250 kg N/ha for the rest of the land.12 In this way we partially
deviate from the theoretical part of the analysis but in turn obtain a greater
realism.13 To comply with EU directives many member states of the EU have
introduced specific regulations including licensing required for housing animals,
compulsory low-emission methods for the application of animal manure to land,
storage of manures and slurries to enable a better agronomic utilization and
prohibited periods for land spreading (usually the winter months of November–
February).14 This member state specific regulation, however, is not considered in
the analysis to concentrate on the principal characteristics of the problem.
Table 2 Products and inputs prices
Parameters Values
pc (€/tons) 148
ps (€/swine) 9.24
pb (€/kg N) 0.12
pg (€/kg N) 0.25
pm (€/kg N) 0.62
pw (€/m3) 0.013
Source Government of Aragon (2005, 2007)
12 The objective of these limitations is to reduce nitrate emissions and other polluting substances which
are contained in manure, for instance, heavy metals Zn, Cu, etc. The specific magnitude of the N limits is
in kilograms of NO3–N per hectare.13 It would have also been possible to consider the N limitations in the theoretical part of the study.
However, it would have complicated the analytical treatment of the model whenever a constraint is
binding but it would not have yielded any more general insight.14 The Dutch legislation also includes the obligation to cover storage facilities for animal manure and the
imposition of levies if the annual N and P balance exceeds some pre-established maximum. Denmark has
focused on two general mitigation measures: the improvement of N use efficiency of animal manure (and
consequently a reduction in commercial fertilizer use), and the retention of N in the crop-soil system by
increasing plant cover on agricultural fields during autumn and winter.
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In Table 3 we present the values of the relevant variables obtained by solving the
private and social decision problems with a limit of 250 kg N/ha and with no
limitation. Basically, the differences between the private and social outcomes refer
to the use of manure: in comparison with the private solution, the social optimum
requires reducing the amount of manure applied following bad practices, increasing
the amount of manure and mineral fertilizer applied following good practices.
Table 3 shows that farmers without N limitations do not apply mineral fertilizer at
all because it leads to acquisition costs, whereas organic fertilizer is costless.
Without N limitations the private optimum is characterized by the application of
manure following bad practices and no application of mineral fertilizer at all. Upon
imposing N limitations, farmers reduce the amount of manure and substitute it by
the application of mineral fertilizer. In the absence of any N limitations the privately
optimal nitrogen emissions per hectare need to be decreased by approximately 30 %
to achieve the socially optimal nitrogen emission. The farmer’s margin per hectare
without taking account of taxes and subsidies decreases by 3–4 % if the social
outcome is realized.
For the rest of the numerical study we concentrate on the case were the N
limitations are not binding for the sake of the brevity of the exposition.15 To
establish the social optimum we have designed the two-part instruments described
above to induce the adoption of good practices. In our numerical study, we
calculated the two-part instruments for the previously described situations given a
Table 3 Results for the private and the social problem with and without N limits
Variables Without limitation With limitation
Private
problem
Social problem Private
problem
Social problem
Corn production (~qC) in
tons/ha
13.7 13.7 13.7 13.7
Swine production (~qS) per ha 110 101.25 67 66
Nitrogen applied with bad
practices (xb) in kg N/ha
431.5 190.4 250 152.4
Nitrogen applied with good
practices (xg) in kg N/ha
0.0 183.6 0.0 94.3
Mineral nitrogen applied (xm)
in kg N/ha
0.0 0.0 61.7 53.2
Total nitrogen applied
in kg N/ha
431.5 374 311.7 300
Water applied (xw) in m3/ha 6470 6470 6323 6323
Total emissions (e) in kg N/ha 269 180 166.6 90
Margin of the farm (in €/ha)
(in brackets SNM)
2903.7
(2554.1)
2807.8 (no taxes/
subsidies) (2573.8)
2531.8
(2315.2)
2512.5 (no taxes/
subsidies) (2395.5)
15 The result for the case where the N-limit is in place does not vary significantly from the presented
results. The corresponding tables can be obtained from the authors upon request.
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marginal economic damage of 1.3 €/kg of nitrogen and m3. The results are shown in
Table 4.
Since Situation I assumes that the regulator can observe the emissions produced
by each farmer, the resulting tax on emissions has to be equal to the marginal
economic damage of pollution. In Situation II the regulator has full information and
he/she can impose taxes on fertilizers equal to their respective marginal damages.
Since the sign of the taxes related to fertilizer are positive, these taxes are proper
taxes, while the land-use tax is a subsidy, as demonstrated in the theoretical part of
the paper. Situation III corresponds to the case in which only the amount of inputs
can be monitored but not the way in which they are applied. In this situation, the
social optimum can be established by imposing the tax tb, defined in Situation II, on
the entire amount of manure generated, a tax of tm on the amount of mineral
fertilizer purchased and a subsidy of tb � tg on the amount of manure applied
employing good practices (which requires a certificate from the accredited verifier).
In this way good practices receive a refund of 0.137 €/kg N. Similarly, cultivated
land is subsidized to compensate the non-proportional taxes of fertilizer per hectare.
Situation IV involves a tax of tqcon the amount of corn produced. Furthermore, it
requires a tax tb on the entire amount of manure generated and a rebate of tb -tg on
the manure applied following good practices. The irrigation of the crop and the
cultivation of land are subsidized.
In the case of Situation V, the production of corn and swine is taxed. It also
requires a tax on the entire amount of manure generated, a subsidy of tb -tg on the
amount of manure applied using good practices (which may require a certificate
Table 4 Numerical results for different two-part instruments
Taxes First-best
outcome
Two-part Instruments
Situation I Situation II
Tax on
polluting
inputs and
land
Situation III
Tax on
polluting and
non-polluting
inputs
Situation IV
Tax on polluting
and non-polluting
inputs and output
Situation V
Tax on polluting
and non-polluting
inputs and outputs
tqc(€/tons) – – – 19.67 19.67
tqs(€/swine) – – – – 0.435
tb (€/kg N) – 0.236 0.236 0.156 0.109
tg (€/kg N) – 0.099 -0.137
(tb - tg)
-0.148 (tb - tg) -0.039 (tb - tg)
tm (€/kg N) – 0.091 0.091 – –
th (€/ha) – -17.404 -17.404 -245.26 –
tw (€/m3) – – – -0.0021 -0.0021
te (€/kg N) 1.30 – – – –
Economic impact
SNM (€/ha) 2573.8 2573.8 2573.8 2573.8 2573.8
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from the accredited verifier) and a subsidy per unit of water applied. Imposing a tax
on the two outputs allows the tax on mineral fertilizer and land use to be suppressed.
A comparison of the SNM for the three situations confirms that the two-part
instruments are capable of replicating the social optimum.
In addition, we conducted a sensitivity analysis of the values of the marginal
environmental damage caused by nitrate emissions. We increased water treatment
costs from 1 to 2.5 €/kg of nitrate. Figure 1 illustrates the change in the use of good
and bad practices when the marginal economic damage of pollution increases. As
expected, the use of good practices expands as the social damage of emissions
increases (see Fig. 1).
In Table 5 we also present the corresponding two-part instruments for Situations
II, IV and V under different marginal costs of pollution (water treatment costs). As
the marginal economic damage of pollution increases, both taxes and subsidies
increase. The difference between taxes and subsidies increases in absolute but not in
relative terms as the marginal environmental damage increases, since the marginal
environmental damage is constant.
Moreover, for Situations II, IV and V we calculated the values of the elasticities
for all the taxes and subsidies with respect to the marginal environmental damage.
The calculated values are in the range of j0:8j to j1:1j; implying that the variation in
the marginal environmental cost considered leads to a proportional variation in the
taxes or subsidies.
5 Conclusions
Since nonpoint source emissions cannot be attributed to particular polluters, a first-
best tax on nitrate emissions is not a viable option for policy makers. Alternatively,
a mix of pure environmental regulations in the form of two-part instruments can be
designed to obtain combinations of taxes and subsidies on observable inputs and
outputs that induce the socially optimal level of pollution. These voluntary but
economic incentive-based instruments maintain most of the properties of a first-best
Pigouvian tax while minimizing the need for monitoring and enforcement. Our
analysis aims to contribute to the literature with respect to the design and
0
50
100
150
200
250
300
1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
Marginal cost ofpollution( /kg)
Ap
plie
d m
anu
re (
kg/h
a)
Bad practices Good practices
Fig. 1 The socially optimal levels of manure applied using good and bad practices for different levels ofthe marginal cost of pollution
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application of this approach. In particular, it explores the potential of two-part
instruments to solve the specific problems affecting nonpoint source pollution
control in agriculture. One of the main characteristics of nonpoint source pollution
in agriculture is the fact that it is not only the amount of the polluting input that is
responsible for the amount of nitrate emissions but also the way the input is applied.
Since the regulator cannot distinguish between good and bad practices, we introduce
Table 5 Optimal taxes/subsidies as a result of different marginal costs of pollution
Marginal cost of
pollution (€/kg)
Taxes/subsidies
tqC
(€/tons)
tqS
(€/swine)
tm(€/kg N)
tb(€/kg N)
tg(€/kg N)
th(€/ha)
tw(€/m3)
1
Situation II – – 0.070 0.181 0.076 -13.388 –
Situation IV 15.131 – – 0.120 -0.114 -188.66 -0.001
Situation V 15.131 0.334 – 0.084 -0.030 – -0.001
1.3
Situation II – – 0.091 0.236 0.099 -17.404 –
Situation IV 19.670 19.670 – 0.156 -0.148 -245.26 -0.0021
Situation V 19.670 0.435 – 0.109 -0.039 – -0.0021
1.5
Situation II – – 0.105 0.272 0.114 -20.082 –
Situation IV 22.697 – – 0.179 -0.170 -282.99 -0.0021
Situation V 22.697 0.502 – 0.126 -0.045 – -0.0021
1.7
Situation II – – 0.119 0.308 0.129 -22.759 –
Situation IV 25.724 – – 0.203 -0.193 -320.73 -0.0022
Situation V 25.724 0.568 – 0.143 -0.051 – -0.0022
1.9
Situation II – – 0.133 0.345 0.144 -25.437
Situation IV 28.750 – – 0.227 -0.216 -358.46 -0.0025
Situation V 28.750 0.635 – 0.159 -0.057 -0.0025
2.1
Situation II – – 0.147 0.381 0.159 -28.114 –
Situation IV 31.776 – – 0.251 -0.238 -396.19 -0.0032
Situation V 31.776 0.702 – 0.176 -0.063 – -0.0032
2.3
Situation II – – 0.161 0.417 0.174 -30.792 –
Situation IV 34.802 – – 0.275 -0.261 -433.93 -0.0034
Situation V 34.802 0.769 – 0.193 -0.069 – -0.0034
2.5
Situation II – – 0.175 0.454 0.189 -33.469 –
Situation IV 37.829 – – 0.299 -0.284 -471.66 -0.0034
Situation V 37.829 0.836 – 0.210 -0.074 – -0.0034
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the figure of an accredited verifier to overcome the associated asymmetric
information problem. This requires farmers to pay the tax that corresponds to using
bad practices on the entire manure generated at the farm. Only farmers that present a
certificate issued by the accredited verifier, stating the amount of manure and that it
has been applied using good practices, receive the subsidy for this amount of
manure.
In particular, we have found that there are many ways of achieving the social
optimum: a combination of taxes on polluting inputs and a subsidy on land use, or a
combination of taxes on outputs and bad practices while subsidizing a non-polluting
input and good practices. Finally, the analysis presented in this paper shows how
economic incentives can be designed to improve acceptance of the best manage-
ment practices.
Acknowledgments The authors gratefully acknowledge the support of the Ministerio de Ciencia e
Innovacion Grants Econ2010-17020, and RTA2010-00109-C04-01 and of the Government of Catalonia
(Barcelona Graduate School of Economics, Grants XREPP, and 2009 SGR189).
Appendix: Heterogeneity of the firms
So far we have assumed that the n firms are identical. If we drop this assumption we
can classify the firms in k groups. The firms that belong to group j, j ¼ 1; . . .; k; have
identical characteristics, i.e. they can be described by the same production function
f jð�Þ, the same emission function h jl ð�Þ; l ¼ b; g;m, the same production and
application cost of manure pjb and p
jb and by the number of firms nj that form part of
group j. The choice variables of each firm of group j are given by xjb; x
jg; x
jm; x
jw; and
xjh: Consequently the social decision problem reads as
ZPk
j¼1
f jðx j
ft;x j
wÞnjxj
h
0
pcðqcÞdqc þZ
Pk
j¼1
ðx j
bþx
jgÞnjx
j
h=c
0
psðqsÞdqs
� njxjh½pwx j
w þ pmx jm þ p
jbx
jb þ p j
gx jg þ ph� � D
Xk
j¼1
njxjhe j
!
Adapting the notation also for the farmer’s margin function and following the
steps described above, we obtain that the first-order conditions for the social and
private problems. A comparison of these conditions allows us to determine group
specific taxes t jqc; t j
qs; t j
b; tjg; t
jm; t
jw; t
jh so that farmers faced with these taxes would
behave optimally from a social point of view. These taxes would respond to
Situation II.
However, the deriving the optimal taxes requires that the social planner knows
the production and emission functions of each group j as well as the different costs
of swine production and the application of the manure. Assume that the regulator
only knows the emission function of each group j, but not the production function
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and costs of each group. In the case that the regulator knows the distribution of the
production functions and costs over all groups a permit trading scheme for manure
applied following good practices can be implemented. More precisely, the regulator
knows the functions f jð�Þ, the values of pjb, p
jb, nj and the share of each group j with
respect to all firms. Furthermore, it is necessary that the regulator has established an
accredited verification system for good practices. Within this setting, the regulator
can calculate the optimal application of all inputs for the entire sector, but not for
each individual firm. Consequently, the regulator can determine the optimal
emissions of the entire sector that result from the application of manure following
bad practices E�b and following good practices E�g. The quantity E�b can be
approximated by imposing a tax t�b on manure that corresponds to the average
marginal damage of manure over all groups. The quantity E�g can be established by a
permit trading system for manure applied following good practices. The exchange
of the permits has to be weighted by the differences in the emission function of each
group, i.e. if one kg of manure applied following good practices in group 1 results in
twice as much emissions as in group 2, firms in group 1 have to have twice as many
permits as firms in group 2 given the same amount of manure. The price of the
permits is established in the market, and the participating firms get a refund of t�b.
The conditions for this scheme are outlined at the beginning of the section
Situation III.
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