INTRODUCTION TO BIOECONOMIC MODELS

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INTRODUCTION TO BIOECONOMIC MODELS FOR FISHERY
- THE SCHAEFER-GORDON MODEL
Dr. Mahfuzuddin Ahmed International Center for
Living Aquatic Resources Management
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What is a Fishery?
Fishery is a stock or stocks of fish and the
enterprises that have the potential of exploiting
them
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Fish Stock and Fishery Management
Influence of socioeconomic and institutional
factors
A complex process of integration of resource
biology and ecology
Behavior of fishers and policymakers
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Syndrome of Overexploitation
Both biological and economic overexploitation
Failure of market (under unrestricted access)
from optimally allocating fishery resources
Unclear property rights regime
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Syndrome of Overexploitation . . .

• Conflicting interest over rights and duties can
  lead to fisheries collapse

• Generate externalities between resource-users
  (Seijo et al 1998)

? stock externalities ? crowding
externalities ? technological externalities ? ecol
ogically based externalities ? techno-ecological
externalities
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Developing Country Syndrome

• High exclusion cost
• Social trap and the free rider behavior
• High transaction cost

? information cost ? enforcement
cost ? contractual cost

• Inadequate legal and institutional framework

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Fishery Management

• Decisionmaking aiming at a sustainable management
  of fish stocks
• Biological, ecological, economic, social and
  legal analysis
• Identify and quantify the objectives and goals of
  management
• Select appropriate combination of performance
  variables and determine the control variable

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Fishery Management . . .

• Determine alternative management strategies and
  implementation mechanism
• Monitor and evaluate the impacts of alternative
  management strategies and plans
• Revise and redo plans, if necessary

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Bioeconomic Model

• Assumes allocation of property rights as a way to
  mitigate risks of stock overexploitation
• Bioeconomic Model allows the evaluation of the
  fishery in biological, economic and ecological
  sense
• Provide an optimal allocation of efforts and
  output and help achieve the desired level of
  performance criteria

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The Basic Biological Model
Assumptions

• Single fish stock
• Stock growth over time (logistic growth)
• Model

G dP f(P) dt
(1)
G growth P initial population
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The Basic Biological Model . . .
The growth of population is proportional to
initial population, i.e.,
G aP
(2)
a intrinsic growth
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The Basic Biological Model . . .
There must be a maximum size of population that
can be supported. It is called Environmental
Carrying Capacity (ECC) denoted by K. Hence,
G aP(K-P)/k aP(1 - P) K
(3)
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The Basic Biological Model . . .
Maximum growth occurs when population size is
half of ECC, i.e.,
G a(1 - 2P) 0 K
Hence,
P K/2
(4)
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The Basic Biological Model . . .

The biological productivity curve
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The Effect of Fishing the Short-Run
Once fishing is introduced yield or catch at any
period will depend on

• size of fish population
• amount of fishing effort

(5)
Y y (P,f)
Y yield f fishing effort
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The Fishing Effort
Economic measure

• boat, gear, crew and other inputs required for
  fishing
• called as nominal effort (f) and is calculated by
  using standardized measure such as
  vessel-ton-days

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The Fishing Effort ...
Biological measure

• Effective effort (F) the fraction of the average
  population taken by fishing
• F is often calculated as the negative of natural
  logarithm of proportion of fish surviving fishing
  in a year

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The Fishing Effort ...

• Both nominal and effective efforts are related by

F qf
(6)

q catchability coefficient represents
the state of technical efficiency
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The Fishing Effort .

• Using nominal effort we can define yield
  equation for short-run as

(7)
Y qfP
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Yield and population size

Short-run yield as a function of population size

• for a given level of nominal effort, yield will
  vary with population size

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Diminishing returns to population size

Short-run yield with diminishing returns to
population
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This gives a short-run yield equation as
Y qPfa
(8)

Where 0 lt alt 1
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Diminishing Returns to Nominal Effort
- upper limit to yield in the short run
(9)
Y qfbP

Short-run yield with diminishing returns to
nominal effort
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The Long-Run Equilibrium in a Fishery
Combining biological production with the yield
function
G aP(K-P)/k aP(1 - P) K
Y qfbP
(3)
(9)

We obtain
G aP(1-P)-qfbP K
(10)
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The Long-Run Equilibrium

The impact of fishing on the population size
For an effort level f1, a population P2 and a
yield of Y2 may be sustained into the long run,
because yield from fishing, Y2 will be balanced
by the growth of stock. G2
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The Long-Run Equilibrium .
To find equilibrium let us set equation (10) to
zero which gives

P K(1-qfb) a
(11)
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The Long-Run Equilibrium . . .
For the chosen effort level, equation (11) tells
us the sustainable population Different effort
levels will produce different sustainable
yield We can now derive a sustainable yield
function by using equations (9) and (11)

(11)
P K(1-qfb) a
Y qfbP (9)
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The Long-Run Equilibrium . . .
These give us
(12)
Ys Kfqb (1-qfb) a

If b 1, sustainable yield is a simple quadratic
function of effort. In this case the sustainable
yield curve will simply be the mirror image of
the biological productivity curve.
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The Long-Run Equilibrium . . .
The relationship between biological productivity
curve and sustainable yield curve for various
values of b (0 lt b lt 1) is shown by

Sustainable yield curves
The greater are diminishing returns (lower b )
the longer it takes to reach a maximum
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The Long-Run Equilibrium . . .
Setting equation (12) to zero and solving for f
gives
(13)
fmax (a/q) 1/b
- can be referred to as the effort that reduces
sustainable yield to zero (extinction of stock)
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The Long-Run Equilibrium . . .
MSY - Differentiate (13) with respect to effort
and set it to zero
(14)
fmsy (a/2q) 1/b
If b 1, MSY is half of fmax
In general, fmsy (1/2)1/bfmax
(15)
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The Economics of Fishing - Revenue

Revenue as a function of fishing effort
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Long-run total revenue function
TRf pYs
Which by substitution from equation (12) gives
TRf pKqfb(1-qfb) a
(16)
Which is a function of f
ARf TRf f
(17)
MRf d(TRf) df
(18)
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The Economics of Fishing - Cost
TCf cf
ACf MCf

Cost as a function of fishing effort
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The Bioeconomic Equilibrium

The open-access equilibrium
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Model Limitations
1. All processes affecting stock productivity
(e.g. growth, mortality and recruitment) are
subsumed in the effective relationship between
effort and catch. 2. The catchability coefficient
q is not always constant, and may differ due to
e.g. different aggregation behavior of pelagic
and sedentary resources. - factors related to
differential gear selectivity by age/lengths are
not taken into account
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Model Limitations . . .
3. CPUE is not always an unbiased index of
abundance. - relevant to sedentary resources with
patchy distribution and without the capacity of
redistribution in the fishing ground once fishing
effort is exerted - sequential depletion of
patches also determines a patchy distribution of
resource users, precluding model applicability
4. Variations in spatial distribution of the
stock are usually ignored, as well as the
biological processes that generate biomass, the
intra/interspecific interactions, and stochastic
fluctuations in the environment and in population
abundance.
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Model Limitations . . .
5. Ecological and technological interdependencies
and differential allocation of fishing effort in
the short term are not usually taken into
account. 6. Improvement in technology and fishing
power determines that q often varies through
time. 7. It becomes difficult to distinguish
whether population fluctuations are due to
fishing pressure or natural processes. - in some
fisheries, fishing effort could be exerted at
levels greater than twice the optimum.
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Other Models
1. Dynamic Bioeconomic Model (Smith) 2.
Yield-Mortality Models - exponential -
precautionary
3. Age Structured Bioeconomic Model 4.
Intertemporal Analysis
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Other considerations for extension of bioeconomic
models 1. Ecological and technological
interdependence 2. Social and institutional
factors
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Overview of Models

Differing impacts of diminishing returns to
nominal effort on sustainable yield
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Overview of Models

The impact of fishing when diminishing returns to
population are present
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Overview of Models

The sustainable yield curve when diminishing
returns to population are present
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Overview of Models

The effect of shifting revenue curves on the
open-access equilibrium
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Overview of Models
Fundamental relationship between catch, effort
and costs in a fishery
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Overview of Models

Market equilibrium of fishery sector in a
supply-demand model
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Overview of Models
Gordon-Schaefer Model
Sustainable a) biomass, b) yield and c) total
sustainable revenues (TSR) and costs (TC).
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Overview of Models
Population logistic growth model for K 3.5
million tonnes and r 0.36
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Overview of Models
Open access regime. A) Sustainable average and
marginal yields b) average and marginal costs
and revenues, as a function of effort under open
access conditions
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Gulf of Thailand

Market equilibrium of fishery sector in a
supply-demand model
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Gulf of Thailand

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Gulf of Thailand

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Gulf of Thailand