Bioeconomic model of Eastern Baltic cod under the influence of nutrient enrichment

Bioeconomic model of Eastern Baltic cod under the influence of nutrient enrichment tài liệu, giáo án, bài giảng , luận v...

N AT U R A L R E S O U R C E M O D E L IN G Vo lu m e , N u m b e r , M ay 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 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 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 6t h july 2012 Accepted 4t h june 2012 C o py rig ht c 2 W ile y P e rio d ic a ls, In c 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 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 eects including temperature, salinity, and oxygen (Kă oster 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 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 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 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+1 = (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 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 ) (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+1 = (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) ρt (πt + ρλt+1 ((St − Ht )Gt + Rt − St+1 )) L= 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 the Lagrange model are: (6) ∂L = ρt (πH − ρλt+1 Gt ) , ∂Ht (7) ∂L = ρt (πS + ρλt+1 (Gt + (St − Ht )GS ) ∂St + ργ +1 λt+γ +1 RS − ρt λt , 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 = (8) (9) πH , ρGt λt = πS + ρλt+1 (Gt + (St − Ht )GS ) + ργ +1 λt+γ +1 RS In equilibrium, all variables are stationary over time, and the t subscript can therefore be dropped The restriction (4) implies H=S− (10) 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 (12) πS (S − R) GS + ργ RS = + r +1 G+ πH G 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 ( ππ S + 1) is called the marginal stock effect H (MSE), which represents the stock density influence on harvesting costs (Clark and ) Munro [1975], Bjorndal [1988]) The term (S −R GS + ργ RS in (12) is the marginal G 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 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 (13) Objective : maximize NPV U = Ht T t=0 ρt U (Ht , St ) St+1 = (St − Ht ) Gt + Rt , Subject to : where U (Ht , St ) = 1−n π(Ht , St )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 −n UH π(Ht , St ) ∗ πH 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 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 (14) Nt = k i=1 N T OTi , 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 BIOECONOMIC MODEL OF EASTERN BALTIC COD 265 TABLE Biological and environmental data: N has been estimated, SSB and Recruits are from ICES [2011a] Year SSB (1000 tones) 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 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 [2005]): (15) 2 + cNt−γ St−γ Rt = aSt−γ Nt−γ + bSt−γ 266 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 Source: ICES, Fishkeriregnskabsstatistik, Fiskeristatistisk ˚ arb og and own calculations or the alternative form is (16) Rt = aNt−γ + bSt−γ + cNt−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 estimated stock–recruitment function for the Eastern Baltic cod is the following8 (17) 2 Rn t = 0.2015826St−2 Nt−2 − 0.0016263St−2 − 0.0058455St−2 Nt−2 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 from 1966 to 2009, w = 0.209 kg (ICES [2010b]), the final stock–recruitment function is BIOECONOMIC MODEL OF EASTERN BALTIC COD 267 TABLE Estimation of the Eastern Baltic cod stock–recruitment function using the quadratic model and the data for 1966–2009 Variables Estimation – 0.0016263 ∗ Spawning stock (St – ) Nitrogen (Nt – ) Nitrogen square (Nt – 2 ) R2 F statistic DW statistic rho 0.2015826 ∗∗ – 0.0058455 ∗∗ 0.53 14.92 1.668 0.688 Note: The dep endent variable is Rt /St – and n = 39 The m o dels have b een estim ated with first order auto correlation, using the Prais–W insten transform ed regression estim ator ∗ p < 0.05 ∗∗ p < 0.01 determined (18) Rt = wR nt = 0.042131St−2 Nt−2 − 0.00034St−2 − 0.001222St−2 Nt−2 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 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 (19) Gt = eδ t , where δt is called the net natural growth rate, which equals the instantaneous growth rate minus the instantaneous natural mortality rate We assume that nitrogen 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 : (20) δt = δ(St ) = d + f St 268 N V THANH FIGURE Recruits as a function of SSB and nitrogen concentration From (1) and (19), the net natural growth rate (δ) may also be calculated according to the following formula (21) (St+1 − Rt ) = (St − Ht )eδ t ⇒ δt = ln St+1 − Rt S t − Ht Table 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 ) < 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: (22) δt = 1.140578 − 0.0012049St BIOECONOMIC MODEL OF EASTERN BALTIC COD 269 TABLE Estimation of the natural growth for the Eastern Baltic cod using data for 1966–2009 Variables Estimation 1.140578∗∗ 0.0012049∗∗ 0.33 26.78 1.463 Constant Spawning stock (St ) R2 F statistic DW statistic Note: The dep endent variable is δ for the m o del 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 )e1.140578−0.0012049S t (23) + 0.042131St−2 Nt−2 − 0.00034St−2 − 0.001222St−2 Nt−2 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: (24) π(Ht , St ) = pHt − Ct (St , Ht ), 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: f (25) Ct = cti hti , i 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]) f (26) Ct = ct hti = ct Ht = i Cbt Cbt , Ht = hbt m 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 h fisheries in period t and m = Hb t is the Bornholm average share of the cod landing t 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 = αb Stβ hβbt2 , (27) where St is the spawning stock in period t; αb , β , β are the parameters that need to be estimated Substituting (27) into (26) yields (28) Ct = αb Stβ hβbt2 = αb mβ −1 Stβ Htβ = αStβ Htβ , m where α = αb mβ −1 Using the data from the Bornholm cod fisheries, the estimation for the variable cost function is described in Table 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 BIOECONOMIC MODEL OF EASTERN BALTIC COD 271 TABLE Estimation of the variable cost function for the Bornholm cod fishery using data for 1995–2008 Variables Constant Spawning stock (S) Harvest (hb ) R2 F statistic DW statistic AIC Estimation Standard error 4.08∗∗ ∗ – 0.4 1.04∗∗ 0.76 17.55 1.31 – 2.49 0.79 0.18 0.18 – – – – Note: The dep endent variable is total cost and n = 14 The m o del has b een estim ated 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 ˚ Arbog [1995–2008]), the total variable cost for the Baltic Sea cod fisheries is written, using (28) (30) C= 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] 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 the current level (scenario 1) to the optimal level (scenario 3), keeping TAC at the 272 N V THANH FIGURE 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 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 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 BIOECONOMIC MODEL OF EASTERN BALTIC COD 273 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 Note: Scenario 1: nitrogen concentration level 2009 & recovery m anagem ent plan; Scenario 2: 15% nitrogen reduction and recovery m anagem ent plan; Scenario 3: optim al nitrogen level and recovery m anagem ent plan; Scenario 4: nitrogen concentration level 2009 and optim al harvest p olicy; Scenario 5: 15% nitrogen reduction and optim al harvest p olicy; Scenario 6: optim al nitrogen level and optim al harvest p olicy 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 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 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 NPV under the different nitrogen concentration levels (r = 4%) 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 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 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 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 05/01/2011) Others affect changes in biomass of a fish population over time including emigration, immigration, and environmental factors This term equals zero when the optimization problem is solved The shadow price will be changed in this case 276 N V THANH Available 15/11/2010) at http://www.ices.dk/Ocean/asp/helcom/helcom.asp?Mode=1 (Accessed See Table A1 for a detail description Full function is R t = 0.2015826S t −2 N t −2 − 0.0016263S t2−2 − 0.0058455S t −2 N t2−2 + 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 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 (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 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.] BIOECONOMIC MODEL OF EASTERN BALTIC COD 277 Appendix Economic data (average per firm annually) for Bornholm fishing firms1 from 1995 to 2008 (1000 DKK) N o N am e 1995 1996 1997 1998 G ro ss re ve nu e 976.40 1075.1 1577.2 1531.6 R e ve nu e fro m c o d 554.00 653.3 1122.2 1006.3 S h a re o f c o d : (1 )/ (2 ) Va ria b le c o st e x c lu d in g sh a re c o ntra c t 737.20 869.9 1278.4 1187.6 F ix e d w a g e c o ntra c t c o st 208.80 240.2 405.8 421.9 D ay s a t se a o f sk ip p e r 15.10 9.9 11.8 18.7 137.90 138.6 223.3 223.4 153.00 148.50 235.10 242.10 1.36 1.62 1.73 ‘ D ay s a t se a o f c re w M a n d ay s o f fi x e d w a g e c o ntra c t Wa g e p e r d ay o f fi x e d w a g e c o ntra c t: (5 )/ (6 ) M a n d ay s o f fi sh e rm e n (sh a re re m u n e tio n ) M a n d ay s o f p a rtn e rs (sh a re re m u n e tio n ) 0.57 137.50 8.10 0.61 185.5 9.2 0.71 176.2 0.66 1.74 190.9 10.1 25.3 M a n d ay s o f sh a re c o ntra c t 145.60 194.70 186.30 216.20 376.76 S h a re c o ntra c t c o st: (7 ) × (8 ) 198.70 314.93 321.57 10 D e p re c ia tio n s 162.20 171.8 200.6 177.3 11 Va ria b le c o st: (4 ) + (9 ) – (1 ) 773.70 1013.03 1399.37 1387.06 438.99 615.58 995.67 911.34 100 148.1 12 Va ria b le c o st o f c o d : (3 ) × (1 ) 13 C a tch o f c o d , m e tric to n s 14 U n it va ria b le c o st o f h a rve st: (1 )/ (1 ), 0 82.20 5.34 6.16 6.72 91.2 9.99 D K K / to n o r D K K / k g 15 C o d c a tch fro m B o rn h o lm , 0 to n s 16 C o d c a tch fro m B a ltic , 0 to n s 17 To ta l va ria b le c o st fo r B o rn h o lm c o d fi sh e rie s: 14.47 107.712 77262.35 17.009 121.877 101570.96 14.107 10.914 88.6 67.429 154328.81 117562.44 (1 ) × (1 ) 18 C o d p ric e fro m D a n ish A c c o u nt S ta tistic 19 N u m b e r o f fi sh in g fi rm s in B o rn h o lm 9.13 176 0.13 8.35 165 0.14 8.33 155 0.16 9.44 129 20 C a tch sh a re o f B o rn h o lm c o d fi sh e rie s: (1 )/ (1 ) 21 P ric e in d e x (1 0 = ) 0.16 22 R e a l va ria b le c o st (2 0 p ric e s) 23 R e a l u n it c o st (2 0 p ric e s) 5.99 6.76 7.22 24 R e a l c o d p ric e (2 0 p ric e s) 10.23 9.17 8.95 9.96 25 R e a l to ta l va ria b le c o st o f B o rn h o lm c o d 86611.00 111505.18 165785.12 124007.13 4686 4785 4890 4980 492 676 1070 961 10.54 fi sh e rie s: (1 ) × (2 ) (Continued) 278 N V THANH Appendix (Continued) No 1999 2000 2001 2002 2003 1702 1249 1224 1143 1351 880 841 693 0.79 1291 0.70 937 0.69 855 456 271 253 412.00 438.00 451.00 10 182 148 138 0.61 836 239 396.00 2004 2005 2006 1089 936 1135 1292 1782 868 698 539 689 856 1201 380 0.64 814 233 384.00 0.58 809 187 382.00 0.61 854 200 438.00 0.66 972 273 409.00 2007 0.67 1240 383 391.00 2008 0.44 789 174 333.00 157 151 155 144 138 161 11 1521.00 1227.00 1168.00 1075.00 1047.00 1036.00 1148.00 1243.00 1470.00 968.00 154 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 15 13.759 10.159 16 72.989 17 161781.85 18 19 20 13.12 134 0.19 89.168 117571.95 14.45 136 0.11 9.512 91.325 113155.73 15.54 141 0.10 7.032 67.74 83426.77 8.293 71.386 83213.91 7.323 67.768 73976.60 7.209 55.254 7.696 65.532 4.924 50.843 78748.75 79059.42 67369.23 9.64 5.541 42.235 53396.13 16.1 13.69 13.45 14.96 15.54 17.67 16.93 128 124 124 113 96 68 126 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 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