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Bioeconomic Module Parameters

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emycottrant edited this page Jun 29, 2026 · 4 revisions

This page provides a reference list of the main parameters and variables used in the Economic Module.

For the equations where these quantities are used, see Bioeconomic Module Mathematical Formulation. For the conceptual interpretation of the module, see Bioeconomic Module Concepts and Assumptions. For the data needed to estimate or provide these parameters, see Bioeconomic Module Data Requirements.

Overview

The Economic Module uses parameters describing harvesting costs, consumer preferences, demand elasticities and substitution possibilities. Some parameters are estimated from data, while others are taken from the literature or assumed.

The main groups of quantities are:

  • indices, used to identify species, size classes and time;
  • biological quantities, generally provided by OSMOSE or derived from OSMOSE outputs;
  • harvest and accessibility quantities;
  • economic quantities, such as prices, costs, revenues and profits;
  • estimated parameters;
  • parameters taken from the literature or assumed.

Indices

Symbol Description
$i$ Species index
$s$ Size-class index
$t$ Time index
$k$ Size-class index used in summations
$j$ Species or size-class index used in summations, depending on the equation
$I$ Number of species
$S$ Number of size classes
$t_0$ Initial year
$T$ Time horizon

Biological quantities

These quantities describe the biological population and are generally provided by OSMOSE or derived from OSMOSE outputs.

Symbol Description
$l_{i,s}$ Length of fish species $i$ in size class $s$
$l_s$ Length of fish in size class $s$
$w_{i,s}$ Weight of fish species $i$ in size class $s$
$N_{i,s,t}$ Number of fish of species $i$ in size class $s$ in a given year
$B_{i,t}$ Total available or accessible biomass of species $i$ in year $t$

Harvest and accessibility quantities

These quantities describe how fish are retained, accessed and harvested by the fishery.

Symbol Description
$q_{i,s}(\sigma_{i,t})$ Probability of retainment for species $i$ and size class $s$
$q_{i,s,t}$ Catchability, or the proportion of individuals in a size class that are retained in the net
$\sigma_{i,t}$ Mesh size for species $i$ in year $t$
$\sigma_t$ Mesh size in year $t$
$\omega_i$ Selectivity accuracy, assumed to be constant
$H_{i,t}$ Total harvested biomass of species $i$ in year $t$
$h_{i,s,t}$ Biomass of fish harvested from species $i$ and size class $s$ in year $t$
$F_{i,s,t}$ Fishing mortality for species $i$ and size class $s$ in year $t$
$F_{i,t}^{max}$ Maximum fishing mortality for species $i$ in year $t$

Economic quantities

These quantities describe prices, costs, revenues, profits and utility.

Symbol Description
$p_{i,s,t}$ Price per kg of species $i$ and size class $s$ in year $t$
$C_{i,t}$ Cost of harvesting species $i$ in year $t$
$\Pi_{i,t}$ Fishers' profit for species $i$ in year $t$
$\pi_{i,t}$ Profit margin for species $i$ in year $t$
$\nu_t$ Utility of fish consumption in year $t$
$u(\nu_t)$ Total utility in year $t$
$NPV$ Net present value
$\delta$ Discount factor
$P_{i,t}$ Composite price term used in demand parameter estimation
$H_{i,t}$ Composite harvest term used in demand parameter estimation

Estimated parameters

The following parameters are estimated from data.

Parameter Description
$c_{i,0}$ Baseline costs of harvesting in the year $t_0$
$\tau_i$ Time trend on fishing costs (positive or negative)
$\chi_i$ Stock elasticity. If $>1$ the stock is hypersensitive: fishing costs decline fast with accessible biomass. If $<1$ the stock is hyperstable and fishing costs remain relatively constant with the available biomass
$\beta_{i,s}$ Consumer preferences for different sizes ($s$) of each species ($i$). $\sum_s \beta_{i,s}=1$
$\alpha_i$ Consumer preferences for different species ($i$). $\sum_i \alpha_i=1$
$\eta$ Elasticity of demand for fish
$\gamma$ Weight of fish consumption in total utility. When $\eta=1$ it is the total expenditure on fish

Parameters from the literature

The following parameters are taken from the literature or assumed.

Parameter Description
$\mu_i$ Elasticity of substitution between different sizes of a species ($i$). Higher values indicate easier substitutability
$\sigma$ Elasticity of substitution between species of fish. Should be lower than $\mu_i$ since sizes are better substitutes than species

Cost parameters

The cost function uses three main parameters.

Parameter Role
$c_{i,0}$ Defines the baseline harvesting cost at the reference year $t_0$
$\tau_i$ Defines the time trend in baseline harvesting costs
$\chi_i$ Defines how harvesting costs respond to accessible biomass

Baseline harvesting costs may increase with increasing fuel prices or decrease with technological advancement. The time trend in baseline costs is represented as:

$$ c_{i,t}=c_{i,0} e^{\tau_i(t-t_0)} $$

The stock elasticity parameter $\chi_i$ determines how strongly harvesting costs decrease when accessible biomass increases.

Elasticity parameters

Elasticity parameters describe how easily consumers can substitute among different fish products.

Parameter Role
$\mu_i$ Elasticity of substitution between different sizes of species $i$
$\sigma$ Elasticity of substitution between species
$\eta$ Elasticity of demand for fish

The elasticity of substitution between species should be lower than the elasticity of substitution between sizes, since sizes are better substitutes than species.

Control variables

The social optimum formulation refers to future control variables in the fishery. In the current formulation, these are future harvests and mesh sizes.

Symbol Description
$H_{i,t}$ Future harvest of species $i$ in year $t$
$\sigma_{i,t}$ Future mesh size for species $i$ in year $t$

Notes on parameterisation

For the parameterisation, the module requires biological and economic information such as profit margins, prices per kg, individual weights, catchability, population numbers, harvest by size class, and accessible biomass.

The calibration of cost parameters is based on catch, accessible biomass and profitability data. Species and size-class preferences are estimated using the inverse demand function assuming market equilibrium.

The elasticities of substitution between size classes $\mu_i$ and between species $\sigma$ are either taken from the literature or assumed.

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