Bioeconomic model of eastern baltic cod under the influence of nutrient enrichment

nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) NRM nrm˙137 16:1 Dispatch: 7-21-2012 CE: AFL Journal MSP No No of pages: 29 7-21-2012 PE: Matthew N AT U R A L R E S O U R C E M O D E L I N G Vo l u m e 00, N u m b e r , 2 BIOECONOMIC MODEL OF EASTERN BALTIC COD UNDER THE INFLUENCE OF NUTRIENT ENRICHMENT 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 NGUYEN VIET THANH ∗ Department of Environmental and Business Economics Centre for Fisheries & Aquaculture Management & Economics (FAME) University of Southern Denmark and Faculty of Development Economics, VNU University of Economics and Business E-mail: thanhmpa@gmail.com Q1 Abstract The ob jective of this paper is to study the economic management of Eastern Baltic cod (Gadus morhua ) under the influence of nutrient enrichment Average nitrogen concentration in the spawning areas during the spawning season of cod stock is chosen to be an indicator of nutrient enrichment 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 Introduction The objective of this paper is to study the economic management 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 ∗ Corresponding author Nguyen Viet Thanh, Department of Environmental and Business Economics Centre for Fisheries & Aquaculture Management & Economics (FAME) University of Southern Denmark and Faculty of Development Economics, Q2 VNU University of Economics and Business e-mail: nvt@sam.sdu.dk Received by the editors on t h july 2012 Accepted 4t h june 2012 C o p yr i g h t c 20 12 W i l e y P e r i o d i c a l s , I n c nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 16:1 N V THANH 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 [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 exploitation of the cod stocks by gradually reducing and maintaining the fishing mortality 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], nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 BIOECONOMIC MODEL OF EASTERN BALTIC COD Q3 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Rockmann et al [2007], HELCOM [2009]) When excess inputs of nutrients are introduced 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, decomposition 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 (Begon 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 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: nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 16:1 N V THANH (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 reductions? cod fisheries benefit from nutrient This paper proceeds as follows: The next section describes the model The following section is an empirical analysis of the Eastern Baltic cod The paper concludes with a summary derived from the empirical analysis The bioeconomic model The bioeconomic model is traditionally based both on a biological model and an economic model of the fishery The social objective 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 optimal 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]): (1) St + = (St − Ht ) Gt + Rt , 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 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 BIOECONOMIC MODEL OF EASTERN BALTIC COD 5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 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 ) (2) Rt = R(St−γ , Nt −γ ) Both functions are assumed to be continuous and differentiable 2.2 The bioeconomic model It is assumed that the net benefit of the fishery 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: T (3) (4) ρt π(Ht , St ), Objective : maximize NPV = Ht Subject to : t =0 St + = (St − Ht )Gt + Rt , where ρ = 1+ r is the discount factor, and r is the discount rate The harvest has to be positive so Ht ≥ 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 T (5) L= ρt (πt + ρλt + ((St − Ht )Gt + Rt − St +1 )) t =0 If the stock is considered a capital, the term4 (St − Ht )Gt + Rt − St +1 is the change in capital in period t + Then λt + is the current value shadow price of the resource in period + The partial deviates of nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 16:1 N V THANH 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 the Lagrange model are: 35 36 37 38 39 40 (12) 41 42 7-21-2012 (6) ∂L = ρt (πH − ρλt +1 Gt ) , ∂Ht (7) ∂L = ρt (πS + ρλt +1 (Gt + (St − Ht )GS ) ∂St + ργ + λt + γ + RS − ρt λt , 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 = (8) (9) π H , ρGt λt = πS + ρλt +1 (Gt + (St − Ht )GS ) + ργ + λt + γ + RS In equilibrium, all variables are stationary over time, and the t subscript can therefore be dropped The restriction (4) implies (10) H =S − S−R G Equation (9) will then be (11) πS + ρλ Gt + S−R GS + ργ RS G = λ And substituting λ from (8) into (11) results in the rule for optimal stock level πS (S − R) +1 G + GS + ργ RS = + r πH G Equation (12) is called the discrete-time analog of the golden rule for capital accumulation in natural resource economics (Clark and Munro π [1975]) In the left hand side of this equation, the term ( π S + 1) is H called the marginal stock effect (MSE), which represents the stock density influence on harvesting costs (Clark and Munro [1975], Bjorndal nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 BIOECONOMIC MODEL OF EASTERN BALTIC COD [1988]) The term (S −R ) G S + ργ RS in (12) is the marginal productivity It consists of t G the part is related to the growth of wo parts: first 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 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 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 from harvesting fish T (13) Objective : maximize NPV Ht Subject to : U = ρt U (Ht , St ) t =0 St + = (St − Ht ) Gt + Rt , where U (H t , S t) = 1−n π(H t , S t)1 −n is the utility function from harvesting fish Furthermore, ≤ n < 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 π(Ht , St )−n ∗ πS π = = S π(Ht , St )−n ∗ πH πH UH 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) nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 16:1 N V THANH 3.1 Data Data on the annual cod landings, SSB, and recruitments are available directly from ICES database (ICES [2010a]) The total nitrogen indicator (NTOT ) is derived from the HELCOM database.6 To formulate a proper nitrogen 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 k (14) Nt = N T OTi i= , k where Nt is the nitrogen indicator in year t , k is the number of observations, and N T OTi 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 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 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 3.2 Recruitment function The stock–recruitment relationship of the Eastern Baltic cod is assumed to follow a quadratic function, and the nitrogen concentration is included as follows (Simonit and Perrings nrm˙137 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Biological and environmental data: N has been estimated, SSB and Recruits are from ICES [2011a] Recruits (millions) N (mM/m ) Year SSB (1000 tones) Recruits (millions) N (mM/m ) 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 172.018 228.679 233.958 222.659 208.842 184.181 198.996 211.991 262.952 339.545 355.564 326.914 379.201 579.671 696.743 666.132 670.941 645.258 657.667 544.911 399.371 320.470 430.264 370.921 354.063 306.727 240.011 264.787 322.278 432.140 506.893 303.683 293.397 479.002 829.398 615.355 425.886 689.813 693.590 472.374 302.921 253.078 260.214 368.089 na na na 15.3622 15.2414 13.1179 14.8874 16.3683 15.9865 18.2519 15.7158 16.3753 13.9564 19.0587 18.6566 18.5581 20.1841 22.1226 21.2992 25.5562 23.7282 21.9113 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 299.273 240.273 216.024 151.586 92.864 112.710 191.730 236.994 163.779 135.620 109.078 90.298 115.853 104.135 82.992 80.153 78.901 63.750 78.656 93.942 111.253 186.327 224.300 122.489 128.357 82.752 136.406 181.985 127.263 119.558 115.509 88.058 149.121 152.307 174.929 135.682 122.186 111.907 107.209 160.148 127.414 160.234 204.938 198.143 21.3975 22.3235 17.3061 12.3441 18.1909 21.2248 21.0654 21.6316 22.145 20.2688 20.5933 23.0713 20.9427 20.9891 21.4832 19.6571 20.0716 21.1544 21.3767 20.7835 21.9704 22.1991 7-21-2012 SSB (1000 tones) BIOECONOMIC MODEL OF EASTERN BALTIC COD Year nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) TABLE 16:1 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 10 7-21-2012 N V THANH TABLE Data for the Bornholm cod fisheries Year Total variable cost (million DKK) Total landing (1000 tons) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 86.611 111.505 165.785 124.007 166.505 117.572 110.546 79.579 77.752 68.331 71.445 70.390 58.972 45.204 14.467 17.009 14.107 10.914 13.759 10.159 9.512 7.032 8.293 7.323 7.209 7.696 4.924 5.541 S ou rce: IC E S , F ish keriregn skab sstatistik , F iskeristatistisk ˚ arb og an d ow n calcu lation s [2005]): (15) Rt = aSt −γ Nt −γ + bS2t −γ + cN2t −γ St −γ or the alternative form is (16) Rt = aNt −γ + bSt −γ + cN2t −γ St −γ Juvenile cod is assumed to join in spawning stock at age 3, so the delay period is γ = The estimation of the recruitment functions for the Eastern Baltic cod are described in Table The model explains 53% the variance of the dependent variable, and all the parameters 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 derived from VPA (Knowler [2007]) The 16:1 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 16 7-21-2012 16:1 N V THANH 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 autocorrelation 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 (29) Cb = 59.15 × S −0.4 × hb1.04 Given the average share of Bornholm cod landing from 1995 to 2008: m = 0.13 (ICES, FiskeristatistiskArbog [1995–2008]), the total variable cost for the Baltic Sea cod fisheries is written, using (28) Cb = 54.51 × S − 0.4 × H 1.04 m Figure 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] (30) C= 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 second 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 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 Scenarios 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 BIOECONOMIC MODEL OF EASTERN BALTIC COD 16:1 17 FIGURE Total revenue (TR), total variable cost (TC), and profit for the Eastern Baltic cod fisheries the current level (scenario 1) to the optimal level (scenario 3), keeping TAC at the 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 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 reduction 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 18 7-21-2012 16:1 N V THANH TABLE 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 (%) 6 10 12 11,185 9,865 8,751 7,805 6,998 6,307 5,711 11,245 9,916 8,795 7,843 7,032 6,336 5,737 11,252 9,922 8,800 7,848 7,036 6,340 5,740 18,619 16,689 15,038 13,617 12,388 11,320 10,387 19,312 17,299 15,576 14,095 12,814 11,701 10,730 19,397 17,373 15,642 14,153 12,866 11,747 10,772 N ote: S cen ario 1: n itro gen centra tio n level 2009 & recove ry m an agem ent p lan ; S cen ario 2: 15% n itro gen red u ctio n an d recovery m an agem ent p lan ; S cen ario 3: op tim al n itro gen level an d recovery m an agem ent p lan ; S cen ario 4: n itro gen centration level 2009 an d op tim al h arvest p olicy; S cen ario 5: 15% n itro gen red u ctio n an d op tim al h arvest p olicy; S cen ario 6: op tim al n itro gen level an d op tim a l h arvest p olicy Given a discount rate of 4% annually, the move from scenario to scenario produces a benefit of about 6.3 billion DKK over 10 years, which is approximately 127 times higher than the move from scenario to scenario In addition, the move from scenario to scenario 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 to scenario It is implied that the optimal harvest policy also plays an important role in producing the benefit from the nitrogen reduction scenarios 3.6 The approach to the optimal stock level Figure 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 BIOECONOMIC MODEL OF EASTERN BALTIC COD 16:1 19 FIGURE NPV under the different nitrogen concentration levels (r = 4%) Figure shows the approach in relation to the optimal stock and optimal harvest (r = 0.04) Given the initial SSB in 2008–2010 (ICES [2011]), it takes about 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 corresponding 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 20 7-21-2012 16:1 N V THANH FIGURE Optimal approach to the steady state (r = 0.04) 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 at about 308 thousand tons, which is about half of the optimal stock biomass level 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 BIOECONOMIC MODEL OF EASTERN BALTIC COD 21 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 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 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 Acknowledgments 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 ENDNOTES 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 Source: http://www.helcom.fi/helcom/en GB/aboutus/ (Accessed 2011) 05/01/ Others affect changes in biomass of a fish population over time including emigration, immigration, and environmental factors nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 22 7-21-2012 16:1 N V THANH This term equals zero when the optimization problem is solved The shadow price will be changed in this case Available at http://www.ices.dk/Ocean/asp/helcom/helcom.asp?Mode=1 (Accessed 15/11/2010) See Table A1 for a detail description Full function is R t = 0.2015826S t −2 N t −2 − 0.0016263S t − − 0.0058455S t −2 N t −2 + 0.688μ t −1 + εt 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 timedependent 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 (Fishkeriregnskabsstatistik), 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 1997 1998 Gross revenue Revenue from cod Share of cod: (1)/(2) Variable cost excluding share contract Fixed wage contract cost Days at sea of skipper Days at sea of crew Man days of fixed wage contract Wage per day of fixed wage contract: (5)/(6) Man days of fishermen (share remuneration) Man days of partners (share remuneration) Man days of share contract Share contract cost: (7) × (8) Depreciations Variable cost: (4) + (9) – (10) 976.40 554.00 0.57 737.20 208.80 15.10 137.90 153.00 1.36 1075.1 653.3 0.61 869.9 240.2 9.9 138.6 148.50 1.62 1577.2 1122.2 0.71 1278.4 405.8 11.8 223.3 235.10 1.73 1531.6 1006.3 0.66 1187.6 421.9 18.7 223.4 242.10 1.74 137.50 185.5 176.2 190.9 8.10 9.2 10.1 25.3 10 11 145.60 198.70 162.20 773.70 194.70 314.93 171.8 1013.03 186.30 321.57 200.6 1399.37 216.20 376.76 177.3 1387.06 23 (Continued) 7-21-2012 1996 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 1995 BIOECONOMIC MODEL OF EASTERN BALTIC COD Name nrm˙137 Q4 No ‘ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Appendix Economic data (average per firm annually) for Bornholm fishing firms1 from 1995 to 2008 (1000 DKK) 16:1 nrm˙137 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 24 No Name 19 20 1997 1998 438.99 82.20 5.34 615.58 100 6.16 995.67 148.1 6.72 911.34 91.2 9.99 14.47 107.712 77262.35 17.009 121.877 101570.96 14.107 88.6 154328.81 10.914 67.429 117562.44 9.13 8.35 8.33 9.44 176 0.13 165 0.14 155 0.16 129 0.16 4686 492 5.99 10.23 86611.00 4785 676 6.76 9.17 111505.18 4890 1070 7.22 8.95 165785.12 4980 961 10.54 9.96 124007.13 16:1 (Continued) 7-21-2012 21 22 23 24 25 Statistic Number of fishing firms in Bornholm Catch share of Bornholm cod fisheries: (15)/(16) Price index (1900 = 1) Real variable cost (2000 prices) Real unit cost (2000 prices) Real cod price (2000 prices) Real total variable cost of Bornholm cod fisheries: (19) × (22) 1996 N V THANH 12 Variable cost of cod: (3) × (11) 13 Catch of cod, metric tons 14 Unit variable cost of harvest: (12)/(13), 1000 DKK/ton or DKK/kg 15 Cod catch from Bornholm, 1000 tons 16 Cod catch from Baltic, 1000 tons 17 Total variable cost for Bornholm cod fisheries: (12) × (19) 18 Cod price from Danish Account 1995 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) Appendix (Continued) 2001 2002 2003 2004 2005 2006 2007 2008 10 11 12 13 14 1702 1351 0.79 1291 456 412.00 182 1521.00 1207.33 102.68 11.76 1249 880 0.70 937 271 438.00 148 1227.00 864.50 74.70 11.57 1224 841 0.69 855 253 451.00 138 1168.00 802.52 67.46 11.90 1143 693 0.61 836 239 396.00 157 1075.00 651.77 54.94 11.86 1089 698 0.64 814 233 384.00 151 1047.00 671.08 66.88 10.03 936 539 0.58 809 187 382.00 155 1036.00 596.59 59.06 10.10 1135 689 0.61 854 200 438.00 144 1148.00 696.89 63.80 10.92 1292 856 0.66 972 273 409.00 138 1243.00 823.54 80.17 10.27 1782 1201 0.67 1240 383 391.00 161 1470.00 990.72 72.41 13.68 868 380 0.44 789 174 333.00 154 968.00 423.78 43.98 9.64 7-21-2012 (Continued) nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 2000 nrm˙137 1999 BIOECONOMIC MODEL OF EASTERN BALTIC COD No 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 Appendix (Continued) 25 16:1 nrm˙137 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 No 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 N V THANH 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 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 26 Appendix: (Continued) 7-21-2012 16:1 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 7-21-2012 BIOECONOMIC MODEL OF 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Management—Experiences and Future Directions.‛ Mar Pol 30, 181–188 A Nissling [2004], ‚Eff ects of Temperature on Egg and Larval Survival of Cod (Gadus morhua) and Sprat (Sprattus sprattus) in the Baltic Sea—Implications for Stock Development.‛ Hydrobiologia 514(1–3), 115–123 H Osterblom [2008], The Role of Cod in the Baltic Sea, Baltic Sea 2020, 27 Q7 K Radtke [2003], ‚Evaluation of the Exploitation of Eastern Baltic Cod (Gadus morhua callarias L.) Stock in 1976ffi 1997.‛ ICES J Mar Sci 60(5), 1114–1122 W.E Ricker [1987], ‚Computation and Interpretation of Biological Statistics of Fish Populations.‛ Bull Fish Res Board Can 191, 1–382 C Rockmann, U.A Schneider, M.A St John, and R.S.J Tol [2007], ‚Rebuilding the Eastern Baltic Cod Stock under Environmental Change—A Preliminary nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 BIOECONOMIC MODEL OF EASTERN BALTIC COD Approach Using Stock, Environmental, and Management Constraints.‛ Nat Resour Model 20(2), 223–262 C Rockmann, R.S.J Tol, U.A Schneider, and M.A St John [2009], ‚Rebuilding the Eastern Baltic Cod Stock Under Environmental Change (part ii): Taking into Account the Costs of a Marine Protected Area.‛ Nat Resour Model 22(1), 1–25 P Sandberg [2006], ‚Variable Unit Costs in an Output-Regulated Industry: The Fishery.‛ Appl Econ 38(9), 1007–1018 S Simonit and C Perrings [2005], ‚Indirect Economic Indicators in BioEconomic Fishery Models: Agricultural Price Indicators and Fish Stocks in Lake Victoria.‛ ICES J Mar Sci 62(3), 483–492 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 29 M.D Smith and L.B Crowder [2005], Valuing Ecosystem Services with Fishery rents: A lumped-Parameter Approach to Hypoxia in the Neuse River Estuary, The Nicholas School of Environment and Earth Sciences at Duke University, 56 O Tahvonen [1991], ‚On the Dynamics of Renewable Resource Harvesting and Pollution Control.‛ Environ Resour Econ 1(1), 97–117 R Voss, H.-H Hinrichsen, M.F Quaas, J.O Schmidt, and O Tahvonen [2011], ‚Temperature Change and Baltic Sprat: From Observations to Ecological-Economic Modelling.‛ ICES J Mar Sci 68, 1244–1256 L Westin and A Nissling [1991], ‚Eff ects of Salinity on Spermatozoa Motility, Percentage of Fertilized-Eggs and Egg Development of Baltic cod (Gadus morhua), and Implications for Cod Stock Fluctuations in the Baltic.‛ Mar Biol 108(1), 5–9 K Wieland, A Jarre-Teichmann, and K Horbowa [2000], ‚Changes in the Timing of Spawning of Baltic Cod: Possible Causes and Implications for Recruitment.‛ ICES J Mar Sci 57(2), 452–464 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 Queries Q1 Author: Please check the author affiliation as typeset Q2 Author: Please check correctness Corresponding address as typeset for Q3 Author: A running head short title was not supplied; please check if this one is suitable and, if not, please supply a short title that can be used instead Q4 Author: Please check the Appendix as typeset Q5 Author: Please provide publisher location for reference Begon et al [2006] Q6 Author: Please provide publisher location for reference Conrad and Clark [1995] Q7 Author: If this is not the one page article, please provide page range for reference Osterblom [2008] [...]... 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 h m = Hb t is the Bornholm average share of the cod landing The total t variable cost of Bornholm cod fisheries is assumed to be the. .. 36 37 38 39 40 41 42 7-21-2012 BIOECONOMIC MODEL OF EASTERN BALTIC COD 16:1 17 FIGURE 2 Total revenue (TR), total variable cost (TC), and profit for the Eastern Baltic cod fisheries the current level (scenario 1) to the optimal level (scenario 3), keeping TAC at the 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... − 0.4 × H 1.04 m 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... 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 nrm˙137 nrm2009v2.cls (2012/05/18 v1.1 Standard LaTeX document class) 7-21-2012 16:1 1 2 3 BIOECONOMIC MODEL OF EASTERN. .. function of the Eastern Baltic cod fisheries in period t can be defined as follows: (24) π(Ht , St ) = pHt − Ct (St , Ht ), 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: f Ct = (25) cti hti , i where Ct is the total variable cost of the fishery in period t , cti is the unit cost of. .. 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 second harvest policy is the optimal one, which keeps the harvest at optimal level The nitrogen policies are kept at the. .. Distribution of Cod Larvae in the Bornholm Basin, Baltic Sea.‛ Mar Ecol Prog Ser 154, 91–105 O Heikinheimo [2008], ‚Average Salinity as an Index for Environmental Forcing on Cod Recruitment in the Baltic Sea.‛ Boreal Environ Res 13(5), 457–464 HELCOM [2009], Eutrophication in the Baltic Sea—An Intergrated Thematic Assessment of the Eff ects of Nutrient Enrichment and Eutrophication in the Baltic Sea Region Baltic. .. though the cod fisheries benefit from the optimal pollution control 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. .. 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. .. 30, 181–188 A Nissling [2004], ‚Eff ects of Temperature on Egg and Larval Survival of Cod (Gadus morhua) and Sprat (Sprattus sprattus) in the Baltic Sea—Implications for Stock Development.‛ Hydrobiologia 514(1–3), 115–123 H Osterblom [2008], The Role of Cod in the Baltic Sea, Baltic Sea 2020, 27 Q7 K Radtke [2003], ‚Evaluation of the Exploitation of Eastern Baltic Cod (Gadus morhua callarias L.) Stock