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
References Amstrong, C. P. (2007), ‘A note on the ecological-economic modeling of marine reserves in fisheries’, Ecological Economics 62, 242-250. Böhringer, C. and A. Löschel (2006), ‘Computable general equilibrium models for sustainability impact assessment: Status quo and prospects’, Ecological Economics 60, pp. 49-64. Chumacero, R.A. and K. Schmidt-Hebbel (2005), ‘General equilibrium models: an overview’, in Chumacero, R.A. and K. Schmidt-Hebbel (eds.), General Equilibrium
Models for the Chilean Economy, Santiago, Central Bank of Chile. Conrad, K. (1999), ‘Computable general equilibrium models for environmental economics and policy analysis’, in van den Bergh, J.C.J.M. (eds), Handbook of
Environmental and Resource Economics 2002, Edward Elgar, Cheltenham, pp. 10601088. Conrad, K. (2001), ‘Computable general equilibrium models in environmental and resource economics’, in Tietenberg, T. and H. Folmer (eds), The International Yearbook
of Environmental and Resource Economics 2002/2003, pp. 66-114. Dervis, K., J. De Melo and S. Robinson (1982), General Equilibrium Models for
Development Policy, New York: Cambridge University Press. Devarajan, S. and S. Robinson (2002), ‘The influence of computable general equilibrium models on policy analysis’, TMD discussion paper No. 98, IFPRI. Eichner, T. and R. Pethig (2007), ‘Harvesting in an integrated general equilibrium model’,
Environmental and Resource Economics 37, pp. 233-252. Failler, P. and H. Pan (2007), ‘Global value, full value, societal costs; capturing the true cost of destroying the marine ecosystems’, Social Science Information 46 No. 1, special issue. FAO Fisheries and Aquaculture Department (2007), The State of World Fisheries and
Aquaculture 2006, Rome, FAO publications.
42
Finnoff, D. and J. Tschirhart (2005), ‘Linking dynamic economic and ecological general equilibrium models’, Working paper, University of Wyoming. Gordon, H. S. (1954), ‘The economic theory of a common-property resource: the fishery’,
Journal of Political Economy, 62, pp. 124-42. PECHDEV final Report (2007), "A Computable General Equilibrium (CGE) Model in
Fisheries: Policy Analysis with Evidence from Five European Regions", Failler, P. (ed.), EU Funded RTD Project 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. Quinn, T. J. and R. B. Deriso (1999), Quantitative Fish Dynamics, Oxford University Press. Schaefer, M. B. (1957), ‘Some considerations of population dynamics and economics in relation to the management of the commercial marine fisheries’, Journal of the Fisheries
Research Board of Canada, 14, pp. 669-81. Seung, C. K. and E. C. Waters (2006), ‘A review of regional economic models for fisheries management in the U.S.’, Marine Resource Economics 21, No. 1. Thorpe, A., C. Reid, R. van Anrooy and C. Brugere (2005), ‘When fisheries influence national policy-making: an analysis of national development strategies of major fish producing nations in the developing world’, Marine Policy 29, No. 3, 211-222. Thorpe A., D. Whitmarsh and P. Failler (2007), The Situation in World Fisheries, UNESCO-EOLSS, article # 5-05-05-04, http://www.eolss.net.
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
