CEMARE Research Paper P163
A regional computable general
equilibrium model for fisheries
H Pan, P Failler and C Floros
Centre for the Economics and
Management of Aquatic Resources
University of Portsmouth
Burnaby Terrace
1-8 Burnaby Road
Portsmouth
PO1 3AE
United Kingdom
First published University of Portsmouth 2007
Copyright © University of Portsmouth 2007
All rights reserved. No part of this paper may be
reproduced, stored in a retrievable system or
transmitted in any form by any means without written
permission from the copyright holder.
For bibliographic purposes this publication may be
cited as: Pan, H., Failler, P., and Floros, C. 2007. A
regional computable general equilibrium model
for fisheries. CEMARE Res. pap. no.163.
Contact Author:
Haoran Pan
CEMARE
(Centre for the Economics
and Management of Aquatic Resources)
University of Portsmouth
Burnaby Terrace
1-8 Burnaby Road
Portsmouth
PO1 3AE
E-mail: [email protected]
ISSN 0966-792X
A regional computable general equilibrium model for fisheries
Haoran Pan1, Pierre Failler and Christos Floros
Centre for the Economics and Management of Aquatic Resources (CEMARE)
Department of Economics
University of Portsmouth
October 2007
Abstract: This paper presents a regional computable general equilibrium (CGE) model
with a detailed description of the fisheries sector and consumption of aquatic products.
The model is developed under the background that the world fisheries policy is shifting
from resource utilisation towards sustainable development and poverty reduction, and
that applied general equilibrium analysis remains a big gap in fisheries economics. It adds
several new contributions to both general equilibrium modelling and fisheries economic
analysis. In the model, fisheries are studied at microeconomic level – the bottom-up fish
producers, which are further connected to top-down non-fishery economic sectors;
economic activity of fishing is dynamically linked to the biological process in order to
fully capture the endogenous interactions between economic and ecological systems;
consumption of aquatic products is simulated in a nested, hierarchy system to allow for
substitution of species; fisheries development and regional economic growth are
coordinated together for policy analysis. The model is designed to provide room for new
fisheries policy analysis in general and study five European fishery regions1 in particular,
but the empirics in the paper just serve to test the model with the real data in Salerno and
two simple policy scenarios.
Keywords: Fisheries, CGE modelling, poverty reduction, sustainability of natural aquatic
resources
JEL classifications: C68, O13, Q22, Q56,Q57
1
Corresponding author, Centre for the Economics and Management of Aquatic Resources (CEMARE)
Department of Economics, University of Portsmouth, Burnaby Terrace, 1-8 Burnaby Road, Portsmouth,
PO1 3AE, United Kingdom. Tel +44 (0)2392 844 085, Fax: +44 (0) 2392 844614. Email:
[email protected]
1
A regional computable general equilibrium model for fisheries
1. Introduction
The goal of the world-wide fisheries policy is changing from utilisation to sustainability
of the natural aquatic resource. Sustainability means how the fisheries can retain the
natural resource at a sustainable level and in the meantime deliver affordable aquatic
products to consumers including the poor in developing countries. This change results
from some central problems currently facing the fisheries industry. Typically, as fishing
efficiency improves, natural aquatic resources are declining towards an unsustainable
level; no matter how the natural resource would be better utilised, it alone cannot be
enough to meet the persistently increasing demand for aquatic products, due to both
economic and population growth; and no matter how the natural resource is exploited,
poverty in the fisheries society continues to deteriorate in most developing fisheries
regions (Thorpe, Withmarsh and Failler, 2007).
Traditional fisheries economics has greatly contributed to the old fisheries policy, but it is
limited in helping the new fisheries policy for several reasons. Firstly, traditional fisheries
economics aims to improve fishing efficiency, which in general is incompatible with
natural resource reservation and welfare distribution. Both social and environmental
contents have missed in the optimisation context of fisheries economics (Failler and Pan,
2007). Secondly, the microeconomic foundation of traditional fisheries economics lies on
bio-economic relations between fishing activity, capture and natural aquatic resource
growth (Gordon, 1954; Shaeffer, 1957). Bio-economic models are built to conduct
stylised analysis on one or two commercially important species, with simplified
biological growth functions of the species. This foundation, now receives most attacks on
its simple specification of biological systems (Quinn and Deriso, 1999) and on its neglect
of concern about biodiversity as well (Amstrong, 2007). Thirdly, the concentration on the
harvesting fisheries has led the fisheries economics to pay little attention to the nonharvesting fisheries and lose macroeconomic connection to the fisheries with non-fishery
economic sectors. Recently, there is increasing recognition that the non-harvesting
fisheries including fish processing, fish marketing, aquaculture, fishing support, and
recreational fisheries play important roles in the fisheries sector and have profound
2
implications on the harvesting fisheries (FAO, 2007). It is also a misunderstanding that
the fisheries can be reasonably studied in isolation of the non-fishery part of the economy
because the fisheries sector usually contributes a small share of the economy. However,
the fact is that although the fisheries may affect the economy a little, the impact of the
rest of the economy on the fisheries is greater through factor movement, consumption,
investment, regional or international trade, and development policy (Thorpe et al, 2005).
Fourthly, traditional fisheries economics has devoted greatly to building a theory of the
rent of common pool property on natural aquatic resources, but has never developed
effective economic instruments based on the theory to guide the fisheries. One of the
reasons for this is that the fisheries bio-economic models lack a price mechanism and
structural relations and therefore are inappropriate for policy analysis. Finally, the
sustainable development is a long-term issue, which requires analysis on long-term
behaviours and effects, and economy-wide transitions towards long-term equilibrium or
disequilibrium, whereas most existing fisheries policies and regulations are short-term
instruments designed to soften imminent problems rather than to resolve them
fundamentally.
There exist economic theories and methods that have not been well adopted by the
fisheries economics, but would have great potential to complement it in order to assist the
new fisheries policy. In the past, several input-output models were built to analyse the
macroeconomic interrelations between the fisheries and other economic sectors. However,
the fisheries input-output analysis has two main drawbacks; one is that it normally sets up
exogenous demands to drive fisheries production and another is its lack of price
mechanisms. General equilibrium analysis has obvious advantages over input-output
analysis in that it not only considers all sectors in a national or regional economic
framework, but also generates production and consumption on the basis of agents’
behaviour and includes a powerful mechanism of price adjustment, which gives much
room for policy analysis. The last three decades have witnessed the greatest success of
the application of CGE models in policy analysis of tax reform, structural adjustment,
international trade, income distribution, environment, and macroeconomics (Robinson,
2002; Chumacero and Schmidt-Hebbel, 2005). Recently, the CGE modelling in
integration with energy, atmospheric concentrations and climate systems has
3
overwhelmed other methods in the analysis of climate change policy (Conrad, 1999 and
2001). More recently, the CGE modelling is proposed for sustainability impact analysis
(Böhringer and Löschel, 2006). In contrast, only few researchers have conducted the
general equilibrium analysis for the fisheries industry and most of them are stylised rather
than applied analysis. Seung and Waters (2006) reviewed an unpublished research that
has built up an applied general equilibrium model for the Oregon regional fisheries
(Houston et al, 1997). The study specifies five fishing sectors, five fish-processing
sectors and 24 other sectors, three types of factor income, household income categories,
two government expenditures, imports and exports, and investment. According to the
review, it sounds as if the Oregon model is a static CGE model, which cannot be
appropriately tied to marine biological process, the impact of fishing activity on marine
systems therefore is not assessed, and the feedback from marine systems to economic
systems is exogenously given. In other words, the model does not specify endogenous
interactions between the fisheries and fish stock changes. There is another group of
fisheries economic models that simulate both economic and ecological systems and
integrate them together, using general equilibrium theory (Eichner and Pethig, 2007;
Finnoff and Tschirhart, 2005). Those models only specify a small or simplified, dynamic,
optimising economic component but concentrate on dynamic interactions of species in
ecosystem. They may possess some general equilibrium features but are different from
standard, multisectoral, SAM-based CGE models.
The main goal of this paper is to develop a regional CGE model with fisheries details to
provide a tool for policy analysis and policy making of fishery management and regional
economic development. The model has the capacity to evaluate the socio-economic
contributions of fishing activities and the regional economic impacts attributable to
fishery policies. In addition to the price and structural relations as specified in standard
CGE modelling, four new contributions for the fisheries general equilibrium modelling
appear in this research. Firstly, the fisheries sector is split into harvest, aquaculture, fish
processing, and fish marketing sectors – all of which are treated in parallel to other
economic sectors. Within the harvesting sector, fishers are further distinguished by the
métier2. The fishing activity of each métier may produce multiple species of fish and each
species of fish may be harvested by multiple métiers. Secondly, households are divided
4
into multiple types such as fisheries, agriculture, industry and capital-income households,
according to their income source. The separation would allow the assessment of the
fishery society’s welfare change and to simulate households’ consumption and
investment behaviour in response to fisheries management and economic development
policies. Thirdly, the research develops a nested, hierarchy system for consumption,
where aquatic products are categorised into several types, namely raw and processed
products, basic and luxury brands, and different species, allowing for each type to be
differentiated in response to relative price change. Fourthly, fishing activity is connected
to biological systems to capture dynamic interactions between capture and biomass
growth. The idea here is that fishing activity affects biomass stock, which changes the
CPUE (Catch Per Unit Effort) values, which in turn have an impact on fishing activity.
Furthermore, the model takes forward-looking investment decisions on sector
development to project future situations, and is based on the regional SAM (Social
Accounting Matrix) to calibrate parameters.
The model developed in this paper is the basic model, which specifies the general model
structure. To apply it to any regional economy, the model will need certain modifications
subject to each region’s special economic conditions. Section 2 describes the general
structure of the applied model. Section 3 applies the model to the Salerno economy in
Italy to illustrate how it can be used to study fishery-related issues. Finally, we conclude
the work in section 4.
2. The structure of the model
2.1 Producers and consumers
Since the focus of the model is on fisheries, we make detailed specifications about the
fisheries producers and for simplicity aggregate all non-fishery industrial sectors into a
single industrial sector, and all non-fishery service sectors into a single service sector. We
treat the agriculture and energy sector separately, considering their special relations with
fisheries. Modern fishing activity relies heavily on fossil fuels, the emissions of which are
believed responsible for climate change. Thus, the separate consideration of the energy
sector would provide convenience for study of interrelations between fisheries and
climate change policies. Agriculture has the closest link with fisheries, not only because
5
agricultural and aquatic products are highly substitutable, but also because production
factors are highly mobile between the two sectors. The fisheries producers include
harvesting, aquaculture, fish processing, and fish marketing producers. We break down
the harvesting producer into a number of métiers (the bottom-up producers), so that the
top-down structure of the model can be connected to the bottom-up specification of fish
production.
The basic model distinguishes between seven consumers namely: households depending
on the fisheries owner or manager, households depending on the skilled fisheries worker,
households depending on the unskilled or small-scale fisheries worker, agriculture
households, non-fishery and non-agriculture households, household depending on capital
income, government, and the foreign consumer. This classification enables policy
analysis to assess the welfare change of the fisheries society, and allows for consumers
different consumption propensity to aquatic products.
2.2 Commodity and production factors
The model assumes that each of the agriculture, energy, industry, services, aquaculture,
and fish processing sectors only produces a single product, while each of the harvesting
and fish marketing sectors may produce multiple products. The fisheries products are
defined according to multi-classification into a hierarchy system, where the species are
first categorised into basic and luxury brands of fish, then each of the brands is
distinguished between two types, namely raw fish and processed aquatic products, and
finally each type consists of a number of individual species.
There could be various settings on the mobility of production factors. Considering that
the agriculture, energy, industry and services sectors are highly aggregate sectors, we
assume that capital is specific to each of the sectors to internalise capital mobility within
the sectors. Fisheries sectors are connected with bottom-up specifications, we therefore
allow for capital mobility between producers in each of the fisheries sectors.
Corresponding to the household classification, labour is classified into the fisheries owner
or manager, the skilled fisheries worker, the unskilled or small-scale fisheries worker,
farmers, and other sectors employment. Both rental and wage rates are determined in
factor markets subject to equilibrium conditions.
6
2.3 Consumer behaviour
Household consumption is defined according to a multi-level nested system (appendix A).
The model distinguishes five types of household consumers each of which is assumed to
consist of identical consumers. At the top level, each type of household wishes to
maximise their inter-temporal utility across time periods by optimally allocating
aggregate consumption over time periods (the Ramsey rule) subject to inter-temporal
budget constraints. The representative consumer’s objective is:
T
T
W = max ∑ (1 + stp ) ⋅ u (ct ) = max ∑ (1 + stp ) ⋅ ln(ct )
t −1
t =1
t −1
t =1
Here stp is the social or pure time preference or discount rate and ct is the aggregate
consumption in volume at time t . The utility function is the logarithm of aggregate
consumption. The time duration has T periods.
Subject to:
T
E1 ≡ ∑ (1 + γ )
t =1
T −t
T
⋅ PACt ⋅ ct + sT = ∑ (1 + γ )
T −t
t =1
⋅ yt + (1 + γ ) ⋅ s0
T
where E1 is total expenditure during the periods, γ is the real interest rate, PACt and yt are
the price of aggregate consumption and the income at time t , and s0 and sT are exogenous
initial and end period savings, respectively. The left-hand side of the above equation is
the consumer’s total spending and the right-hand side the total income during that period.
The Lagrangian for the above inter-temporal optimisation problem can be written as:
T
T
⎡T
⎤
t −1
T −t
T
T −t
L = ∑ (1 + stp ) ⋅ u (ct ) + λ ⋅ ⎢∑ (1 + γ ) ⋅ yt + (1 + γ ) ⋅ s0 − ∑ (1 + γ ) ⋅ PACt ⋅ ct − sT ⎥
t =1
t =1
⎣ t =1
⎦
The first order conditions together with the budget constraint give the following solution
system for consumption variables c1 c2 ... cT :
T
T
t =1
t =1
T −t
T −t
T
∑ (1 + γ ) ⋅ PACt ⋅ ct + sT = ∑ (1 + γ ) ⋅ yt + (1 + γ ) ⋅ s0
7
(1 equation)
u ' (ct ) =
1+ γ
1 + stp
⋅ u ' (ct +1 ) or ct =
⋅ ct +1
1 + stp
1+ γ
( T − 1 equation)
Obviously, consumption demand depends on both the consumption price and income
level, which are determined in the price system and factor income distribution.
Having defined aggregate consumption in each period, the next step moves to the second
level of the consumption system to disaggregate the aggregate consumption in each
period into four consumption or commodity categories, namely composite agricultural
and aquatic product (aa), energy (eng), industrial product (ind), and services (sev). The
demands for these products are derived from the minimisation of consumption
expenditure at a given level of utility in a specific period. Assuming that each of the
consumption or commodity categories also includes a minimum obliged consumption as
a part, and that budget share of expenditure on each category is fixed and all shares add
up to one, we can adopt the Stone-Geary utility function to define the following total
expenditure function in period t :
4
4
i =1
i =1
E2 ≡ PACt ⋅ ct = ∑ PDCt ,i ⋅ c t ,i + u (ct ) ⋅ ∏ PDCtβ,ii , i ∈ (aa, eng , ind , sev )
where E2 is total expenditure for the second level of consumption at period t , PDCt ,i is
commodity i’s price of the disaggregate consumption, c t ,i the minimum obliged or
subsistence consumption of commodity i and β i the marginal budget share of
consumption of commodity i . Minimising the above expenditure function, we obtain the
Hicksian derived demand function with respect to each commodity.
4
⎛ βi ⎞ ⎛
⎟ ⋅ ⎜ PACt ⋅ ct − ∑ PDCt ,i ⋅ c t ,i ⎞⎟
ct ,i = c t ,i + ⎜⎜
⎟
i =1
⎠
⎝ PDCt ,i ⎠ ⎝
(4 equations)
The above equation says that the Hicksian derived demand for a commodity depends on
relative prices, aggregate consumption, and shares. The minimum obliged consumption
c t ,i can be either exogenously given or endogenously determined according to defined
relationships with relative prices, aggregate consumption, budget shares, and expenditure
elasticity3.
8
Among the four commodities at the second level of consumption, energy, industrial
product and services are final products produced by respective sectors, while composite
agricultural and aquatic product is a hypothetical product, which needs to be
disaggregated further into agricultural and aquatic products at the third level of
consumption. Such design allows for greater substitution between the two products. Here,
we assume the CES utility function with the following expenditure function:
(
−σ aa
−σ aa
E3 ≡ PFt , aa ⋅ ct , aa = u (ct , aa ) ⋅ α agr ⋅ PFt1,agr
+ α aqu ⋅ PFt1,aqu
)
1
1−σ aa
Where E3 is the total expenditure for agricultural and aquatic products, PFt , aa and ct , aa are
the price and consumption of the composite agricultural and aquatic product, respectively.
σ aa is the substitution elasticity at the third level of consumption, and α agr and α aqu are
share parameters of agricultural and aquatic price, respectively. Minimising the above
expenditure function, we obtain the Hicksian derived demand function with respect to
each of agricultural and aquatic products.
α i ⋅ PFt −,iσ
ct ,i =
⋅ PFt , aa ⋅ ct , aa , i ∈ (agr , aqu )
∑α i ⋅ PFt1,i−σ
aa
(2 equations)
aa
i
Where agricultural product, ct , agr , is the final product of the agricultural sector, but
aquatic product, ct , aqu , is a composite product of the aquatic sector, which needs to be
disaggregated further into two types, namely basic and luxury aqua-products, to allow for
lower substitution between them. This moves us to the fourth level of consumption. We
again assume the CES utility function and have the following expenditure function:
(
)
1
1−σ aqu 1−σ
aqu
1− σ
E4 ≡ Pt , aqu ⋅ ct , aqu = u (ct , aqu ) ⋅ α bb ⋅ PFt ,bb aqu + α lb ⋅ PFt ,lb
Where E4 is the total expenditure for basic and luxury brand aquatic products, σ aqu is the
substitution elasticity at the fourth level of consumption, and α bb and α lb are the share
parameters of basic and luxury brand aquatic prices, respectively. Minimising the above
expenditure function, we obtain the Hicksian derived demand function with respect to
each of basic (bb) and luxury (lb) brand aquatic products.
9
−σ aqu
α i ⋅ PFt ,i
ct ,i =
1− σ
∑α i ⋅ PFt ,i
aqu
⋅ PFt , aqu ⋅ ct , aqu , i ∈ (bb, lb )
(2 equations)
i
Here each of the basic and luxury brand aquatic products is distinguished between raw
fish and processed products in order to consider substitution between them. This is done
through the CES utility function and the following expenditure function:
(
E5,i ≡ PFt ,i ⋅ ct ,i = u (ct ,i ) ⋅ α i , ra PFt1,i−, σrf i + α i , pr PFt1,i−,σpfi
)
1
1−σ i
, i ∈ (bb, lb )
where E5, i is total expenditure for basic or luxury brand aquatic product, σ i is substitution
elasticity at the fifth level of consumption, and α i , rf and α i , pf are shared parameters of
the price of raw fish and processed aqua-product under the basic or luxury category,
respectively. Minimising the above expenditure function, we obtain the Hicksian derived
demand function with respect to each raw fish (rf) and processed aqua-products (pf)
under basic or luxury brands.
ct ,i , j =
α i , j ⋅ PFt −,iσ, j
⋅ PFt ,i ⋅ ct ,i , i ∈ (bb, lb ), j ∈ (rf , pf )
∑α i, j ⋅ PFt1,i−,σj
i
i
(4 equations)
i
At the bottom level of consumption each category of raw fish and processed aquaproducts under the basic or luxury brand is distinguished among different species. We use
the CES utility functions here to allow for higher substitution among the species (sp). The
expenditure functions are as follows:
1
E6,i , j ≡ PFt ,i , j ⋅ ct ,i , j
1−σ i , j
⎛
1− σ ⎞
= u (ct ,i , j ) ⋅ ⎜ ∑ α i , j , s ⋅ PFt ,i , j ,is, j ⎟
, i ∈ (bb, lb ), j ∈ (rf , pf ) and s ∈ (1...sp j )
⎝ s
⎠
where E6,i , j is the total expenditure of each consumption category on the species, σ 6,i, j is
the substitution elasticity at the sixth level of consumption, and α i , j , s is the shared
parameter of the price of each species of fish, respectively. Minimising the above
expenditure function, we obtain the Hicksian derived demand function with respect to
each species of fish.
10
−σ i , j
ct ,i , j , s
α i , j , s ⋅ PFt ,i , j , s
=
⋅ PFt ,i , j ⋅ ct ,i , j , i ∈ (bb, lb ), j ∈ (rf , pf ) and s ∈ (1...sp j )
1− σ
⋅
PF
α
∑ i , j , s t ,i , j , s
i, j
s
( 2 × (splu + spba ) equations)
These demands are final products of the harvesting, aquaculture, or processing sectors.
For simplicity, we do not model marketed and home-consumed aqua-products here.
Instead, we assume that all aqua-products are marketed. In future research, one may
either assume fixed proportions of total aqua-products are marketed or follow the above
example to model substitution between marketed and home-consumed aqua-products.
In summary, the consumption system consists of T + 4 + 2 + 2 + 4 + 2 × (spbb + splb )
equations, T + 8 of which are composite products and the rest are real products produced
by producers in the model.
2.4 Producer behaviour
The production also follows a multi-level nested system (appendix B) in which producers
maximise the net present value of revenue (profits) across time by optimally employing
intermediate and factor inputs for production activity over time periods. The model
distinguishes four general producers namely: agriculture, energy, industry and service,
and the fishery producers (which is then further classified into a number of fisheryrelated producers including several harvesting producers (the métiers), several
aquaculture producers, several processing sectors, and a marketing sector). The number
of harvesting, aquaculture, or processing producers varies subject to regional
specifications. The production of all producers is assumed to use the nested CES
technology, but different producers may have different values of substitution elasticity.
2.4.1 Agriculture, energy, industry or service producers
At the top level, aggregate production in each period uses composite intermediate
products, labour, and capital; the demands of which are given at the FOC conditions. The
demands for intermediate products, labour, and capital are static, while the supply of
capital is dynamically determined through investment. It is assumed that substitutability
is high between the top-level inputs in each of the four general non-fishery sectors. The
11
general producer produces a single output and maximises their inter-temporal profit for a
particular duration of time subject to inter-temporal constraints of capital accumulation.
V j = max ∑ (1 + rlir ) ⋅ (PCt ,i ⋅ X t ,i − PIOt ⋅ X t ,io − wt ⋅ Lt − rt ⋅ K t − PI t ⋅ I t ) ,
T
−t
t =1
i ∈ (agr , eng , ind , sev ) and j ∈ (agr , eng , ind , sev )
Here rlir is the real long-term interest rate, X t , X t ,io , Lt , K t and I t are the general
producer j ’s output, composite intermediate input bundle, labour, capital, and
investment, respectively. PCt ,i , PIOt , wt , rt and PI t are the corresponding prices and
agr , eng , ind and sev represent agriculture, energy, industry and service respectively.
For convenience, we omit the j subscript for all input terms.
Subject to:
K t +1 = (1 − δ ) ⋅ K t + I t , and K1 , KT given
where K t is producer j ’s capital stock at time t , δ the depreciation rate of capital, K1 the
exogenous initial capital stock, and KT the terminal capital stock that can be either
exogenous or endogenous. Assuming aggregate production in each period takes the CES
technology, we have:
ρ nf −1
⎛
ρρ
⎜ ρ
ρ
ρ
ρ
X t , j = ⎜ α io nf ⋅ X t ,io nf + α l nf ⋅ Lt nf + α k nf ⋅ K t
⎜
⎝
1
1
ρ nf −1
1
ρ nf −1
ρ nf
⎞
⎟
⎟
⎟
⎠
ρ nf
ρ nf −1
,
j ∈ (agr , eng , ind , sev )
where α io , α l and α k are the share parameters of X t ,io , Lt and K t , which are adjusted
to the base year data. ρ nf is the elasticity of substitution between X t ,io , Lt and K t in
non-fishery sectors. This dynamic optimisation problem can be conveniently solved with
the Bellman recursive method for the following solutions:
demand for intermediate product, X t ,io
⎛ PC ⎞
= α io ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ PIOt ⎠
12
ρ nf
(1 equation)
⎛ PC ⎞
demand for labour, Lt = α l ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ wt ⎠
ρ nf
⎛ PC ⎞
demand for capital, K t = α l ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ rt ⎠
(1 equation)
ρ nf
(1 equation)
PCt +1, j
⎛
⎞
⎟⎟
supply of capital, K t +1 = α k ⋅ X t +1, j ⋅ ⎜⎜
(
)
(
)
+
⋅
−
−
⋅
1
rlir
PI
1
δ
PI
t
t
+
1
⎝
⎠
ρ nf
( T − 1 equation)
and demand for investment, I t = K t +1 − (1 − δ )K t
At the second level, the intermediate product is the CES function of a composite
agricultural and aquatic product (aa) and a composite product of energy, industrial
product and service (eis). The substitutability between them is assumed to be low. Given
the total demand for aggregate intermediate products, minimising the production cost, we
have:
Z t ,io = min PAAt ⋅ X t , aa + PEISt ⋅ X t , eis
where X t , aa and X t , eis are demands for aa and eis, respectively. PAAt and PEISt are their
prices.
Subject to:
ρ io
X t ,io
ρ io −1 ρ −1
1
⎛ 1 ρρio −1
⎞ io
ρ io ⎟
io
= ⎜ α aaρ io X t , aa
+ α eisρ io X t , eis
⎜
⎟
⎝
⎠
Where α aa and α eis are parameters adjusted to the base year data. ρio is the elasticity of
substitution between X t , aa and X t , eis . The solutions of this problem are as follows:
⎞
⎟⎟
⎠
demand for composite aa product, X t , aa
⎛ PIOt
= α aa ⋅ X t ,io ⋅ ⎜⎜
⎝ PAAt
demand for composite eis product, X t , eis
⎛ PIOt
= α eis ⋅ X t ,io ⋅ ⎜⎜
⎝ PEISt
13
ρ io
(1 equation)
⎞
⎟⎟
⎠
ρ io
(1 equation)
(
where PIOt = α aa ⋅ PAAt1− ρ io + α eis ⋅ PEISt1− ρ io
)
1
1− ρ io
by duality.
Further down to the third level of production, given X t , aa and X t , eis , minimising the
production cost, we have:
Z t , aa = min PINTt , agr ⋅ X t , agr + PINTt , aqu ⋅ X t , aqu
where X t , agr and X t , aqu are demands for agricultural products (agr) and aquatic products
(aqu), respectively. PINTt , agr and PINTt , aqu are their prices.
Subject to:
ρ aa −1
ρ aa
ρ aa −1
ρ aa
⎛ ρ
ρ aa
aa
X t , aa = ⎜ α agr
⋅ X t , agr + α aqu
⋅ X t , aqu
⎜
⎝
1
1
⎞
⎟
⎟
⎠
ρ aa
ρ aa −1
Where α agr and α aqu are parameters adjusted to the base year data. ρ aa is the elasticity of
substitution between X t , agr and X t , aqu . The conditional demand functions of this problem
are:
⎞
⎟
⎟
⎠
ρ aa
X t , agr
⎛ PAAt
= α agr ⋅ X t , aa ⋅ ⎜
⎜ PINT
t , agr
⎝
X t , aqu
⎛ PAAt ⎞
⎟
= α aqu ⋅ X t , aa ⋅ ⎜
⎜ PINT
⎟
t , aqu ⎠
⎝
(1 equation)
ρ aa
(1 equation)
Similar for X t , eis , we have:
Z t , eis = min PINTt , eng ⋅ X t , eng + PINTt ,ind ⋅ X t ,ind + PINTt , sev ⋅ X t , sev
where X t , eng , X t ,ind and X t , sev are demands for energy, industrial product, and service
respectively. PINTt , eng , PINTt ,ind and PINTt , sev are their prices.
Subject to:
14
ρ eis
X t , eis
ρ eis −1
ρ eis −1
ρ eis −1 ρ −1
1
1
⎛ ρ1
⎞ eis
ρ eis
ρ eis
ρ eis
ρ eis
ρ eis ⎟
eis
⎜
= α eng ⋅ X t , eng + α ind ⋅ X t ,ind + α sev ⋅ X t , sev
⎜
⎟
⎝
⎠
where α t , eng , α t ,ind and α t , sev are parameters adjusted to the base year data. ρ eis is the
elasticity of substitution between X t , eng , X t ,ind and X t , sev . The conditional demand
functions of this problem are:
X t , eng
⎛ PEISt
= α eng ⋅ X t , eis ⋅ ⎜
⎜ PINT
t , eng
⎝
⎞
⎟
⎟
⎠
⎛ PEISt
⋅ X t , eis ⋅ ⎜⎜
⎝ PINTt ,ind
⎞
⎟
⎟
⎠
X t ,ind = α ind
X t , sev
⎛ PEISt ⎞
⎟
= α sev ⋅ X t , eis ⋅ ⎜⎜
⎟
PINT
t , sev ⎠
⎝
ρ eis
(1 equation)
ρ eis
(1 equation)
ρ eis
(1 equation)
2.4.2 Fish harvest producers
The model distinguishes a number of different fish harvesters by métier, which is defined
as a specific fleet equipped with a specific gear, targeting a specific species and including
other species as by-products. A representative métier (appendix C) maximises its intertemporal profit for a particular duration of time subject to inter-temporal constraints of
biomass change and capital accumulation.
Vhar , j = max ∑ (1 + rlir ) ⋅ (PCt , j ⋅ Yt , j − PINTt ,i ⋅ X t ,i − wt ⋅ Lt − rt ⋅ K t − PI t ⋅ I t ),
T
−t
t =1
i ∈ (sp2 , sp3 , agr , eng , ind , sev ) and j ∈ (1...mt )
where har indicates the harvesting sector, Yt , j is métier j ’s harvesting activity that
produces multiple species of fish and mt represents the métiers or harvesters. For the
input terms in the above equation, we omit the subscript j .
Subject to:
K t +1 = (1 − δ ) ⋅ K t + I t , and K1 given
15
The harvest activity uses a CES technology with a low value of substitution elasticity.
ρ har
ρ har −1
ρ har −1
ρ har −1 ρ −1
1
1
⎛ ρ1
⎞ har
ρ har
ρ har
ρ har
ρ har
har
⎜
,
+ α l ⋅ Lt
+ α k ⋅ K t ρ har ⎟
Yt , j = α i ⋅ X t ,i
⎜
⎟
⎝
⎠
i ∈ (sp2 , sp3 , agr , eng , ind , sev ) and j ∈ (1...mt )
The harvested fishes are computed through:
X t ,i , j = θt ,i , j ⋅ Yt , j , i ∈ (1...sp1 ) and j ∈ (1...mt )
(i x j equations)
where sp1 indicates the harvested species, θ t ,i , j is the CPUE (Catch Per Unit of Effort)
variable in the terminology of fisheries economics. In the model this is an endogenous
variable and defined as:
θt ,i , j = θ r ,i , j ⋅
BM t .i
, i ∈ (1...sp1 ) and j ∈ (1...mt )
BM r ,i
(i x j equations)
where BM t ,i is the biomass stock of species i , which is assumed to be available for all the
métiers harvest activity, and r indicates a reference year.
Total biomass of species i depends on the natural growth of the biomass and the total
catch in a previous period. Biomass growth can be computed based on simply assumed
functions such as linear, logistic, exponential, or others. The biomass change can also be
assessed from comprehensive biological model systems, where biological interactions are
taken into account to a considerable extent. Here, we consider the following growth
functions, namely linear, logistic, Pella and Tomlinson exponential, and Fox general
growths, with respect to different species. In follow-up research we may connect the
model with an external biological model to assess biomass growth.
For the linear growth of biomass:
mt
BM t ,i = (1 + ϕi ) ⋅ BM t −1,i − ∑ X t −1,i , j , i ∈ (1...sp1 )
j =1
For the logistic growth of biomass:
16
BM t ,i = (1 + ϕt ,i ) ⋅ BM t −1,i − ∑ X t −1,i , j
mt
j =1
= BM t −1,i
mt
⎛ BM t −1,i ⎞
⎟⎟ ⋅ BM t −1,i − ∑ X t −1,i , j
+ ϕi ⋅ ⎜⎜1 −
CAPi ⎠
j =1
⎝
, i ∈ (1...sp1 )
For the Pella and Tomlinson exponential growth of biomass:
BM t ,i = (1 + ϕt ,i ) ⋅ BM t −1,i − ∑ X t −1,i , j
mt
j =1
= BM t −1,i
µ −1
mt
⎛ ⎛ BM
⎞
t −1, i ⎞
⎜
⎟⎟ ⎟ ⋅ BM t −1,i − ∑ X t −1,i , j
+ ϕi ⋅ 1 − ⎜⎜
⎜ ⎝ CAPi ⎠ ⎟
j =1
⎝
⎠
, i ∈ (1...sp1 )
For the Fox growth of biomass:
BM t ,i = (1 + ϕt ,i ) ⋅ BM t −1,i − ∑ X t −1,i , j
mt
j =1
= BM t −1,i
mt
⎛ ln BM t −1,i ⎞
⎟⎟ ⋅ BM t −1,i − ∑ X t −1,i , j
+ ϕi ⋅ ⎜⎜1 −
ln CAPi ⎠
j =1
⎝
, i ∈ (1...sp1 )
where ϕt ,i is the growth rate of biomass, ϕi the intrinsic growth rate parameter, and
CAPi the environmental carrying capacity parameter of species i . µ is a parameter
specially for the Pella and Tomlinson exponential growth function. When µ = 2 , the Pella
and Tomlinson exponential growth is equivalent to the logistic growth. The third term on
the right-hand side is the total catch per species, a summing up across all métiers.
Maximising the objective function, subject to the above constraints where BM t ,i and K t ,
and Yt , j are the state and control variables, respectively, The Bellman recursive method is
used to solve the problem for the following demands:
demand for general products, X t ,i
⎛ PCt , j ⎞
⎟
= α i ⋅ Yt , j ⋅ ⎜⎜
⎟
PINT
t ,i ⎠
⎝
ρ har
, i ∈ (sp2 , sp3 , agr , eng , ind , sev )
(i x j equations)
⎛ PCt , j ⎞
⎟⎟
demand for labour, Lt = α l ⋅ Yt , j ⋅ ⎜⎜
⎝ wt ⎠
ρ har
(j equation)
17
⎛p ⎞
demand for capital, K t = α k ⋅ Yt , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ rt ⎠
ρj
( T − 1 equation)
PCt +1, j
⎛
⎞
⎟⎟
supply of capital, K t +1 = α k ⋅ Yt +1, j ⋅ ⎜⎜
(
)
(
)
+
⋅
−
−
⋅
1
rlir
PI
1
δ
PI
t
t +1 ⎠
⎝
ρ har
( T − 1 equation)
and demand for investment, I t = K t +1 − (1 − δ )K t .
Demand for biomass stock of each of the sp1 species, in the case of the linear growth of
biomass:
BM t +1,i =
PCt +1, j
(1 + rlir ) ⋅ PCt , j
[
⋅ (1 + ϕi ) ⋅ BM t ,i − θ t ,i , j ⋅ Yt +1, j
]
Furthermore
BM t +1,i
BM t +1,i
=
(1 + ϕi ) ⋅ BM t ,i − θt ,i , j ⋅ Yt +1, j (1 + ϕi ) ⋅ BM t ,i − θt ,i , j ⋅ Yt , j + θ t ,i , j ⋅ Yt , j − θt ,i ⋅ Yt +1, j
=
PCt +1, j
BM t +1,i
=
BM t +1,i + θ t ,i , j ⋅ (Yt , j − Yt +1, j ) (1 + rlir ) ⋅ PCt , j
The above condition states that taking all other fishing activities as given, the activity j ’s
marginal costs will be equivalent in long-run equilibrium,
PCt +1, j
(1 + rlir ) ⋅ PCt , j
= 1 , if the
activity remains constant over time, Yt +1, j = Yt , j . However, if the activity is intensified,
Yt +1, j > Yt , j , its long-run equilibrium marginal costs will be higher than before:
PCt +1, j
(1 + rlir ) ⋅ PCt , j
> 1.
Similarly, for the logistic growth of biomass it is:
BM t +1,i =
⎡⎛
⎤
⎛ 2 ⋅ BM t ,i ⎞ ⎞
⎟⎟ ⎟ ⋅ BM t ,i − θ t ,i , j ⋅ Yt +1, j ⎥
⋅ ⎢⎜⎜1 + ϕi ⋅ ⎜⎜1 −
(1 + rlir ) ⋅ PCt , j ⎢⎣⎝
CAPi ⎠ ⎟⎠
⎥⎦
⎝
PCt +1, j
For the Pella and Tomlinson growth of biomass it is:
18
BM t +1,i
µi −1
⎡⎛
⎤
⎛
⎛ BM t ,i ⎞ ⎞⎟ ⎞⎟
⎜
⎜
⎟⎟
=
⋅ ⎢ 1 + ϕi ⋅ 1 − µi ⋅ ⎜⎜
⋅ BM t ,i − θ t ,i , j ⋅ Yt +1, j ⎥
⎜
(1 + rlir ) ⋅ PCt , j ⎢⎜⎝
⎥
⎝ CAPi ⎠ ⎟⎠ ⎟⎠
⎝
⎣
⎦
PCt +1, j
And for the Fox growth of biomass it is:
BM t +1,i =
⎡⎛
⎤
⎛ 1 + ln BM t ,i ⎞ ⎞
⎟⎟ ⎟ ⋅ BM t ,i − θ t ,i , j ⋅ Yt +1, j ⎥
⋅ ⎢⎜⎜1 + ϕi ⋅ ⎜⎜1 −
(1 + rlir ) ⋅ PCt , j ⎣⎢⎝
ln CAPi ⎠ ⎟⎠
⎝
⎦⎥
PCt +1, j
2.4.3 Aquaculture producers
Aquaculture is regarded to consist of a number of different producers, each of which
represent a group of identical individual producers and specialises in a single species of
fish, subject to a low substitutable technology. A representative aquaculture producer
maximises its inter-temporal profit for a particular duration of time subject to intertemporal constraints of capital accumulation:
Vacu , j = max ∑ (1 + rlir ) ⋅ (PCt , j ⋅ X t , j − PINTt ,i ⋅ X t ,i − wt ⋅ Lt ,i − rt ⋅ K t ,i − PI t ⋅ I t ,i ) ,
T
−t
t =1
i ∈ (sp1 , sp3 , agr , eng , ind , sev ) , j ∈ (1...sp2 )
where acu indicates the aquaculture sector and sp2 both the aquaculture producers and
the species that each of the producers specialises in farming.
Subject to:
K t +1,i = (1 − δ )K t ,i + I t ,i , and K1,i given
where K t ,i is the capital stock of each aquaculture producer. The production adopts the
CES function with a small value of substitution elasticity:
ρ acu
X t, j
ρ acu −1
ρ acu −1
ρ acu −1 ρ −1
1
1
⎛ 1
⎞ acu
= ⎜ α iρacu ⋅ X t ,iρacu + α lρacu ⋅ Lt ρacu + α kρacu ⋅ K t ρacu ⎟
⎜
⎟
⎝
⎠
i ∈ (sp1 , sp3 , agr , eng , ind , sev ) , j ∈ (1...sp2 )
The resulted production demands are as follows:
19
demand for intermediate products, X t ,i
⎛ PC ⎞
= α i ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ PCt ,i ⎠
⎛ PC ⎞
demand for labour, Lt = α l ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ wt ⎠
ρ acu
(i x j equations)
ρ acu
⎛ PCt , j ⎞
⎟⎟
demand for capital, K t = α l ⋅ X t , j ⋅ ⎜⎜
⎝ rt ⎠
(j equation)
ρ acu
(j equation)
PCt +1, j
⎛
⎞
⎟⎟
supply of capital, K t +1 = α k ⋅ X t +1, j ⋅ ⎜⎜
⎝ (1 + rlir ) ⋅ PI t − (1 − δ ) ⋅ PI t +1 ⎠
ρ acu
(j x T-1 equations)
and demand for investment, I t = K t +1 − (1 − δ )K t .
2.4.4 Fish processing producers
Similar to the aquaculture sector, the fish processing production is assumed to consist of
a number of different producers, each of which represents a group of identical individual
producers and specialises in the procession of a single species of fish, subject to a low
substitutable technology. The representative fish processing producer maximises its intertemporal profit for a particular duration of time subject to inter-temporal constraints of
capital accumulation.
V pro , j = max ∑ (1 + rlir ) ⋅ (PCt , j ⋅ X t , j − PCt ,i ⋅ X t ,i − wt ⋅ Lt − rt ⋅ K t − PI t ⋅ I t )
T
−t
t =1
i ∈ (sp1 , sp2 , agr , eng , ind , sev ) and j ∈ (1...sp3 )
where pro indicates the processing sector, and sp3 both the processing producers and the
species that each of the producers specialises in processing. Subject to:
K t +1 = (1 − δ )K t + I t , and K1 given
where K t is capital stock and I t investment in the processing sector. The production
adopts the CES function with a small value of substitution elasticity:
20
ρ pro
X t, j
ρ pro −1
ρ pro −1
ρ pro −1 ρ −1
1
1
⎛ 1
⎞ pro
ρ pro
ρ pro
ρ pro
ρ pro
ρ pro
ρ
⎜
= α i ⋅ X t ,i
+ α l ⋅ Lt
+ α k ⋅ K t pro ⎟
⎜
⎟
⎝
⎠
i ∈ (sp1 , sp2 , agr , eng , ind , sev ) and j ∈ (1...sp3 ) .
The resultant production demands are as follows:
demand for intermediate products, X t ,i
⎛ PC ⎞
= α i ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ PCt ,i ⎠
⎛ PC ⎞
demand for labour, Lt = α l ⋅ X t , j ⋅ ⎜⎜ t , j ⎟⎟
⎝ wt ⎠
ρ pro
(i x j equations)
ρ pro
⎛ PCt , j ⎞
⎟⎟
demand for capital, K t = α l ⋅ X t , j ⋅ ⎜⎜
⎝ rt ⎠
(j equation)
ρ pro
(j equation)
PCt +1, j
⎛
⎞
⎟⎟
supply of capital, K t +1 = α k ⋅ X t +1, j ⋅ ⎜⎜
⎝ (1 + rlir ) ⋅ PI t − (1 − δ ) ⋅ PI t +1 ⎠
ρ pro
(j x T-1 equations)
and demand for investment, I t = K t +1 − (1 − δ )K t .
2.5 The government
Government collects its revenues from various taxes, levies and tariffs. Government
expenditure includes government consumption, transfer, and savings. The basic model
assumes that all the three expenditures are proportional fixed and that the government
consumption follows the observed consumption pattern.
2.6 Capital account
Total savings come from both households and government savings. Because the basic
model assumes endogenous households consumption and exogenous government
consumption, the households and government savings can be determined from the
difference between household disposable income and consumption, and the difference
between government revenue and consumption and transfers, respectively. In the model,
investment is endogenously determined by producers’ production. Total investment and
21
savings are not necessarily in balance because of capital flows to or from outside of the
regional economy.
2.7 The commodity markets
In a closed regional economy, total domestic demand for each product includes
intermediate demand of production, final demand of consumption and investment.
X tD, h = ∑ X t , h , j + Ct , h + GCt , h ,C + ∑ I t , h , j ,
j
j
h ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 ) and j ∈ (agr , eng , ind , sev, mt , sp2 , pro )
Total domestic supply of each product is generated from respective production.
X tS, h = X t , h , h ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
In an open regional economy, total domestic products are split between regional and
outside-regional markets. The latter includes both the rest of the national economy and
abroad. The domestic products that go to regional markets are the supply of domestic
products to regional markets, and the domestic products that go to outside-regional
markets are the regional export. The producer maximises total revenues by allocating
domestic products between regional and outside-regional markets, subject to the function
of constant elasticity of transformation (CET).
Max PDt ,i ⋅ XDDt ,i + PEXPt ,i ⋅ XEt ,i
Subject to:
ρ CET ,i −1
ρ CET ,i −1
⎛
1
ρ
ρ CET ,i
ρ CET ,i
XDt ,i = TCi ⋅ ⎜ (1 − ϑCET ,i )ρ CET ,i ⋅ XDDt ,i CET ,i + ϑCET
, i XEt , i
⎜
⎝
1
⎞
⎟
⎟
⎠
ρ CET ,i
ρ CET ,i −1
i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
where ρCET ,i is the elasticity of transformation, TCi the scale parameter of the CET
function, ϑCET ,i the share parameter;
XDt ,i , XDDt ,i and XEt ,i are total transformed
domestic production, the domestic products supplied to regional markets, and the
regional exports, respectively. PDt ,i is the purchasing price of domestic products,
22
and PEXPt ,i the price of export. The solution of this problem gives demands for
XDDt ,i and XEt ,i as follows:
⎛ PTDt ,i ⎞
⎟
XDDt ,i = (1 − ϑCET ,i ) ⋅ XDt ,i ⋅ ⎜⎜
⎟
PD
t ,i ⎠
⎝
⎛ PTDt ,i ⎞
⎟
XEt ,i = ϑCET ,i ⋅ XDt ,i ⋅ ⎜⎜
⎟
PEXP
t ,i ⎠
⎝
ρ CET ,i
ρ CET ,i
where PTDt ,i is the price of total transformed domestic product.
The supply of domestic products to domestic markets and the supply from foreign
markets or from imports constitute the total supply to domestic markets. The producer or
consumer minimises total costs by choosing between domestic and foreign products
according to Armington assumption:
Min PDt ,i ⋅ XDDt ,i + PIMPt ,i ⋅ XM t ,i
Subject to:
ρ AMT ,i
ρ AMT ,i −1
ρ AMT ,i −1 ρ
1
⎛
⎞ AMT ,i −1
1
ρ AMT ,i
ρ AMT ,i
ρ AMT ,i ⎟
S
⎜
ρ
(
)
X t ,i = ACi ⋅ 1 − ϑ AMT ,i AMT ,i XDDt ,i
+ ϑ AMT ,i XM t ,i
⎜
⎟
⎝
⎠
i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
where ρ AMT ,i is the elasticity of Armington substitution, ACi the scale parameter of the
Armington function, ϑ AMT ,i the share parameter; XM t ,i the import and PIMPt ,i the price
of import. The solution of this problem gives demands for XDDt ,i and XM t ,i as follows:
⎛ P ⎞
XDDt ,i = (1 − ϑ AMT ,i ) ⋅ X ⋅ ⎜⎜ t ,i ⎟⎟
⎝ PDt ,i ⎠
ρ AMT ,i
S
t ,i
where Pt ,i is the price of total supply to domestic markets. Rearranging the equation
above, we can see that total supply X tS,i can be solved with XDDt ,i
23
X
S
t ,i
= (1 − ϑAMT ,i )
−1
⎛ PDt ,i ⎞
⎟
⋅ XDDt ,i ⋅ ⎜⎜
⎟
⎝ Pt ,i ⎠
ρ AMT ,i
Consequently, import is solved with:
⎛ Pt ,i ⎞
⎟
XM t ,i = ϑ AMT ,i ⋅ X ⋅ ⎜⎜
⎟
PIMP
t ,i ⎠
⎝
ρ AMT ,i
S
t ,i
in equilibrium, total supply and demand of each commodity converge to the equality
through adjustment of prices:
X tD,i = X tS,i ⇒ Pt ,i , i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
2.8 Factor markets
There are various ways to model factor markets. Since the regional economy can be
regarded as a small open economy, it is reasonable to assume that once there are
shortages in local labour markets the local region can attract enough labour forces from
other regions of the national economy. Thus, in the basic model, we derive the labour
demands from production, fix the wage rates at observed levels, and make the labour
supplies flexible to meet the demands. The model assumes different capital markets with
respect to different sectors. In non-fishery sectors, capital is assumed to be sector-specific,
where rental rate is determined from capital equilibrium conditions. In fishery sectors,
capital is assumed to be mobile across bottom-up producers within each of the sectors.
Thus, for each fishery sector there is a single capital constraint, which determines a
unique rental rate for all producers of the sector. The capital supply in a period is formed
from the capital stock net of depreciation and investment in previous periods. The
investment may come from the local region’s savings, the rest of the national economy,
or abroad. The basic model assumes four types of labour that are immobile across sectors
as defined in section 2.2:
demand for capital in non-fishery sector: K t , j , j ∈ (agr , eng , ind , sev )
demand for capital in fishery sector:
∑K
t, j
, j ∈ (mt , sp2 , sp3 )
j
24
supply of capital: (1 − δ j ) ⋅ K t −1, j + INVt −1, j
equilibrium in capital markets:
(1 − δ )⋅ K
j
t −1, j
∑ [(1 − δ )⋅ K
j
+ INVt −1, j = K t , j , j ∈ (agr , eng , ind , sev )
t −1, j
]
+ INVt −1, j = ∑ K t , j , j ∈ (mt , sp2 , sp3 )
j
j
total demand for each type of labour:
∑L
t, j
, j ∈ (agr , eng , ind , sev, mt , sp2 , sp3 )
j
total supply of each type of labour is determined from demand side: L t
in equilibrium: L t = ∑ Lt , j
j
2.9 The price system
The price system of commodity and factor consists of endogenous leading prices,
endogenous derived prices, and exogenous prices. In the basic model, import and labour
prices are exogenous. Because the regional economy may import or export from or to
both the rest of the national economy and abroad, we assume that it faces a unique import
or export price that combines both the national and international prices of a commodity.
Thus, the exogenous import price can be taken in domestic currency without involving an
exchange rate. The endogenous leading prices are the prices that adjust to clear
commodity or factor markets in equilibrium. In the basic model, these are the prices of
final real commodities:
Pt ,i , i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
and the prices of capital:
rt ,i , i ∈ (agr , eng , ind , sev, mt , sp2 , sp3 )
The endogenous derived prices are derived from the leading prices through either the
dual function of production or the taxation on real commodity. The first set of the derived
prices is the producer prices of domestically produced commodities, PDt ,i , which can be
derived through the Armington dual function.
25
Pt ,i =
(
1
1− ρ
1− ρ AMT ,i
ρ AMT ,i
ρ
⋅ (1 − ϑ AMT ,i ) AMT ,i ⋅ PDt ,i AMT ,i + ϑAMT
, i ⋅ PIMPt , i
ACi
)
1
1− ρ AMT ,i
The export price is an endogenous price, which can be neither lower nor higher than the
producer price of domestically produced commodity, and thus must equal to it:
PEXPt ,i = PDt ,i
Once both PDt ,i and PEXPt ,i are obtained, the price of the total transformed domestic
product can be derived through the CET dual function:
PTDt ,i =
(
1
1− ρ
1− ρ CET ,i
ρ CET ,i
ρ
⋅ (1 − ϑCET ,i ) CET ,i ⋅ PDt ,i CET ,i + ϑCET
, i ⋅ PEXPt , i
TCi
)
1
1− ρ CET ,i
The producer commodity prices PDt ,i , need to be converted into the producer activity
prices in the harvesting sector, where the fishing activity produces multiple products.
PYt , j = ∑θ t ,i , j ⋅ PDt , j , i ∈ (1...sp1 ), j ∈ (1...mt )
i
where θ t ,i , j is the CPUE (catch per unit of effort) variable as defined in section 2.4.2.
By deducting the production tax and subsidy from the producer price, we obtain the unit
cost of domestic production for each producer:
PCt , j =
PYt , j
1 + τ pt + τ sub
, j ∈ (agr , eng , ind , sev, mt , sp2 , sp3 )
where τ pt and τ sub are rate of production tax and subsidy, respectively.
The sales price of intermediate products is the leading price of each commodity
augmented by the indirect tax.
PINTt ,i = (1 + τ it ) ⋅ Pt ,i , i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
where τ it is the rate of indirect tax.
The consumer price of the final product for consumption and investment is the leading
price plus the indirect tax and VAT.
26
PFt ,i = (1 + τ it ) ⋅ (1 + τ va ) ⋅ Pt ,i , i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 )
where τ va is the rate of value-added tax.
The investment price by commodity can be converted into the investment price by
sector PI , through a converter ν :
PI t , j = ∑ν i , j ⋅ PFt ,i ,
i
i ∈ (agr , eng , ind , sev, sp1 , sp2 , sp3 ) and j ∈ (agr , eng , ind , sev, mt , sp2 , sp3 )
Corresponding to the nested production scheme in agriculture, energy, industry, and the
service sectors, there is a set of nested prices for hypothetical, composite intermediate
commodities. Let j ∈ (agr , eng , ind , sev ) indicate agriculture, energy, industry, and the
service sectors, the prices of hypothetical, composite intermediate commodities are:
1
1− ρ aqu , j 1− ρ aqu , j
t ,i
(
)
PINTt , aqu , j = ∑ α i , j ⋅ PINT
, i ∈ (sp1 , sp2 , sp3 )
i
(
1− ρ aa , j
t , agr
PAAt , j = α agr , j ⋅ PINT
(
+ α aqu , j ⋅ PAQU
1− ρ eis , j
t , eng
PEISt , j = α eng , j ⋅ PINT
(
1− ρ io , j
t, j
PIOt , j = α aa , j ⋅ PAA
1− ρ aa , j
t, j
1− ρ eis , j
t , ind
+ α ind , j ⋅ PINT
+ α eis , j ⋅ PEIS
1− ρ io , j
t, j
1
1− ρ aa , j
)
1− ρ eis , j
t , sev
+ α sev , j ⋅ PINT
1
1− ρ eis , j
)
1
1− ρio , j
)
Corresponding to the nested consumption scheme for consumers, there is a set of nested
prices for hypothetical, composite aquatic commodities. Let h ∈ (h1 , h2 , h3 , h4 , h5 ) indicate
the types of households, then:
(
PFt , h ,i , j = ∑ α h , s ⋅ PFt ,i , j ,hs,i , j
1−σ
1
1−σ h ,i , j
)
, i ∈ (bb, lb ) , j ∈ (rf , pf ) and s ∈ (sp1 , sp2 , sp3 )
s
where PFt , h ,i , j is the price of hypothetical, composite aquatic commodities for
consumption of basic or luxury brands, and raw or processed fish.
27
(
PFt , h ,i = ∑ α h ,i , j ⋅ PFt , h ,i ,hj,i
1−σ
1
1− σ h ,i
)
, i ∈ (bb, lb ) and j ∈ (rf , pf )
j
where PFt , h ,i is the price of hypothetical, composite raw and processed fish commodities
for consumption of basic or luxury brands.
(
PFt , h , aqu = ∑ α h ,i ⋅ PFt , h ,i h ,aqu
1− σ
1
1−σ h ,aqu
)
, i ∈ (bb, lb )
i
where PFt , h , aqu is the price of hypothetical, composite basic and luxury aquatic
commodities for aquatic consumption.
(
PDCt , h , aa = ∑ α h ,i ⋅ PFt , h ,i h ,aa
1−σ
1
1−σ h ,aa
)
, i ∈ (agr , aqu )
i
where PDCt , h , aa is the price of hypothetical, composite agricultural and aquatic
commodities for disaggregate consumption.
∑ PDC
=
∑c
t , h,i
PACt , h
⋅ ct , h, i
i
, i ∈ (aa, eng , ind , sev )
t , h,i
i
where PACt , h is the price of hypothetical, composite commodities for aggregate
consumption.
3. An application to the Salerno regional economy of Italy
3.1 The data
The Salerno SAM table is compiled from the data in 2001 under the Pechdev project
(Pechdev, 2007). It includes 29 sectors and 37 commodities, a single type of labour, a
single type of capital, fishery and non-fishery households, six types of government tax or
subsidy, households and government consumption and savings, investment, institutional
transfers, and both capital and commodity flows with the rest of the national and
international economy. The region’s fisheries include harvesting and processing sectors
but no aquaculture. The fish marketing service is embodied in normal service sectors, not
28
given separately. The harvesting sector consists of five métiers, namely bottom trawler,
purse seiner, small-scale fisheries, multi-purpose fisheries, and tuna fisheries. They
harvest 13 species such as blue fin tuna, anchovies, common cuttlefish, common octopus,
red mullet, deepwater rose shrimp, European pilchard, European hake, giant red shrimp,
blue and red shrimp, striped mullet, spot tailed mantis squid, Norway lobster, and other
species. Among them anchovies, red mullet, deepwater rose shrimp, European hake,
striped mullet and Norway lobster are regarded as the high-value brand of fish, the rest
are the low-value brand of fish, in this research. The fish processing sector only processes
blue fin tuna, anchovies, and other species. It is regarded to consist of three processors,
each of which specialises in one species. For simplicity, in this exercise we aggregate the
original disaggregate agriculture, energy, industrial, and service sectors into four
aggregate sectors, namely agriculture, energy, industrial and service sector. The typical
SAM used for the modelling is illustrated in appendix E. Because of space limitation, we
cannot present the complete SAM with detailed account information. The full dataset can
be made available upon request.
The Salerno model assumes that biomass growth of the species in question follows either
the Fox exponential or the Pella and Tomlinson generalised growth model, both of which
belong to the family of the surplus production models. The incorporation of the surplus
production models into the economic model is an expedient way to integrate the fishery
economy with the ecological system, because the surplus production models simplify the
relations between the population biomass and yield, and express the relations in explicit
forms while requiring fewer parameters. Recently, there have been propositions of using
the age-structured models to describe the biological system in more detail. The most
advanced trend in the integration is to directly link the economic model with the external,
comprehensively-built biological model (Failler and Pan, 2007). The biological data on
the growth models are collected and estimated by the biologists under the Pechdev
project (Pechdev, 2007). Table 1 presents some typical biological data, where ϕ is the
intrinsic growth rate of biomass, µ the parameter of the growth functions, r the ratio of
Salerno catch in the total biomass area, and cap the carrying capacity.
Table 1 Biological data on the species and growth functions
29
Species
Bluefin tuna
Anchovies
Common cuttlefish
Common octopus
Red mullet
Deepwater rose shrimp
European pilchard
European hake
Giant red & blue shrimp
Striped mullet
Spottail mantis squillid
Norway lobster
Other species
φ
2.89
9.39
29.77
29.52
9.33
-0.85
3.78
-0.82
-0.87
-1.08
12.52
2.03
5.67
µ
1.00
1.00
1.00
1.00
1.00
0.55
1.00
0.67
0.64
0.55
1.00
1.00
1.00
r
0.07
0.03
0.15
0.06
0.03
0.47
0.02
0.47
0.47
0.44
0.28
0.02
0.08
Cap (k €)
3979031
67214
20434
18745
4484
11593
93744
11161
17696
9625
7279
332912
1426979
BM (k €)
1459554
24727
7517
6896
1648
2000
3425
1152
4803
1456
4941
24476
524956
Type of growth
Fox
Fox
Fox
Fox
Fox
Pella&Tomlinson
Fox
Pella&Tomlinson
Pella&Tomlinson
Pella&Tomlinson
Fox
Fox
Fox
3.2 Calibrations and baseline projection
The Salerno model is calibrated using the regional SAM data and additional elasticity
data, following a standard procedure. The SAM data is in 2001 value. The elasticity data
is unavailable, so we have assumed that there are three cases, namely low, medium and
high substitutions with corresponding values of 0.1, 0.9, and 2. The assumed values of
elasticity of substitution are listed in table 2.
30
Table 2 Elasticity of substitution
Elasticity
ρgf
Value
2
Equation
ρio
0.1
Production of composite intermediate product
ρaa
0.9
Production of composite agro&aqua product
ρeis
0.9
Production of composite energy, inductrial and service product
ρaqu
2
ρhar
0.9
Production of wild fish
ρpro
0.9
Production of processed fish
ρCET
-0.5
CET function
ρAMT
0.5
Armington function
σaa
2
σaqu
0.1
Consumption of aquatic product
σbb
0.9
Consumption of basic brand fish
σlb
0.9
Consumption of luxury brand fish
σbb,rf
2
Consumption of basic brand, raw fish
σbb,pf
2
Consumption of basic brand, processed fish
σlb,rf
σlb,pf
2
2
Consumption of luxury brand, raw fish
Consumption of luxury brand, processed fish
Non-fishery productions
Production of composite aquatic product
Consumption of agricultural and aquatic product
Before calibration, a number of exogenous variables also need to be assigned values,
which are specified in table 3.
Table 3 Values of exogenous variables
Exogenous variable
Social time preference rate
Depreciation rate
Nominal long-term interest rate
Import price
Wage rate
Symbol
stp
δ
NLIR
PIMP
ω
Value
0.03
0.05
0.08
1
1
The first task of calibration is to find a set of prices, which can balance the SAM values.
Once the prices are found out, volumes can be obtained. With the information above, all
parameters necessary to the various functions can be calibrated. After calibration, the
model is ready to solve a baseline case. For the Salerno case, we can run the model
annually from the base year, 2001, to the end year, 2010. The model results depend on
31
the values of a number of substitution elasticity, but do not vary significantly with
different values 4 . Figure 1 shows the activity levels of the five métiers across time.
During the period, multi-purpose fisheries will grow mostly among others, by over 20%
per year. The multi-purpose métier mainly targets high value fishes and so sound
economically efficient. Tuna fisheries will grow by 2.5% per year in the first eight years,
but decline in the last two years, due to continuous declines in tuna stock. Purse seiners
are the smallest métier among the five, but it will grow steadily by 16% per year. Bottom
trawlers will keep fairly constant, growing only by 2% per year. The only shrinking
activity is the small-scale fisheries, which will decline by 15% per year, reflecting the
disadvantage of the small-scale fisheries in competition. Typically, it suggests that the
multi-purpose fisheries will outfight the bottom trawlers and small-scale fisheries in
competition, since they target similar species. Overall, total harvesting activity will
expand by 5% per year.
Figure 1 The activity of metiers
30000
Output (k Euro)
25000
20000
15000
10000
5000
0
2000
2001
2002
2003
2004
2005
2006
Bottom trawlers
Purse seiners
Multi-pourpose fisheries
Tuna fishery
2007
2008
2009
2010
2011
Small-scale fisheries
The expansion of harvesting activity will not be rewarded with higher capture. Rather,
the total capture will grow very little. This reflects the fact that the deterioration in
biomass stock affects harvesting activity negatively. In figure 2 (where biomass stock is
scaled down to 100 times less in order to host the three curves in the same figure), the
harvesting activity and capture is initially at the same point in the base year, but diverges
widely as the biomass stock steadily declines. If the biomass stock remained constant, the
32
harvesting activity and capture will overlap throughout the period. However, in this case
it is the lower level of biomass stock that reduces the catchability per fishing effort, so
that harvesting the same amount of fish will require more and more fishing effort.
Figure 2 The changes of harvesting activity, capture and biomass stock
80000
70000
K Euro
60000
50000
40000
30000
20000
10000
0
2000
2001
2002
2003
2004
2005
Harvesting activity
2006
Fish capture
2007
2008
2009
2010
2011
Biomass stock
From figure 3 we can see that the biomass stock of almost all species will decline
throughout the period. In particular, the anchovy and European pilchard are approaching
extinction. Purse seiners are the only métier that is responsible for anchovy capture.
Obviously, its 16% growth rate is a great force destroying the biomass stock of anchovies.
This problem is also exactly the same for the European pilchard, which is only harvested
by purse seiners.
Figure 3 The biomass stocks
30000
25000
K Euro
20000
15000
10000
5000
0
Bluefin
tuna
Anchovies Common
cuttlefish
Common Red mullet Deepwater European European
octopus
rose
pilchard
hake
shrimp
Giant red
and blue
shrimp
Striped
mullet
Spottail
mantis
squillid
Norway
lobster
Other
species
3.3 Scenarios
This paper focuses on the presentation of the model, scenario simulations are only
intended to test the model’s ability of incorporating policy analyses. The first scenario
relates to species protection. In the last section the baseline projection reveals that due to
rapid expansion of the purse seiners activity both anchovies and European pilchards will
33
be harvested towards an unsustainable level. To protect the species from extinction, we
assume a 20% tax on consumption of these species to depress demands and thus
production. Figure 4 shows that the consumption tax can effectively prevent both
anchovies and the European pilchard from rapid decrease, but instead the European hake
and Norway lobster will decline greatly due to the substitution effect. This shows that
while an economic instrument is applied to protect certain species, it may harm other
species as trade-off. What would happen if a uniform tax is applied to all species? This
leads to our second scenario where we assume a 10% consumption tax on all the species.
Figure 5 illustrates that the total catch may increase or decrease for different species, but
the biomass stock of all the species will increase from the baseline. However, the
households’ consumption of aquatic products will decrease by 10%. The impact of the
tax is not limited within the harvesting sector, but can spread over to other sectors. We
will not discuss detailed results in this paper.
Figure 4 The biomass stock of four species under a 20% tax on anchovies and European pilchard
30000
25000
K Euro
20000
15000
10000
5000
0
Anchovies
European pilchard
European hake
34
Norway lobster
Figure 5 The change of total catch and end-year biomass
3.00
Ratio
2.50
2.00
1.50
1.00
0.50
Bl
ue
f in
tu
na
An
ch
Co
ov
m
ie
m
s
on
cu
ttl
Co
ef
m
is
m
h
on
oc
to
pu
s
De
Re
ep
d
w
m
at
ul
er
le
t
ro
se
Eu
sh
r im
ro
pe
p
an
pi
lc
ha
Eu
G
rd
ia
ro
nt
pe
re
an
d
ha
an
ke
d
bl
ue
sh
rim
St
p
r ip
Sp
e
ot
d
ta
m
il m
ul
le
an
t
t is
sq
ui
No
l lid
rw
ay
lo
bs
te
O
r
th
er
sp
ec
ie
s
0.00
Total catch
End-year biomass
4. Conclusions
The establishment of this general equilibrium model which focuses on fisheries provides
us with great room to explore policy implications relevant to fisheries. It enables us to
simulate dynamic changes of fishing effort and biomass stock, competition between
capture and aquaculture, resource movement between sectors, industrial transitions,
employment and income distribution in fisheries society, and demand change in response
to price change etc. Moreover, it provides a foundation for quantitative analysis of the
integration of fisheries with regional or national development policy.
The basic model cannot be designed uniformly for each region. Subject to each region’s
economic specialities, the model has to be tailor-made to a certain extent. For each region,
the classifications with respect to consumer, producer, and commodity have to be
redefined, and the construction of the regional SAM is a challenging task. Because of
data limitation, we have used assumed rather than estimated substitution elasticity, which
may lead to different results.
Linking the economic and ecological systems in the model is a new attempt, which
captures the endogenous interactions of the two systems. For simplicity in this research
we provisionally present the ecological system with surplus growth models. It is desirable
to model the ecological system in a more detailed and in-depth way. However, we do not
35
recommend doing this in the CGE model, because the task would be beyond an
economist’s ability and add more complexity to the modelling work. Instead, we would
prefer to have the economic and biological models developed independently and
sophisticatedly and continue to link them externally.
The small empirical exercise demonstrates that the model has great potential and
flexibility for policy analysis. In particular, it reveals the possible trends of fisheries
production and species dynamics for the Salerno fisheries, and finds out that the taxbased instruments protecting certain species may harm other species at the same time and
cannot be effective. However, a uniform marine resource protection tax applied to all
species will lead profound results to not only the species but also fish production and
consumption, and further to the society. This calls integrated impact analysis of
ecological, economic and social systems.
Acknowledgements
The co-authors thank the EU for their financial support. This work has been carried out
with the financial support of the Commission of the European Communities Fifth
Framework Programme, QLRT-2000-02277 “Development of new tools and models to
evaluate the contribution of aquaculture and fishing activities to the development of
coastal areas and their socio-economic interactions with other competing sectors”
(PECHDEV). It does not necessarily reflect the Commission’s views and in no way
anticipates future policy in this area. The authors also wish to thank Emmanuel Chassot,
Loretta Malvorosa and Vicenzo Placenti for preparing part of the empirical data.
36
Appendix A
The nested consumption scheme
Aggregate consumption
Energy
Agro/aquatic product
Agricultural product
Industrial product
Aquatic product
Basic aqua-product
Luxury aqua-product
Raw fish
Species 1…spl
Service
Processed fish
Raw fish
Species 1…sp3,l
Species 1…spb
37
Processed fish
Species 1…sp3,b
Appendix B
The nested production scheme for Agricultural, Energy, Industrial,
or Service producer
Single output per producer
Labour
Intermediate input
Agro&aqua-product
Agro-product
Aqua-product
Capital
EIS product
Energy
38
Industrial
product
Service
Appendix C
The nested production scheme for Fishing producers (the Metiers)
Multiple outputs per activity
Biomass
Production activity by producer
Aqua-product
Labour
Agro-product
Capital
Service
Energy
Industrial product
39
Appendix D
The nested production scheme for Aquaculture or
Fishery processing producer
Single output by the producer
Energy
Industrial product
Service
Capital
Labour
Aqua-product to be consumed
Species 1
……
……
40
……
Species Lf+Bf
Producers
Products
Labour
Capital
Non fisher household
Fisher household
Government
Taxes & subsidies
Foreign
Savings
Total
27816616
12532885
6832203
7657829
7681849 30830
6815281 7641049
16922
16780
4388866
8500259
1315315
8250
6506131
793700
27816616
930721
5181052
4770589 11122
3319207
33928389 6832203 7657829 15771645 41952
41
793700
6506131 6506131 8500259
Total
Savings
Foreign
Taxes & subsidies
Government
Fisher household
Non fisher household
Capital
Labour
Products
The Social
Accounting Matrix
(SAM) for Salerno
Producers
Appendix E: A typical SAM table for Salerno in Italy
27816616
33928389
6832203
7657829
15771645
41952
6506131
6506131
8500259
3319207
4112907
4112907 117674062
793700
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1
For the PECHDEV project funded by the European Commission.
We define the métier as a certain fleet equipped with certain gear and targeting certain species.
3
See Dervis et al (1982) page 483 for an approach based on the Frisch parameter.
2
43
4
We conducted a limited sensitivity analysis by varying the value of elasticity.
44