Acknowledgments. I would like to thank Niels Vestergaard for valuable
advice and comments. I also wish to thank Lars Ravn-Jonsen, Eva Roth, Lone
Grønbæk Kronbak and Urs Steiner Brandt for useful comments. Thanks also to
two anonymous reviewers for helpful comments. The research leading to these results has partly received funding from the European Community’s Seventh Framework Programme [FP7/2007–2013] under grant agreement number 226675. The
KnowSeas project is affiliated with LOICZ and LWEC. Any errors are the responsibility of the author. [This article was corrected on 25 October, 2012 after online
publication. The Acknowledgments section was updated.]

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NATURAL RESOURCE MODELING
Volume 26, Number 2, M ay 2013
BIOECONOMIC MODEL OF EASTERN BALTIC COD UNDER
THE INFLUENCE OF NUTRIENT ENRICHMENT
NGUYEN VIET THANH∗
Centre for Fisheries & Aquaculture Management & Economics (FAME),
Department of Environmental and Business Economics,
University of Southern Denmark, Denmark
Faculty of Development Economics,
VNU University of Economics and Business, Vietnam
E-mail: thanhmpa@gmail.com
Abstract. The objective of this paper is to study the economic man-
agement of Eastern Baltic cod (Gadus morhua) under the inﬂuence of nutri-
ent enrichment. Average nitrogen concentration in the spawning areas during
the spawning season of cod stock is chosen to be an indicator of nutrient en-
richment. The optimal cod stock is deﬁned using a dynamic bioeconomic
model for the cod ﬁsheries. The results show that the current stock level is
about half of the estimated optimal stock level and that the current total
allowable catch (TAC) is about one-fourth of the optimal equilibrium yield.
The results also indicate that the beneﬁt from a reduction in nitrogen very
much depends on the harvest policies. If the TAC is set equal to the optimal
equilibrium yield, the beneﬁt of a nitrogen reduction from the 2009 level to
the optimal nitrogen level would be about 604 million DKK over a 10-year
time horizon, given a discount rate of 4% per year. However, if a recovery
management plan is chosen, the beneﬁt would only be about 49 million DKK
over a 10-year time horizon.
Key Words: Bioeconomic model, Eastern Baltic cod, eutrophication.
1. Introduction. The objective of this paper is to study the economic man-
agement of Eastern Baltic cod (Gadus morhua) under the inﬂuence of nutrient
enrichment. This ﬁsh stock inhabits the regions East of Bornholm in the ICES’
(The International Council for the Exploitation of the Sea) subdivisions 25–32, and
its spawning season begins in early March and ends in September–October (Bagge
and Thurow [1994], Wieland et al. [2000]). It is one of the most important ﬁsh stocks
in the Baltic Sea. In Denmark, it accounts for over 33% of the total cod landed and
contributed about 14% to the total landing value of Danish ﬁsheries in 2009 (Anon
[2009]). In Sweden, it accounted for 4% of the total catch, but it contributed about
19% to the total landing value of Swedish ﬁsheries in 2004 (Osterblom [2008]).
Nine countries currently harvest Eastern Baltic cod: Germany, Finland, Russia,
Estonia, Latvia, Lithuania, Poland, Sweden, and Denmark. Poland, Sweden, and
Denmark had the largest catch shares, which accounted for 22%, 21%, and 17%
of the total cod landing from the eastern Baltic Sea in 2009, respectively (ICES
∗Corresponding author. Nguyen Viet Thanh, Centre for Fisheries & Aquaculture Management
& Economics (FAME), Department of Environmental and Business Economics, University of
Southern Denmark, Denmark, E-mail: thanhmpa@gmail.com
Received by the editors on 6th july 2012. Accepted 4th june 2012.
Copyright c© 2012 W iley Period ica ls, Inc.
259
260 N. V. THANH
[2010a]). The harvesting of eastern cod mainly occurs at the beginning of the year.
For example, in Denmark, landing from January to June accounted for about 73.2%
of the total Eastern Baltic cod landings in 2009 (Anon [2009]). There were about
13,900 ﬁshing vessels with a total 246,345 GT in the Baltic countries (without
Russia) in 2005 (Horbowy and Kuzebski [2006]). Trawls and gillnets are the main
ﬁshing gears for eastern Baltic cod ﬁsheries, which contributed about 70% and 30%
of the total landing in 2009, respectively (ICES [2010b]). In 2010, the total landing
of Eastern Baltic cod was 50,277 tons, which was approximately equal to 12.8% of
the highest landing of 391,952 tons in 1984 (ICES [2010a, 2011]). The ICES has
recommended that TACs should be calculated on the basis of ﬁshing mortality and
the stock spawning biomass (Radtke [2003]). The TACs are annually allocated to
the member states with the same percentages annually (Nielsen and Christensen
[2006]). The TAC for Eastern Baltic cod has been separate from Western Baltic
cod since 2004, and it was set of 56,800 tons in 2010 (ICES [2009]).
Eastern Baltic cod has been managed under a recovery program since 2007 (EC
[2007]). The main target of the recovery program is to ensure the sustainable ex-
ploitation of the cod stocks by gradually reducing and maintaining the ﬁshing mor-
tality rates at certain levels (EC [2007]). The recovery program does not include
changes in nutrient loadings as a policy option. However, the decline of the cod
stock in the early 1990s was considered a consequence of not only ﬁshing pressure
but also environmental eﬀects including temperature, salinity, and oxygen (Ko¨ster
et al. [2009]). During this time, nutrient enrichment was also considered a serious
environmental problem for ecosystems in the Baltic Sea (MacKenzie et al. [2002],
Rockmann et al. [2007], HELCOM [2009]). When excess inputs of nutrients are in-
troduced into ecosystems, which is called eutrophication, the water becomes turbid
from the dense populations of phytoplankton. Large aquatic plants are outcompeted
and disappear along with their associated invertebrate populations. Moreover, de-
composition of the large biomass of phytoplankton cells may lead to low oxygen
concentrations (hypoxia and anoxia), which kill ﬁsh and invertebrates. The outcome
of eutrophication is a community with low biodiversity and low esthetic appeal (Be-
gon et al. [2006]). In 1988, the Helsinki Commission (HELCOM)1 decided to reduce
nutrient inputs by 50% because of the serious eutrophication problem in the Baltic
Sea.2
Insuﬃcient attention has been given to the eﬀect of nutrient enrichment on the cod
stock (Bagge and Thurow [1994], HELCOM [2009]) even though many papers have
studied the eﬀects of temperature, salinity, oxygen, and inﬂows from the North
Sea (Westin and Nissling [1991], Gronkjer and Wieland [1997], Nissling [2004],
Koster et al. [2005], Mackenzie et al. [2007], Rockmann et al. [2007], Heikinheimo
[2008]). Nutrient enrichment can aﬀect both the growth and the reproduction of the
exploited species, and these eﬀects depend on the nutrient concentration level in
the main habitat of the species (Breitburg et al. [2009]). Knowler [2001] empirically
ﬁnds the eﬀects of phosphorus concentration on the recruits of the anchovy stocks
BIOECONOMIC MODEL OF EASTERN BALTIC COD 261
in the Black Sea. Smith and Crowder [2005] ﬁnd the eﬀects of nitrogen loadings on
the growth of the blue crab ﬁshery in the Neuse River Estuary. Finally, Simonit
and Perrings [2005] ﬁnd the eﬀects of nutrient enrichment on the growth of ﬁsh
stocks in Lake Victoria. Compared with these studies, this paper proposes a more
general approach that includes both the ﬁsheries sector and the pollution sector
in a bioeconomic model. With respect to this general approach, Tahvonen [1991]
theoretically develops a model that combines optimal renewable resource harvesting
and optimal pollution control. Murillas-Maza [2003] also theoretically investigates
interdependence between pollution and ﬁsh resource harvest policies. In this paper,
a more realistic growth function is applied by including both the growth and the
recruitment of ﬁsh stock. In addition, the theoretical model is also applied to the
cod stock and nutrient pollution in the Baltic Sea. The following speciﬁc questions
will be discussed:
(1) How does nutrient enrichment aﬀect the Eastern Baltic cod ﬁsheries?
(2) What is the optimal harvest compared with the current level?
(3) How much would the cod ﬁsheries beneﬁt from nutrient reductions?
This paper proceeds as follows: The next section describes the model. The follow-
ing section is an empirical analysis of the Eastern Baltic cod. The paper concludes
with a summary derived from the empirical analysis.
2. The bioeconomic model. The bioeconomic model is traditionally based
both on a biological model and an economic model of the ﬁshery. The social objec-
tive is to maximize the present value of the proﬁt of the involved ﬁshermen over a
certain time horizon subject to the biological model of the ﬁsh stock. We expand
the model to include the consequences of eutrophication. We show how the opti-
mal harvest policy depends on the eutrophication level. In the following section the
model is explained.
2.1. Population dynamic. In a basic form, changes in biomass of an exploited
ﬁsh population over time depend on the recruitment, growth, capture, and natural
death of individuals3 (Ricker [1987], Beverton and Holt [1993]). The spawning stock
is the mature part of the population that spawns. It is also assumed to be the part
of the population exposed to the ﬁshery. Recruitment occurs when the ﬁsh grow
to maturity and enter the spawning stock. It takes some time to progress from
spawning to recruitment; therefore we apply a delayed discrete-time model (Clark
[1976], Bjorndal [1988]):
St+1 = (St −Ht)Gt + Rt,(1)
where St is the spawning biomass at the beginning of period t , and Ht is the
harvest quantity in period t . It is assumed that harvesting occurs at the beginning
262 N. V. THANH
of period t and that, St −Ht is the escapement. The escapement will grow by the
function Gt = G(St). The recruitment is a function of the stock that need γ periods
to grow into maturity Rt = R(St−γ ). To extend the model, we include the nutrient
concentration Nt in both the growth and recruitment functions.
Gt = G(St,Nt)
Rt = R(St−γ ,Nt−γ )
(2)
Both functions are assumed to be continuous and diﬀerentiable.
2.2. The bioeconomic model. It is assumed that the net beneﬁt of the ﬁsh-
ery is a function of total harvest (H ) and spawning stock biomass (SSB) (S ) with
πt = π(Ht, St). The function π is assumed to be continuous, concave, and twice
diﬀerentiable. A general economic objective is to maximize the net present value
(NPV) of the net beneﬁts from the ﬁshery subject to the dynamics of the ﬁsh stock:
Objective : maximize
Ht
NPV =
T∑
t=0
ρtπ(Ht, St),(3)
Subject to : St+1 = (St −Ht)Gt + Rt,(4)
where ρ = 11+r is the discount factor, and r is the discount rate. The harvest has
to be positive so Ht ≥ 0. The maximization problem is restricted by the present
and previous γ years of stock levels. However, we are only interested in ﬁnding the
optimal stock and harvest levels, so the initial conditions are ignored.
Problem (3) may be solved using the Method of Lagrange Multipliers (see e.g.,
Conrad and Clark [1995]). We formulate the (current) Lagrange expression as
L =
T∑
t=0
ρt(πt + ρλt+1((St −Ht)Gt + Rt − St+1)).(5)
If the stock is considered a capital, the term4(St −Ht)Gt + Rt − St+1 is the
change in capital in period t + 1. Then λt+1 is the current value shadow price
of the resource in period 0 + 1. The partial deviates of the Lagrange model are:
∂L
∂Ht
= ρt (πH − ρλt+1Gt) ,(6)
∂L
∂St
= ρt (πS + ρλt+1(Gt + (St −Ht)GS )
+ ργ+1λt+γ+1RS
)− ρtλt ,
(7)
BIOECONOMIC MODEL OF EASTERN BALTIC COD 263
where all the deviations with a prime are taken at time t . The ﬁrst order necessary
condition for optimization requires that deviations (6) and (7) be equal zero are:
λt+1 =
πH
ρGt
,(8)
λt = πS + ρλt+1(Gt + (St −Ht)GS ) + ργ+1λt+γ+1RS .(9)
In equilibrium, all variables are stationary over time, and the t subscript can
therefore be dropped. The restriction (4) implies
H = S − S −R
G
.(10)
Equation (9) will then be
πS + ρλ
(
Gt +
S −R
G
GS + ρ
γRS
)
= λ.(11)
And substituting λ from (8) into (11) results in the rule for optimal stock level
(
πS
πH
+ 1
)
G +
(S −R)
G
GS + ρ
γRS = 1 + r.(12)
Equation (12) is called the discrete-time analog of the golden rule for capital
accumulation in natural resource economics (Clark and Munro [1975]). In the left
hand side of this equation, the term ( πSπH + 1) is called the marginal stock eﬀect
(MSE), which represents the stock density inﬂuence on harvesting costs (Clark and
Munro [1975], Bjorndal [1988]). The term (S−R)G GS + ρ
γRS in (12) is the marginal
productivity. It consists of two parts: the ﬁrst part is related to the growth of the
escapement, and the second part is related to the recruitment. The second part
is discounted with γ periods as a consequence of the delay in maturity. Given a
discount rate of r , equation (12) can be solved for the optimal stock level, S∗, as a
function of nutrient concentration (N ). Furthermore, the optimal harvest level, H ∗,
can be derived from (10). As the recruitment and growth functions are functions of
N , the NPV of the resource when it is optimized is also a function of N .
3. An empirical analysis of Eastern Baltic cod. The bioeconomic model,
as presented in the previous section, is now applied to the Eastern Baltic cod
ﬁsheries under the inﬂuence of nutrient enrichment. The TACs of the cod stock is
expected to be relatively constant, for example, it does not change by more than
15% between two subsequent years (EC [2007]). In this case and following Voss
et al. [2011], the objective of the function is to maximize the NPV of utility function
264 N. V. THANH
from harvesting ﬁsh
Objective : maximize
Ht
NPV U =
T∑
t=0
ρtU(Ht, St)
Subject to : St+1 = (St −Ht)Gt + Rt,
(13)
where U(Ht, St) = 11−n π(Ht, St)
1−n is the utility function from harvesting ﬁsh. Fur-
thermore, 0 ≤ n < 1 is a constant in which, the higher value of n, the more a
constant income stream over time is preferred (Voss et al. [2011]). In this study, n
is chosen 0.5. We have
US
UH
=
π(Ht, St)−n ∗ πS
π(Ht, St)−n ∗ πH
=
πS
πH
.
Equations (10) and (12) can still be used to calculate the optimal stock and
optimal harvest for the Eastern Baltic cod ﬁsheries.5 We use the Rsolnp package in
the R software developed by Ghalanos and Theussl (Ghalanos and Theussl [2011])
to solve the optimization equation (13).
3.1. Data. Data on the annual cod landings, SSB, and recruitments are avail-
able directly from ICES database (ICES [2010a]). The total nitrogen indicator
(NTOT ) is derived from the HELCOM database.6 To formulate a proper nitro-
gen indicator for the cod stock, we use data collected from the stations that, are
located in the ICES’ subdivisions 25, 26, and 28 with bottom depths greater than or
equal to 20 m. In addition, we only use data collected during the spawning season
of the cod stock, which is from March to September. The nitrogen concentration in
the spawning areas during the spawning season is calculated as follows
Nt =
∑k
i=1 NTOTi
k
,(14)
where Nt is the nitrogen indicator in year t , k is the number of observations, and
NTOTi is the nitrogen concentration:
⎧⎪⎨
⎪⎩
in ICES 25, 26 and 28
from March to September of year t
in stations with bottom depth ≥20 m.
Table 1 shows the nitrogen index and the biological data of the Eastern Baltic
cod ﬁsheries from 1966 to 2009.
Statistical data from the Ministry of Food, Agriculture and Fisheries in Denmark
are used to estimate the variable cost function. In particular, a time series set of the
BIOECONOMIC MODEL OF EASTERN BALTIC COD 265
TABLE 1. Biological and environmental data: N has been estimated, SSB and Recruits are
from ICES [2011a].
SSB Recruits SSB Recruits
Year (1000 tones) (millions) N (mM/m3 ) Year (1000 tones) (millions) N (mM/m3 )
1966 172.018 430.264 na 1988 299.273 224.300 21.3975
1967 228.679 370.921 na 1989 240.273 122.489 22.3235
1968 233.958 354.063 na 1990 216.024 128.357 17.3061
1969 222.659 306.727 15.3622 1991 151.586 82.752 12.3441
1970 208.842 240.011 15.2414 1992 92.864 136.406 18.1909
1971 184.181 264.787 13.1179 1993 112.710 181.985 21.2248
1972 198.996 322.278 14.8874 1994 191.730 127.263 21.0654
1973 211.991 432.140 16.3683 1995 236.994 119.558 21.6316
1974 262.952 506.893 15.9865 1996 163.779 115.509 22.145
1975 339.545 303.683 18.2519 1997 135.620 88.058 20.2688
1976 355.564 293.397 15.7158 1998 109.078 149.121 20.5933
1977 326.914 479.002 16.3753 1999 90.298 152.307 23.0713
1978 379.201 829.398 13.9564 2000 115.853 174.929 20.9427
1979 579.671 615.355 19.0587 2001 104.135 135.682 20.9891
1980 696.743 425.886 18.6566 2002 82.992 122.186 21.4832
1981 666.132 689.813 18.5581 2003 80.153 111.907 19.6571
1982 670.941 693.590 20.1841 2004 78.901 107.209 20.0716
1983 645.258 472.374 22.1226 2005 63.750 160.148 21.1544
1984 657.667 302.921 21.2992 2006 78.656 127.414 21.3767
1985 544.911 253.078 25.5562 2007 93.942 160.234 20.7835
1986 399.371 260.214 23.7282 2008 111.253 204.938 21.9704
1987 320.470 368.089 21.9113 2009 186.327 198.143 22.1991
annual cost and the annual catch of the ﬁshing ﬁrms from 1995 to 2009 in Bornholm
(Rønne) are used for the estimation. Most of the ﬁshing ﬁrms are individual persons,
where one person is the sole owner of a ﬁshing vessel with or without any company
structure. Variable costs are the total variable costs of a ﬁshing ﬁrm multiplied by
the share of cod in the total harvest and deﬂated using the consumer price index
(2000 = 1).7 The data for the estimation are described in Table 2.
3.2. Recruitment function. The stock–recruitment relationship of the East-
ern Baltic cod is assumed to follow a quadratic function, and the nitrogen concen-
tration is included as follows (Simonit and Perrings [2005]):
Rt = aSt−γNt−γ + bS2t−γ + cN
2
t−γ St−γ(15)
266 N. V. THANH
TABLE 2. Data for the Bornholm cod ﬁsheries.
Year Total variable cost (million DKK) Total landing (1000 tons)
1995 86.611 14.467
1996 111.505 17.009
1997 165.785 14.107
1998 124.007 10.914
1999 166.505 13.759
2000 117.572 10.159
2001 110.546 9.512
2002 79.579 7.032
2003 77.752 8.293
2004 68.331 7.323
2005 71.445 7.209
2006 70.390 7.696
2007 58.972 4.924
2008 45.204 5.541
Source: ICES, Fishkeriregnskabsstatistik, Fiskeristatistisk a˚rbog and own calculations.
or the alternative form is
Rt
St−γ
= aNt−γ + bSt−γ + cN 2t−γ .(16)
Juvenile cod is assumed to join in spawning stock at age 3, so the delay period is
γ = 2. The estimation of the recruitment functions for the Eastern Baltic cod are
described in Table 3.
The model explains 53% the variance of the dependent variable, and all the pa-
rameters are signiﬁcant at the 5% level or better. Additionally, the models indicate
the autocorrelation in the residuals, which is often noted in time series data de-
rived from VPA (Knowler [2007]). The estimated stock–recruitment function for
the Eastern Baltic cod is the following8
Rnt =0.2015826St−2Nt−2−0.0016263S2t−2−0.0058455St−2N 2t−2 .(17)
In this equation, R is measured in millions, S is measured in thousand tons, and
N is measured in millimole/m3. Given the average weight of cod at age 2 from
1966 to 2009, w = 0.209 kg (ICES [2010b]), the ﬁnal stock–recruitment function is
BIOECONOMIC MODEL OF EASTERN BALTIC COD 267
TABLE 3. Estimation of the Eastern Baltic cod stock–recruitment function using the quadratic
model and the data for 1966–2009.
Variables Estimation
Spawning stock (St –2 ) –0.0016263∗
Nitrogen (Nt –2 ) 0.2015826∗∗
Nitrogen square (Nt –2 2 ) –0.0058455∗∗
R2 0.53
F statistic 14.92
DW statistic 1.668
rho 0.688
Note: The dependent variable is Rt/St – 2 and n = 39. The models have been estimated with ﬁrst order
autocorrelation, using the Prais–Winsten transformed regression estimator.
∗p < 0.05.
∗∗p < 0.01.
determined
Rt = wRnt = 0.042131St−2Nt−2 − 0.00034S2t−2
− 0.001222St−2N 2t−2 .
(18)
In equation (18), R and S are measured in thousand tons, and N is measured in
millimole/m3. The graph of the stock–recruitment function is showed in Figure 1.
The main characteristics of the stock–recruitment function are the following
(1) Maximum recruitment: R∗ = 97 thousand tons (464 millions);
(2) Nitrogen concentration at R∗: N ∗ = 17.24 millimole/m3;
(3) SSB at R∗: SSB∗ = 534 thousand tons.
3.3. The growth function. We use a simple version of the growth function
(see e.g., Bjorndal [1988], Kronbak [2002]). Following Ricker [1987], the growth
function is assumed as follows
Gt = eδt ,(19)
where δt is called the net natural growth rate, which equals the instantaneous
growth rate minus the instantaneous natural mortality rate. We assume that ni-
trogen enrichment has minimal eﬀects on the growth of cod stock and it is ignored
in the growth function.9 The relationship between the net natural growth rate (δ)
and the SSB (S ) is assumed to follow a linear form10:
δt = δ(St) = d + fSt.(20)
268 N. V. THANH
FIGURE 1. Recruits as a function of SSB and nitrogen concentration.
From (1) and (19), the net natural growth rate (δ) may also be calculated ac-
cording to the following formula
(St+1 −Rt) = (St −Ht)eδt ⇒ δt = ln
(
St+1 −Rt
St −Ht
)
.(21)
Table 4 shows the estimation of equation (20) using data for 1966–2009. The
model has signiﬁcant parameters at the 1% level and explains 33% of the variance
of the dependent variable. In addition, δ′(S ) < 0 for all stock levels, which implies
that the net natural growth rate reduces when the stock increases. The net natural
growth rate is described as follows:
δt = 1.140578− 0.0012049St(22)
BIOECONOMIC MODEL OF EASTERN BALTIC COD 269
TABLE 4. Estimation of the natural growth for the Eastern Baltic cod using data for
1966–2009.
Variables Estimation
Constant 1.140578∗∗
Spawning stock (St ) 0.0012049∗∗
R2 0.33
F statistic 26.78
DW statistic 1.463
Note: The dependent variable is δ for the model and n = 44.
∗∗p < 0.01.
From (18) and (22), we have the model of the cod population dynamics under
the inﬂuence of nitrogen:
St+1 = (St −Ht)e1.140578−0.0012049St
+ 0.042131St−2Nt−2 − 0.00034S2t−2
− 0.001222St−2N 2t−2 .
(23)
The main characteristics of this function are the following:
(1) Maximum sustainable yield: MSY = 269 thousand tons,
(2) Nitrogen concentration at MSY: Nmsy = 17.24 millimole/m3,
(3) SSB at MSY: SSBmsy = 564 thousand tons, and
(4) The carrying capacity: Smax = 974 thousand tons.
The Eastern Baltic cod stock may have been closest to its carrying capacity in
late 1970s and early 1980s. The current SSB level of 308.787 thousand tons (ICES
[2011]) is about half of the stock level at the maximum sustainable yield (SSB at
MSY).
3.4. Variable cost function. It is assumed that the total variable cost of
the ﬁsheries is a function of the total harvest (H ) and the SSB (S ) (Clark [1990],
Sandberg [2006], Rockmann et al. [2009]). Since cod is an internationally traded
commodity, it is further assumed that cod ﬁsheries have a perfectly elastic demand
curve. The net beneﬁt function of the Eastern Baltic cod ﬁsheries in period t can
be deﬁned as follows:
π(Ht, St) = pHt − Ct(St,Ht),(24)
270 N. V. THANH
where p is a constant price and, Ct is the total variable cost of the ﬁshery in period
t . The total variable cost of the Eastern Baltic cod ﬁsheries is calculated as follows:
Ct =
f∑
i
ctihti ,(25)
where Ct is the total variable cost of the ﬁshery in period t , cti is the unit cost
of harvest of ﬂeet i in period t, hti is the harvest of ﬂeet i in period t , and f is
the number of ﬂeets. The unit cost of harvest of cod ﬁshing ﬁrms in the Bornholm
region is assumed to be the unit cost of harvest for the entire Eastern Baltic cod
ﬁsheries (Kronbak [2002], Rockmann et al. [2009])
Ct = ct
f∑
i
hti = ctHt =
Cbt
hbt
Ht =
Cbt
m
,(26)
where Ht is the total harvest of the Baltic cod ﬁsheries in period t , ct is the unit
cost of harvest of the Bornholm cod ﬂeet in period t , Cbt is the total variable cost
of the Bornholm cod ﬁsheries in period t , hbt is the total harvest of Bornholm cod
ﬁsheries in period t and m =
∑h
bt∑H
t
is the Bornholm average share of the cod landing.
The total variable cost of Bornholm cod ﬁsheries is assumed to be the following in a
trans-log functional form (Clark [1990], Alaouze [1999], Sandberg [2006], Rockmann
et al. [2007, 2009])
Cbt = αbS
β1
t h
β2
bt ,(27)
where St is the spawning stock in period t ; αb, β1 , β2 are the parameters that need
to be estimated. Substituting (27) into (26) yields
Ct =
αbS
β1
t h
β2
bt
m
= αbmβ2−1S
β1
t H
β2
t = αS
β1
t H
β2
t ,(28)
where α = αbmβ2−1. Using the data from the Bornholm cod ﬁsheries, the estimation
for the variable cost function is described in Table 5.
The model explains 76% of the variance of the dependent variable. The spawning
stock coeﬃcientis signiﬁcant at the 5% level, while the constant and the harvest
coeﬃcients are signiﬁcant at the 1% level. The DW test is inconclusive about au-
tocorrelation in the residuals. However, the Durbin’s alternative test (durbinalt)
for serial correlation and Breusch–Godfrey test for higher order serial correlation
shows that there is no autocorrelation in the residuals. The variable cost function
for Bornholm cod ﬁsheries is written as follows11
Cb = 59.15× S−0.4 × h1.04b .(29)
BIOECONOMIC MODEL OF EASTERN BALTIC COD 271
TABLE 5. Estimation of the variable cost function for the Bornholm cod ﬁshery using data for
1995–2008.
Variables Estimation Standard error
Constant 4.08∗∗ 0.79
Spawning stock (S) –0.4∗ 0.18
Harvest (hb) 1.04∗∗ 0.18
R2 0.76 –
F statistic 17.55 –
DW statistic 1.31 –
AIC –2.49 –
Note: The dependent variable is total cost and n = 14. The model has been estimated using linear
regression.
∗p < 0.05.
∗∗p < 0.001.
Given the average share of Bornholm cod landing from 1995 to 2008: m = 0.13
(ICES, Fiskeristatistisk A˚rbog [1995–2008]), the total variable cost for the Baltic
Sea cod ﬁsheries is written, using (28)
C =
Cb
m
= 54.51× S−0.4 ×H1.04 .(30)
Figure 2 shows the total variable cost (TC), the total revenue (TR) and proﬁt
of the cod ﬁsheries from 1966 to 2009. The total revenue and the proﬁt of the
cod ﬁsheries signiﬁcantly declined in late 1980s because of the collapse of the cod
stock. The variable cost of the cod ﬁsheries was estimated about one billion DKK
annually, which is similar to the study written by Rockmann et al. [2009].
3.5. Harvest policies under the influence of nitrogen enrichment. In
this section, the combination of the two harvest policies and the three nitrogen
policies are evaluated. The ﬁrst harvest policy is a simpliﬁed version of the EU
Management plan that keeps the maximum 15% change of TAC per year. The sec-
ond harvest policy is the optimal one, which keeps the harvest at optimal level. The
nitrogen policies are kept at the 2009 level, 15% reduction level and the optimal
level. Table 6 shows the NPV of proﬁts from the combination of the harvest and
nitrogen policies at the diﬀerent discount rates over a 10-year time horizon. Scenar-
ios 4, 5, and 6, using the optimal harvest policy provide a signiﬁcant increase in the
NPV compared with the cases of keeping TAC at the management plan (scenarios
1, 2, and 3). There is not a large change in the NPV when reducing nitrogen from
the current level (scenario 1) to the optimal level (scenario 3), keeping TAC at the
272 N. V. THANH
FIGURE 2. Total revenue (TR), total variable cost (TC), and proﬁt for the Eastern Baltic
cod ﬁsheries.
same level as the management plan. If the TAC is kept as the management plan,
then the NPV in the case of the 15% nitrogen reduction plan (scenario 2) is slightly
smaller than the case of the optimal nitrogen reduction plan (scenario 3). Table 6
indicates that the optimal harvest policy plays an important role in getting beneﬁts
from nitrogen reduction. The discount rates are varied from 0% to 12% per year. If
TAC were set equal to the optimal equilibrium yield, the beneﬁt of nitrogen reduc-
tion from the 2010 level to the optimal level would vary from 380 million DKK to
about 780 million DKK. However, if the management plan were chosen, the beneﬁt
would only range from 29 million DKK to about 66 million DKK.
Given a discount rate of 4% annually, the move from scenario 1 to scenario 4
produces a beneﬁt of about 6.3 billion DKK over 10 years, which is approximately
127 times higher than the move from scenario 1 to scenario 3. In addition, the move
from scenario 4 to scenario 6 also gives the beneﬁt of about 604 million DKK over
10 years, which is about 12 times higher than the beneﬁt of moving from scenario 1
to scenario 3. It is implied that the optimal harvest policy also plays an important
role in producing the beneﬁt from the nitrogen reduction scenarios.
BIOECONOMIC MODEL OF EASTERN BALTIC COD 273
TABLE 6. NPV of proﬁts (million DKK) from the alternative harvest policies and nitrogen
reduction scenarios over a 10-year time horizon and diﬀerent discount rates (2000 prices).
Scenarios
Discount rate (%) 1 2 3 4 5 6
0 11,185 11,245 11,252 18,619 19,312 19,397
2 9,865 9,916 9,922 16,689 17,299 17,373
4 8,751 8,795 8,800 15,038 15,576 15,642
6 7,805 7,843 7,848 13,617 14,095 14,153
8 6,998 7,032 7,036 12,388 12,814 12,866
10 6,307 6,336 6,340 11,320 11,701 11,747
12 5,711 5,737 5,740 10,387 10,730 10,772
Note: Scenario 1: nitrogen concentration level 2009 & recovery management plan; Scenario 2: 15%
nitrogen reduction and recovery management plan; Scenario 3: optimal nitrogen level and recovery
management plan; Scenario 4: nitrogen concentration level 2009 and optimal harvest policy; Scenario
5: 15% nitrogen reduction and optimal harvest policy; Scenario 6: optimal nitrogen level and optimal
harvest policy.
3.6. The approach to the optimal stock level. Figure 3 shows the NPV
of the proﬁt as a function of nitrogen concentration. At the 2009 nutrient level,
the NPV is about 48.2 billion DKK, given a discount rate of 4% per year. If the
nitrogen concentration were reduced to the optimal level, the NPV would increase
to about 2.2 billion DKK. This beneﬁt equals 4.6% of the NPV, given the 2009
nitrogen concentration level.
Figure 4 shows the approach in relation to the optimal stock and optimal har-
vest (r = 0.04). Given the initial SSB in 2008–2010 (ICES [2011]), it takes about
4 years to approach the optimal harvest and the optimal stock level. The model
suggests that the optimal TAC for the ﬁrst year is about 43 thousand tons, which
corresponds to a stock biomass level of 481 thousand tons. These ﬁgures are smaller
than the recommended TAC from the ICES (64.5 thousand tons) and the corre-
sponding stock biomass level (308 thousand tons) in 2011. The optimal TAC is even
smaller than the 2010 TAC (56.8 thousand tons) and the actual landings (50.277
thousand tons) in 2010. Given the low optimal TAC and the high stock level in
the ﬁrst year, the model predicts that the optimal TAC for the second year is
about 176 thousand tons, which corresponds to a stock biomass of 591 thousand
tons.
The optimal path12 is relatively short, but it may be consistent with the recent
recovery of the Eastern Baltic cod. The spawning biomass of cod stock has been
increased almost threefold since 2008 (ICES [2011]). In 2011, the SSB is estimated
274 N. V. THANH
FIGURE 3. NPV under the diﬀerent nitrogen concentration levels (r = 4%)
at about 308 thousand tons, which is about half of the optimal stock biomass
level.
4. Summary. In this paper, we introduce a bioeconomic model for a renewable
resource with a changing environment. We expand the traditional model to include
nutrient enrichment in the biological part of the bioeconomic model. We show
how the optimal harvest policy depends on the nutrient enrichment level. The
results show that the current stock level is about half of the optimal stock level
and the current TAC is about one-fourth of the optimal equilibrium yield. The
results further indicate that the combination of the optimal harvest policy and
optimal pollution control allow for the highest beneﬁt, while the combination of
the management plan and uncontrolled pollution plan result in the lowest beneﬁt
for the cod ﬁsheries. In addition, the results indicate that the improvement of a
harvest policy produces a much higher beneﬁt from nitrogen reduction than the
improvement of pollution control. It implies that the optimal harvest policy plays
a crucial role in the economic management of Eastern Baltic cod ﬁsheries, even
though the cod ﬁsheries beneﬁt from the optimal pollution control.
BIOECONOMIC MODEL OF EASTERN BALTIC COD 275
FIGURE 4. Optimal approach to the steady state (r = 0.04).
In our model, we assume that all cod ﬁshing vessels are identical and have the
same cost and revenue structure. We also assume that the recruitment of cod stock
is a function of the stock size and nitrogen concentration in the spawning areas.
However, other factors such as temperature, salinity, and inﬂows may aﬀect the
recruitment of the cod stock. In addition, we ignore the eﬀects of the predator–prey
interactions (e.g., with herring) on the SSB of cod stock in our model. Therefore,
the results of this research should be used with a caution.
ENDNOTES
1. Who is responsible for monitoring and implementing the 1988 Ministerial Declaration. The
commission originally includes six countries: Denmark, Sweden, Soviet Union, the Polish People’s
republic, the German Democratic Republic and the Federal Republic of Germany.
2 Source: GB/aboutus/ (Accessed 05/01/2011).
3 Others aﬀect changes in biomass of a ﬁsh population over time including emigration, immi-
gration, and environmental factors.
4 This term equals zero when the optimization problem is solved.
5 The shadow price will be changed in this case.
276 N. V. THANH
6 Available at (Accessed
15/11/2010)
7 See Table A1 for a detail description
8 Full function is
Rt = 0.2015826St−2 Nt−2 − 0.0016263S2t−2 − 0.0058455St−2 N 2t−2
+ 0.688μt−1 + εt.
9 There are more indirect eﬀects through the food web than the eﬀects on recruitment. For
example, nutrient enrichment may cause an increase of phytoplankton population that is eaten
by zooplankton. Sprat, which is the prey for herring, eats zooplankton and cod eats herring.
10 The quadratic function form was tested empirically using data from the eastern Baltic cod
ﬁshery, but the results were not successful. Estimated parameters showed an upward parabola.
11 One of reviewers remains skeptical of a time-series estimate with 14 data points. The Reviewer
suggests that there should be an analysis of outlier and time-dependent eﬀects and tests for
functional form as well as sensitivity analysis. The reviewer also recommends that, with such a
small data set, a simple exercise with a “best ﬁt” algorithm would be preferred to OLS.
12 The optimal path is derived from the Rsolnp package in the R software.
13 According to the selection of accounts and calculation of statistics in Denmark (Fishkerireg-
nskabsstatistik), most of the ﬁshing ﬁrms are individual persons, where one person is the sole
owner of a ﬁshing vessel with or without any company structure. This private individual, the
ﬁshing manager and his family, is the economic unit in the account statistic.
Acknowledgments. I would like to thank Niels Vestergaard for valuable
advice and comments. I also wish to thank Lars Ravn-Jonsen, Eva Roth, Lone
Grønbæk Kronbak and Urs Steiner Brandt for useful comments. Thanks also to
two anonymous reviewers for helpful comments. The research leading to these re-
sults has partly received funding from the European Community’s Seventh Frame-
work Programme [FP7/2007–2013] under grant agreement number 226675. The
KnowSeas project is aﬃliated with LOICZ and LWEC. Any errors are the respon-
sibility of the author. [This article was corrected on 25 October, 2012 after online
publication. The Acknowledgments section was updated.]
BIOECONOMIC MODEL OF EASTERN BALTIC COD 277
Appendix. Economic data (average per ﬁrm annually) for Bornholm ﬁshing ﬁrms1 3 from 1995
to 2008 (1000 DKK)
No. Name 1995 1996 1997 1998
1 G ross revenue 976 .40 1075 .1 1577 .2 1531 .6
2 Revenue from cod 554 .00 653 .3 1122 .2 1006 .3
3 Share of cod : (1)/(2) 0 .57 0 .61 0 .71 0 .66
4 Variab le cost exclud ing share contract 737 .20 869 .9 1278 .4 1187 .6
5 F ixed wage contract cost 208 .80 240 .2 405 .8 421 .9
‘ Days at sea of sk ipp er 15 .10 9 .9 11 .8 18 .7
Days at sea of crew 137 .90 138 .6 223 .3 223 .4
6 Man days of ﬁxed wage contract 153 .00 148 .50 235 .10 242 .10
7 Wage p er day of ﬁxed wage contract: (5)/(6) 1 .36 1 .62 1 .73 1 .74
Man days of ﬁ sherm en (share remuneration) 137 .50 185 .5 176 .2 190 .9
Man days of partners (share remuneration) 8 .10 9 .2 10 .1 25 .3
8 Man days of share contract 145 .60 194 .70 186 .30 216 .20
9 Share contract cost: (7) × (8) 198 .70 314 .93 321 .57 376 .76
10 Depreciations 162 .20 171 .8 200 .6 177 .3
11 Variab le cost: (4) + (9) – (10) 773 .70 1013 .03 1399 .37 1387 .06
12 Variab le cost of cod : (3) × (11) 438 .99 615 .58 995 .67 911 .34
13 Catch of cod , m etric tons 82 .20 100 148 .1 91 .2
14 Unit variab le cost of harvest: (12)/(13), 1000
DKK/ton or DKK/kg
5 .34 6 .16 6 .72 9 .99
15 Cod catch from Bornholm , 1000 tons 14 .47 17 .009 14 .107 10 .914
16 Cod catch from Baltic , 1000 tons 107 .712 121 .877 88 .6 67 .429
17 Total variab le cost for Bornholm cod ﬁ sheries:
(12) × (19)
77262 .35 101570 .96 154328 .81 117562 .44
18 Cod price from Danish Account Statistic 9 .13 8 .35 8 .33 9 .44
19 Number of ﬁ sh ing ﬁ rm s in Bornholm 176 165 155 129
20 Catch share of Bornholm cod ﬁ sheries: (15)/(16) 0 .13 0 .14 0 .16 0 .16
21 Price index (1900 = 1) 4686 4785 4890 4980
22 Real variab le cost (2000 prices) 492 676 1070 961
23 Real un it cost (2000 prices) 5 .99 6 .76 7 .22 10 .54
24 Real cod price (2000 prices) 10 .23 9 .17 8 .95 9 .96
25 Real tota l variab le cost of Bornholm cod
ﬁ sheries: (19) × (22)
86611 .00 111505 .18 165785 .12 124007 .13
(Continued)
278 N. V. THANH
Appendix. (Continued)
No 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
1 1702 1249 1224 1143 1089 936 1135 1292 1782 868
2 1351 880 841 693 698 539 689 856 1201 380
3 0 .79 0 .70 0 .69 0 .61 0 .64 0 .58 0 .61 0 .66 0 .67 0 .44
4 1291 937 855 836 814 809 854 972 1240 789
5 456 271 253 239 233 187 200 273 383 174
9 412 .00 438 .00 451 .00 396 .00 384 .00 382 .00 438 .00 409 .00 391 .00 333 .00
10 182 148 138 157 151 155 144 138 161 154
11 1521 .00 1227 .00 1168 .00 1075 .00 1047 .00 1036 .00 1148 .00 1243 .00 1470 .00 968 .00
12 1207 .33 864 .50 802 .52 651 .77 671 .08 596 .59 696 .89 823 .54 990 .72 423 .78
13 102 .68 74 .70 67 .46 54 .94 66 .88 59 .06 63 .80 80 .17 72 .41 43 .98
14 11 .76 11 .57 11 .90 11 .86 10 .03 10 .10 10 .92 10 .27 13 .68 9 .64
15 13 .759 10 .159 9 .512 7 .032 8 .293 7 .323 7 .209 7 .696 4 .924 5 .541
16 72 .989 89 .168 91 .325 67 .74 71 .386 67 .768 55 .254 65 .532 50 .843 42 .235
17 161781 .85 117571 .95 113155 .73 83426 .77 83213 .91 73976 .60 78748 .75 79059 .42 67369 .23 53396 .13
18 13 .12 14 .45 15 .54 16 .1 13 .69 13 .45 14 .96 15 .54 17 .67 16 .93
19 134 136 141 128 124 124 113 96 68 126
20 0 .19 0 .11 0 .10 0 .10 0 .12 0 .11 0 .13 0 .12 0 .10 0 .13
21 5104 5253 5377 5507 5622 5687 5790 5900 6001 6205
22 1243 864 784 622 627 551 632 733 867 359
23 12 .10 11 .57 11 .62 11 .32 9 .38 9 .33 9 .91 9 .15 11 .98 8 .16
24 13 .50 14 .45 15 .18 15 .36 12 .79 12 .42 13 .57 13 .84 15 .47 14 .33
25 166504 .72 117571 .95 110546 .22 79578 .87 77752 .16 68331 .12 71445 .11 70389 .68 58971 .93 45203 .85
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