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Considering economic equations into FLR_Econ . EFIMAS CS8
IREPA Onlus (V. Placenti HYPERLINK "mailto:placenti@irepa.org" placenti@irepa.org; HYPERLINK "mailto:placenti@argosrl.eu" placenti@argosrl.eu)
Background application
The expected prototype simulation model for the EFIMAS Mediterranean Hake Case Study (CS8) is a bioeconomic simulation model where takes into account a number of species (target and complementary species), fishing systems (fleet segments) and fishing gears. Reflecting the objective into its proposals, the model replicates the main features of the its bioeconomic system, as well as fishermen behaviour and the effects of the main/alternatives management measures on the sector. In the EFIMAS CS8 the main/alternatives management measures are based on a effort control policy and/or also on a economic incentives basis. Effort control policy and economic incentives management considers restrictions on fishing activity (days) and capacity (gross registered tonnage), technical and economic measures (gear selectivity) and taxes/subsidies. Outputs estimates biomass effect variations, employment variations, and public enforcement costs.
Since the general EFIMAS model simulates the evolution of the target biomass among the stocks exploited, complementary catches biomass should be also considered by fleet segments within the geographic area of interest. Moreover, it would be of importance to mimic the Public Administrations intervention on the sector and to measure the effects of the different management policies.
General picture of the economic proposed equations
Economic equations herein proposed are considered to be well performed to the Mediterranean fisheries and its link with management environment. Equations correlates fishing capacity and relative efficiencies as well as fishing activity (days at sea) within fishing mortality. Fishermen behaviour is embowered through a investment function (via net profits), at once time impacting on vessel efficiency, and therefore on fishing mortality. It is assumed that fishermen is a maximizing shortterm profits agent.
The equations system represents a general picture of fisheries starting from the biological and economic and state variation time point (that is, the natural trend of the sector) where biological component affects the economic outcomes at once determining a series of variations in the operators choices which, in turn, influence the state of the system and the biological component. The management affects both the biological and the economic components which may also influence the operators decisions included in the state variation box.
Finally, equations pickup an evaluation of the social (unemployment losses) as well as The third level, marked in yellow, enables us to consider the overall performance of the fishery system, thats cannot as the costs borne by the Public Administration to enforcement the management measures. The latter could be a effort management control and/or economic incentives based policies.
Specific features of the links of the economic equations with the biological ones
A length structured biological model requires a considerable number of input biological data which are not always available for all species captured by each gears and fleet segments of the Hake fisheries. Consequently, a supplementary biological model to assess the catches for the species whose biological data are unknown has been foreseen and interpreted as a generalized global model that simulates the catches of the aggregate of all the other species landed by the fishing gears by the fleet segments. It is straightforward that these species should be classified as a aggregate denominated as other species. Within this aggregate, the catches are estimated using a logistic model (the Schaefer model), which has been modified to take into account also their shortterm effects.
The biological model used to estimate the other species group is formulated as follows:
EMBED Equation.3,
where Ct are the total catches of the other species group resulting from all the fishing system considered, Et is the equivalent fishing effort expressed as aggregate days, and k0 , k1 are parameters of the longterm component.
The first part of the formula expresses the longterm effect according to the Schaefer model. In order to consider the shortterm effect, the estimate of the longterm catches is rectified multiplying it by the percent variation over the aggregate fishing days from the time t1 to the time t.
The equivalent fishing days are obtained using the weighed sum of the total days per system. The use of the equivalent fishing days is needed in order to consider the different productivity of the days per fishing systems and gears. The equivalence is expressed in terms of trawlers taken as reference fishing gear .
To obtain the equivalent fishing days, the aggregate days of each system are multiplied by a correction factor obtained using the ratio between the productivity of each of the systems considered and the productivity of the trawlers. At once, the productivity (CPUE) is measured as the ratio between the catches and the fishing days by each system.
EMBED Equation.3.
The correction factors are then obtained by the following ratio:
EMBED Equation.3.
The equivalent effort in terms of equivalent days is obtained using the formula:
EMBED Equation.3.
Parameters k0, k1 are entered by users out of estimates attained outside of the model. These parameters represent the only input to the model concerning the unstructured biological model. The parameters k0, k1 entered by users are then modified in order to obtain an equilibrium solution. The only information deriving from these parameters is the ratio:
EMBED Equation.3.
Assumed the input parameter a as fixed, the parameters k0 and k1 are updated by the model in order to guarantee the coincidence between the estimated and the actual catches throughout the base year and to follow the steadystate hypothesis also defined within the unstructured model. The new values of k0 and k1 are obtained using the following system of equations:
EMBED Equation.3 ,
The system can also be represented by the following matrix:
EMBED Equation.3,
or, more briefly:
EMBED Equation.3,
where A is the matrix of the coefficients, k is the vector of the unknown and b is the vector of the known quantities.
Within the model, the equation system is solved within the initialisation phase. Then, the new parameters k0 e k1, calculated during this phase are kept constant over the simulation phase.
The economic equations
The economic equations are basically a prices and costs functions plus a series of inputs in a matrixes form. The prices function defines the evolution of prices over time. The production value per each fishing system are obtained by multiplying the prices and the quantities produced defined as an input at the time t = 0. Earnings are considered in the costs function. The output of the economic accounts is represented by the level of (net)profits. Net profits is determined by the natural dynamic of the system as well as by the management policies defined in terms of subsidies and taxes.
The initial input data are the following:
A matrix of catches by species or group of species identified using 12 lines (a line per month) and n columns, where n is the number of the systems considered;
A matrix of prices defined using m lines (where m is the number of species or group of species) and n columns (where n is the number of fishing systems);
A matrix of fishing days defined using 12 lines (a line per month) and n columns, where n is the number of the systems considered;
A matrix of technical data defined using 3 lines (tonnage, number of vessels and number of fishermen) and n columns, where n is the number of the systems considered;
A matrix of costs defined using 7 lines and n columns, where n is the number of the systems considered. The 7 lines correspond to the following costs headings: commercial, fuel, other variable costs, maintenance expenses, other fixed costs, amortizations and interests.
Equations estimates the coefficients defining the relations between the variable costs and the activity, and between the fixed costs and the fleet size. At the same time as it considers the prices broken down by commercial category, the equations estimates these prices. In the latter case, further inputs are the definition of the number of commercial categories and the relations between the prices of these categories by single species. Finally, other input data can be the price flexibility coefficients catches, average days revenues and tonnage revenues.
The following paragraphs describe the functions which determine the trend of the economic variables.
Prices function
In the prototype equations model, prices are broken down by species or group of species and by fishing system. It is also suggested to consider a price differentiation by commercial category, in which these categories are associated to the length classes of a single species. This price differentiation is feasible only with the specie target for which a biological model structured into length classes is foreseen. It is not the case for the aggregate complementary spedies.
Generally speaking, price dynamics can follow two different hypotheses. In the former case, the prices by fishing system (and possibly by commercial category) are assumed as constant and equal to the prices registered over the base year:
EMBED Equation.3.
In the latter case, the prices are assumed as a function of the quantity produced, that is, the catches. The functional relation between prices and catches is defined using a flexibility coefficient per each species and fishing system. The flexibility coefficients are to be estimated offline and included in the model as input parameters. The flexibility between prices and catches is considered as the per cent variation in prices due to the unitary per cent variation in the catches:
EMBED Equation.3;
whereEMBED Equation.3 is the flexibility coefficient per a given species and fishing system.
The prototype equations enables us to classify prices into commercial categories. In order to break down the prices by commercial categories, the following input data are requested: (a) number of commercial categories by species; (b) first length class by category; (c) relation between the prices of each commercial category and the price of the last category.
The price estimate by each commercial category is performed using a system of simultaneous equations subject to the restrictions on the relations between prices (introduced by the user). The other limitation (given the quantities simulated by the biological box) considers the average price equal to the price registered throughout the base year. Thus, the system of equations by each species per each fishing system is formulated as follows:
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3,
where C represents the catches of the species considered and performed using a specific fishing system, Cs the catches of a specific set of length classes or a specific commercial category, ps the average price to be estimated and the a coefficients, the ratios between the prices provided by the user.
The first equation enables us to prevent the average price registered for the species and the fishing system from being varied, whilst the other equations bind the estimate of the single prices to respect the relations defined by the user.
The system of equation can be represented using the following matrix:
EMBED Equation.3.
By identifying the coefficient matrix as A, p the unknown matrix and b the known quantities vector, the system can be synthetically formulated as follows:
EMBED Equation.3.
As previously defined, the prices by commercial category will vary over time on the basis of the total catches according to a single flexibility coefficient.
Structure of the costs
As shown in Table 1, the costs subtracted from the returns to obtain the added value and the revenues per fishing system are divided into groups. The variable costs are a function of the effort as to the components related to fuel and lubricant while the component of the commercial costs is a function of the level of catches.
Fixed costs, instead, are a function of the tonnage, both as regards maintenance expenses and other fixed costs. The labour cost is calculated as a quota equal to 50% of the full amount, within Mediterranean fisheries, that is the difference between returns and variable costs. This statement is justified by the prevalence of party contracts over other payment systems governing the fishery sector.
Gross profit is then obtained from the difference between revenues and intermediate costs; that is, between the sum of variable and fixed costs and the labour cost.
Finally, to obtain net profit, amortizations and interests are subtracted from gross profit. The amortizations are equal to 4% of the value of the fleet below 25 years of age and 2% of the fleet over 25 years of age. The interests, considered as cost opportunity, are calculated as the yearly bond interest rate applied to the vessel value. The vessel value is then estimated as a replacement value. Amortizations and interests will undergo some variations as a consequence of tonnage variations (i.e., variations in number of vessels).
Table SEQ Tabella \* ARABIC 1: Structure of the costs based on the sector economic account
The costs of each fishing system are broken down into the following four groups: (1) variable costs; (2) fixed costs; (3) labour costs, and (4) amortizations and interests. Net taxation (that is, taxes minus subsidies) is to be added to these costs.
Variable costs are then classified under three headings: fuel and lubricant costs, commercial costs and other variable costs. The former, identified as Cf (fuel costs), and the other variable costs (Cvo) are a function of the fishing effort, (that is, tonnage multiplied by average days):
EMBED Equation.3,
EMBED Equation.3.
Conversely, commercial costs (Ccom) are defined as a function of the total catches of the fishing system:
EMBED Equation.3.
Variable costs (CV) can also be estimated in an aggregate way, with the exception of the details of their composition, indeed:
EMBED Equation.3,
EMBED Equation.3,
EMBED Equation.3,
where EMBED Equation.3.
Fixed costs (CF) can, in turn, be subdivided into maintenance expenses (Cm) and other fixed costs (Cfo). In both cases we assume that these costs are a function of the tonnage and are independent from the level of the activity:
EMBED Equation.3,
EMBED Equation.3,
EMBED Equation.3,
Where EMBED Equation.3.
Labour cost (CL) is not estimated on the basis of coefficients, but is calculated as 50% of the total amount, that is the difference between returns (R) and variable costs in which the returns of the fishing system considered clearly result from the product between catches and prices per each of the species considered:
EMBED Equation.3,
EMBED Equation.3.
This statement is justified by the prevalence of party contracts over other systems of labour remuneration.
Gross profit (GP) is obtained by subtracting revenues from labour cost and intermediate costs, i.e. the total amount of variable and fixed costs:
EMBED Equation.3.
Net profit (NP) ) is obtained by subtracting amortizations (AM) and interests (I) from gross profit. The former are equal to 4% of the value of the fleet below 25 years of age and 2% of the fleet over 25 years of age. The latter, considered as cost opportunity, are calculated as the yearly bond interest rate applied to the vessel value. The vessel value is then estimated as a replacement value. Both for the amortizations and the interests, the estimation based on the age of the fleet is rather difficult. Consequently, it is foresaw an estimate based on the overall tonnage of the fleet:
EMBED Equation.3,
EMBED Equation.3.
Thus, net profit will be obtained using the following equation:
EMBED Equation.3,
where NT stands for net taxation; that is, the difference between taxes and subsidies as established by the Public Administration:
EMBED Equation.3.
Relationship between the economic and biological equations
The biological and the economic equations could show different structures both with the temporal dimension of the simulation and the structure of the input data. Biological equations could works on the basis of monthly intervals, whilst the economic equations could shows a yearly dynamic. This distinction is justified by the different features of the two ideal subsystems. Indeed, the biological aspects of the system are linked to the seasonal nature of natural phenomena. The lifecycle of the species exploited, the reproduction periods and the weather conditions affecting fishing mortality must all be taken into account, and need to be arranged into time intervals lower than a year. On the other hand, the economic variables are hardly discernible on the basis of monthly intervals. In particular, the costs of the fishing activity can barely be subdivided into single months unless applying specific estimates. Besides, the decisions made by the operators concerning the investments are usually based on the economic outcome of the preceding year.
As for the structures, the relationship of the biological equations concerns gears and species. On the contrary, within the economic equations, where a single system can use different gears, the distribution/classification of the vessels is defined as a function of the fishing system. These systems are generally defined as a function of the main gear, but it is possible that in some periods of the year the main gear is supported by others. Besides, some systems, such as the smallscale and the polyvalent, fisheries are characterized by the use of different gears, which, in some cases, work simultaneously. In particular, one of the main feature of the Mediterranean fishery, polyvalence, makes the vessels classification by singlegear group simply impracticable.
Within the EFIMAS model, the differences between the biological and the economic equations should be managed using a series of matrixes that allow converting catches and fishing days per system into catches and fishing days per gear. In particular, for each month and species, the catches per gear are obtained by a linear combination of catches per system according to a series of coefficients which identify the percentages of catch distribution per system among the different gears. This equation system can easily be represented with the following matrix:
EMBED Equation.3,
which can be more concisely expressed as follows:
EMBED Equation.3,
where Cs represents the vector of catches by system, Cg is the vector of catches by gear and Ds,g is the matrix of catch distribution by system among gears. This matrix, estimated offline, is included into the equations as an input datum.
The EFIMAS model could performs this operation whenever entering the biological box. When the model returns into the economic box, it performs the inverted operation; that is:
EMBED Equation.3,
which can be expressed by the following matrix:
EMBED Equation.3
where Cg and Cs have the same meaning as the previous matrix, whilst D1g,s represents the matrix of catch distribution by gear among systems.
Matrix Ds g and D1g,s are estimated on the basis of the data recorded over the base year and are kept constant throughout the years of model simulation.
State variation
Within the economic equations, the variations in the state of the system involve the variations that occur within the structural variables as a consequence of the fishermen behaviour and the overall market trend. On the basis of the level of profits, the operators will make their decisions on the average number of fishing days and also on the entry/exit rules of fleet over the following year. In other words, their decisions will affect the overall tonnage exploited in the fishing activity.
The operators behaviour is aimed at maximising the profits: (a) in agreement with the regulations, the level of activity at sea should tend to increase with the increasing of profits; (b) the entry/exit from the sector will be based on the comparison between the profits made over the current year and the profits of the preceding year. Thus, average fishing days and tonnage become a function of the variations of profits according to flexibility coefficients assessed offline and included by the user as input data. As for the average fishing days and the overall fleet tonnage, the equations foresees two possible dynamics. The former assumes the average days and the tonnage as constant and equal to the values registered for the base year:
EMBED Equation.3;
EMBED Equation.3.
The latter hypothesizes a relation between the variations in the average days and the variations in the profits made over the preceding year:
EMBED Equation.3.
A relation between the overall tonnage variations and the variations in the profits made over the preceding year can also be assumed:
EMBED Equation.3,
The coefficients a and b respectively measure the flexibility of the average days and the flexibility of the overall tonnage in comparison with the profits.
The state variations also concern the hypotheses formulated on price dynamic and the differentiation of prices by commercial categories. Finally, the state variation hypotheses include also assumptions concerning the effects of technology investments on fishingrelated mortality. In this case, the equations requires to specify the percentage of profits that, on average, are invested to enhance vessel productivity. The introduction of a flexibility coefficient between investments and fishing mortality could also be required.
Management and economic equations
The main objective of the equations is the simulation of the management measures generally adopted at a national and international level within the sector. As for the Mediterranean fishery, these measures are directed at restricting fishing effort in terms of fleet capacity and activity. Besides, the EFIMAS CS8 prototype equations allows simulating both the technical measures concerning gear selectivity and economic measures, such as variations in tax level and allocation of subsidies to the sector.
In particular, the management measures implemented could be the following:
Variation in selectivity: among the gears considered, the equations should considers a selectivity function for each gear. The input parameters that define this function can be modified by the user for a given year of simulation. This permits to simulate the management measures directed at increasing the selectivity of gears.
Temporary withdrawal: this measure is implemented in relation to a single fishing system. Its implementation is structured into monthly levels and permits to determine the maximum number of fishing days foreseen for each month and fishing system.
Permanent withdrawal: it simulates this measure by means of a proportional reduction in the number of the vessels that use a specific gear. The per cent variation on the gear specified by the user is applied on all the fishing systems that use the same gear.
Levy variations: this is an economic measure that can be implemented both as an increase or a reduction in the taxes imposed on the fishing activity.
Variation subsidies: as with the taxation, this is an economic measure whose implementation allows evaluating the effects of subsidy variations on the sector. The initial value is nil.
Moratorium: this measure represents a ban on a specific gear or the introduction of a ban on its use.
Gear suspension: this measure can be coupled with temporary moratorium. To strengthen its effect, this measure can be associated to a temporary withdrawal. Indeed, temporary withdrawal is implemented with reference to the fishing system, whilst suspension affects the gear. The simultaneous selection of both permits to simulate a withdrawal affecting the whole system and all the vessels of the fleet, though they belong to different systems, but which use the prevalent gear of the system considered.
The management measures are implemented according to the following specifications:
(1) As for the technical measure concerning the selectivity, the equations permits to modify the length of retention by 50% by gear per species:
EMBED Equation.3.
(2) As regards temporary withdrawal, the model allows defining the maximum number of average days by system per month. The variation affects the sector dynamic only in case this number exceeds the maximum limit established.
EMBED Equation.3
where EMBED Equation.3 represents the highest number of average fishing days for the month considered.
With permanent withdrawal, the overall tonnage of the vessels belonging to the systems which use the gear affected by the measure will be reduced by a percentage equal to that specified by the user.
EMBED Equation.3,
where EMBED Equation.3 is the percentage variation of tonnage specified for the management measure.
(3) The economic measures may consist of variations in tax levels or subsidies. The model considers taxes as an additional fixed cost. Within the base year, taxes come under the fixed costs heading. For this reason, the value of the additional cost Taxes (T) is nil:
EMBED Equation.3.
During the simulation, this value can be modified in order to reproduce the associated management measure:
EMBED Equation.3,
where EMBED Equation.3 measures the variation introduced into the level of taxation.
(4) Likewise, subsidies can be considered as an additional revenue granted by the Public Administration to a specific fishing system. This revenue is to be added to the income of the system affected by the measure. At the time t = 0, the value of subsidies is nil. Subsides could undergo variations over the simulation phase:
EMBED Equation.3,
EMBED Equation.3,
where EMBED Equation.3 is the variation in the amount of the granted subsidies.
(4) The moratorium on a gear is simulated by deleting the catch percentages that determine the transformation of catches per system into catches per gear. For instance, if the moratorium affects gear 4 as from time t, the percentages of catches of the distribution matrix should be modified as follows:
EMBED Equation.3.
Likewise, the simulation of gear suspension is also obtained using the matrix of the catch percentages per system. In this case, the variation will be solely temporary and include only specific months.
Management costs
The management costs are those undertaken by the Public Administration to put into effect management measures. In particular, the management costs could represent the financial support granted to the vessels that comply with temporary withdrawal and the costs of decommissioning foreseen by the permanent withdrawal schemes.
With reference to temporary withdrawal, the crew of the vessels affected by this measure are granted the minimum wage provided for by collective agreements. Accordingly, the equations would requires the insertion of the minimum monthly wage. This value can be estimated at the mean of the wage scales established by the contract for the different crew working on board. Then, the equations adjusts the monthly cost for each worker to the overall number of workers affected by the measure and the duration of the measure in number of days.
As to the permanent withdrawal, the EC Regulation provides for a financial support differentiated into Length classes and that varies in proportion to the age and tonnage of the vessel. The equations would requires an average value for GRT units per system considered. The estimate of the total cost for the implementation of the measure is obtained multiplying these values by the overall amount of tonnage forgoing the fleet.
Social costs
The social costs could be considered exclusively in terms of variation in the number of workers employed in the sector. The number of workers per system is linked to the number of vessels using the parameter employed per vessel. This parameter is assumed as constant and is defined in relation to the base year.
The variations in the tonnage of each system are an outcome of both the natural sector dynamic (tonnageprofits flexibility) and the effect of management measures. These variations determine changes in the number of vessels and therefore in the number of workers.
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