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Bioeconomic Module Concepts and Assumptions
This page describes the main concepts and assumptions behind the Economic Module. It explains how the module represents supply, demand, harvest accessibility, fishing costs, consumer preferences, profits and social welfare.
For the full mathematical notation and equations, see Bioeconomic Module Mathematical Formulation. For the list of parameters, see Bioeconomic Module Parameters.
The economic model takes into account supply and demand dynamics. Supply depends mainly on fishing costs that are stock-dependent and technology-dependent. Demand is driven by the price that consumers are willing to pay and by consumer preferences for different species and different size classes.
The module is particularly relevant for size-structured ecological models, because demographic or evolutionary changes within fish populations can affect not only total biomass, but also the size composition of the population. These changes may have economic impacts when consumers have preferences for particular size classes.
The module is organised around three main ideas:
- fish availability and harvest determine fishing costs;
- consumer preferences and substitutability determine prices;
- revenues, costs and consumer utility can be combined to evaluate profit and social welfare.
The supply side describes how the cost of fishing depends on the amount of fish harvested and on the availability of fish in the population.
Fishing costs depend on the availability of fish and the amount of fish harvested. The model assumes perfect selectivity with respect to species, but imperfect selectivity with respect to the size of species. Depending on the gear, larger or smaller fish of a species can be retained by the gear.
The part of the population that could potentially be harvested is called the accessible biomass.
Accessible biomass represents the part of the biological population that is available to the fishery under a given fishing process. It depends on:
- the number of individuals in each size class;
- the weight of individuals in each size class;
- the probability that individuals in each size class are retained by the gear.
For example, with a trawl-like fishing net, the probability of retainment increases with the size of the fish by a sigmoid pattern. In this case, smaller individuals have a lower probability of being retained, while larger individuals have a higher probability of being retained.
The total available, or accessible, biomass of a species is calculated from the retained fraction of each size class. When a total biomass is harvested, this harvest is distributed to the size classes according to retainment. The biomass harvested from each size class therefore depends on the size-specific retainment, individual weight, population numbers and total harvest.
The full equations for retainment, accessible biomass and harvest by size class are given in Bioeconomic Module Mathematical Formulation.
The current formulation makes an important distinction between species selectivity and size selectivity.
For species, the model assumes perfect selectivity. This means that the fishery targets the species being represented and does not mix catches across species through unintended species catch in the economic formulation.
For size classes, selectivity is imperfect. Depending on the gear, larger or smaller fish of a species can be retained with different probabilities. This makes it possible to represent size-dependent accessibility and to study the economic consequences of size-selective fishing.
This assumption is important because changes in the size structure of a population can affect both accessible biomass and the distribution of harvested biomass across size classes.
The costs of harvesting fish increase with harvest and decrease when more fish are accessible.
Baseline harvesting costs may change over time. They may increase, for example, with increasing fuel prices, or decrease with technological advancement. This time trend is represented through a baseline harvesting cost parameter and a cost trend.
The model also includes stock elasticity. This parameter controls how harvesting costs respond to changes in accessible biomass. When stock elasticity is below one, the stock is hyperstable, meaning that at constant effort an increase in available biomass does not necessarily result in a higher harvest.
The full cost equation is given in Bioeconomic Module Mathematical Formulation. The corresponding parameters are described in Bioeconomic Module Parameters.
Fishers' profit is the revenue from selling fish minus the costs of harvesting.
Revenue depends on the biomass harvested from each species and size class and on the corresponding prices. Costs depend on total harvest, accessible biomass and harvesting cost parameters.
The profit margin is the fraction of profits with respect to revenue. It provides a relative measure of profitability and is also used in the calibration of cost parameters.
The full equations for revenue, profit and profit margin are given in Bioeconomic Module Mathematical Formulation. The calibration approach is described in Bioeconomic Module Calibration.
The demand side describes how consumers value fish consumption.
Consumers have preferences for certain species but also for size classes of fish. When preferred species are rare, and therefore expensive, consumers can shift their consumption towards more abundant species, depending on the elasticity of demand.
The more elastic demand is, the easier it is to substitute. The same holds for different size classes of fish, where demand is likely to be even more elastic. In other words, consumers may not pay an extremely higher price for one large fish than for the same weight of small fish.
The module therefore represents two levels of preference and three substitution:
- preferences and substitution among size classes within a species;
- preferences and substitution among different species.
- substitution between fish product and another food commodity
Consumer preferences for size classes are represented by size-class preference parameters. These parameters describe how consumers value different sizes within a species.
Consumer preferences for species are represented by species preference parameters. These parameters describe how consumers value different species relative to each other.
These preferences are important when changes in the biological population alter the composition of catches. For example, if a scenario produces smaller fish, the economic consequences will depend on how consumers value smaller fish relative to larger fish.
The module assumes that consumers can substitute between different products.
Substitution among size classes describes how easily consumers replace one size class of a species with another size class of the same species. Higher values of the size-class substitution elasticity indicate easier substitutability.
Substitution among species describes how easily consumers replace one species with another species. This elasticity should usually be lower than the elasticity of substitution between sizes, because sizes are expected to be better substitutes than species.
Substitution among food products describes how easily a consumers can replace fish by another commodity when the preferred fish product is not available. This elasticity should usually be lower than the elasticity of substitution between species and therefore, also lower than the elasticity of substitution between size-classes.
If a species has only one size class, the consumer cannot substitute between size classes but can still substitute between species.
The utility and inverse demand equations are given in Bioeconomic Module Mathematical Formulation.
Prices are derived from consumer demand and the composition of harvested biomass.
Consumers maximise utility over the consumption of fish. This results in an inverse demand function, where prices depend on the amount harvested, consumer preferences, and the possibilities for substitution among size classes and species.
The calibration of species and size-class preferences assumes market equilibrium. Under this assumption, observed prices and harvests can be used to estimate preference parameters.
The estimation approach is described in Bioeconomic Module Calibration.
In total, the utility derived from fish consumption is the benefit obtained from fish consumption of different species and size classes minus the costs needed for their extraction.
Since individuals discount future utility, the module can represent total net present value over a given time horizon. A social planner, accounting for both consumer and producer surplus, would maximise this net present value over future control variables in the fishery, here future harvests and mesh sizes.
This welfare perspective differs from a private-profit perspective. Private profit focuses on the revenue and costs of fishing. Social welfare combines the benefits of fish consumption with the costs of extraction.
The full net present value formulation is given in Bioeconomic Module Mathematical Formulation.
The current formulation relies on the following assumptions:
- supply depends on stock-dependent and technology-dependent fishing costs;
- demand is driven by consumer willingness to pay and preferences for species and size classes;
- species selectivity is perfect;
- size selectivity is imperfect;
- accessible biomass is the part of the population that could potentially be harvested;
- harvested biomass is distributed among size classes according to retainment;
- fishing costs increase with harvest and decrease when more fish are accessible;
- baseline harvesting costs may increase or decrease over time;
- consumers can substitute among size classes and among species;
- substitution among size classes is expected to be easier than substitution among species;
- prices are derived from consumer utility maximisation;
- calibration of demand parameters assumes market equilibrium;
- social welfare accounts for consumer and producer surplus;
- future utility is discounted.