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May 2000
INTRODUCTION TO BIOECONOMIC MODELS
FOR FISHERY -THE SCHAEFER-GORDON
MODEL
INTRODUCTION TO BIOECONOMIC MODELS
FOR FISHERY -THE SCHAEFER-GORDON
MODEL
Dr. Mahfuzuddin Ahmed
International Center for Living Aquatic Resources Management
Dr. Mahfuzuddin Ahmed
International Center for Living Aquatic Resources Management
May 2000
What is a Fishery? What is a Fishery?
Fishery is a stock or stocks
of fish and the enterprises
that have the potential of
exploiting them
May 2000
Fish Stock and Fishery Management 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
May 2000
Syndrome of Overexploitation Syndrome of Overexploitation
Both biological and economic
overexploitationFailure of market (under
unrestricted access) from optimally
allocating fishery resources
Unclear property rights regime
May 2000
Syndrome of Overexploitation . . . 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
ecologically based externalities
techno-ecological externalities
May 2000
Developing Country Syndrome 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
May 2000
Fishery Management 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
May 2000
Fishery Management . . . 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
May 2000
Bioeconomic Model 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
May 2000
The Basic Biological Model The Basic Biological Model
• Single fish stock
• Stock growth over time (logistic growth)
• Model
Assumptions
G = dP = f(P)dt (1
)
G = growth
P = initial population
May 2000
The growth of population is proportional to
initial population, i.e.,
G = aP (2)
a = intrinsic growth
The Basic Biological Model . . . The Basic Biological Model . . .
May 2000
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)
The Basic Biological Model . . . The Basic Biological Model . . .
May 2000
Maximum growth occurs when population
size is half of ECC, i.e.,
G’ = a(1 - 2P) = 0 K
(4)
Hence,
P = K/2
The Basic Biological Model . . . The Basic Biological Model . . .
May 2000
The biological productivity curve
The Basic Biological Model . . . The Basic Biological Model . . .
May 2000
The Effect of Fishing: the Short-RunThe Effect of Fishing: the Short-Run
Y = y (P,f) (5)
Y = yield
f = fishing effort
Once fishing is introduced yield or catch at
any period will depend on
size of fish population
amount of fishing effort
May 2000
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
The Fishing Effort
May 2000
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
The Fishing Effort ...
May 2000
F = qf (6)
q = catchability coefficient;
= represents the state of technical efficiency
The Fishing Effort ...
» Both nominal and effective efforts are
related by
May 2000
Y = qfP (7)
The Fishing Effort ….
» Using nominal effort we can define yield
equation for short-run as
May 2000
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
May 2000
Short-run yield with diminishing returns to population
Diminishing returns to population size
May 2000
Y = qPf (8)
This gives a short-run yield equation as
Where 0 << 1
May 2000
Y = qfP (9)
Diminishing Returns to Nominal Effort
Short-run yield with diminishing returns to nominal effort
- upper limit to yield in the short run
May 2000
G = aP(1-P)-qfP K
(10)
The Long-Run Equilibrium in a Fishery
G = aP[(K-P)/k]
= aP(1 - P)
K
(3)
Y = qfP
We obtain
Combining biological production with the yield function
(9)
May 2000
The impact of fishing on the population size
The Long-Run EquilibriumThe Long-Run Equilibrium
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
May 2000
The Long-Run Equilibrium
….
The Long-Run Equilibrium
….
P = K(1-qf)a (11)
To find equilibrium let us set equation (10) to zero which gives
May 2000
The Long-Run Equilibrium . . . The Long-Run Equilibrium . . .
(11)
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)
P = K(1-qf) a
Y = qfP (9)
May 2000
Ys = Kfqqf) a
If = 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.
These give us
(12)
The Long-Run Equilibrium . . . The Long-Run Equilibrium . . .
May 2000
The Long-Run Equilibrium . . . The Long-Run Equilibrium . . .
Sustainable yield curves
The greater are diminishing returns (lower ) the longer it takes to reach a maximum
The relationship between biological productivity curve and sustainable yield curve for various values of (0 < < 1) is shown by
May 2000
Setting equation (12) to zero and solving for f gives
fmax = (a/q) 1/ (13)
- can be referred to as the effort that reduces
sustainable yield to zero (extinction of stock)
The Long-Run Equilibrium . . . The Long-Run Equilibrium . . .
May 2000
fmsy = (a/2q) 1/ (14)
If = 1, MSY is half of fmax
MSY - Differentiate (13) with respect to
effort and set it to zero
In general, fmsy = (1/2)1/fmax(15)
The Long-Run Equilibrium . . . The Long-Run Equilibrium . . .
May 2000
Revenue as a function of fishing effort
The Economics of
Fishing - Revenue
May 2000
Long-run total revenue
functionTRf = pYs
TRf = pKqf(1-qf)
a
Which is a function of f
(18)
Which by substitution from equation (12) gives
ARf = TRf
f
MRf = d(TRf)
df
(17)
(16)
May 2000
Cost as a function of fishing effort
The Economics of
Fishing - CostTCf = cf
ACf = MCf
May 2000
The Bioeconomic Equilibrium The Bioeconomic Equilibrium
The open-access equilibrium
May 2000
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
Model Limitations Model Limitations
May 2000
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.
Model Limitations . . . Model Limitations . . .
May 2000
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.
Model Limitations . . . Model Limitations . . .
May 2000
Other Models
1. Dynamic Bioeconomic Model (Smith)
2. Yield-Mortality Models
- exponential
- precautionary
3. Age Structured Bioeconomic
Model
4. Intertemporal Analysis
May 2000
Other considerations for extension of
bioeconomic models
1. Ecological and technological
interdependence
2. Social and institutional factors
May 2000
THANK YOU!THANK YOU!
May 2000
Overview of Models Overview of Models
Differing impacts of diminishing returns to nominal effort on sustainable yield
May 2000
Overview of Models Overview of Models
The impact of fishing when diminishing returns to population are present
May 2000
Overview of Models Overview of Models
The sustainable yield curve when diminishing returns to population are present
May 2000
Overview of Models Overview of Models
The effect of shifting revenue curves on the open-access equilibrium
May 2000
Overview of Models Overview of Models
Fundamental relationship between catch, effort and costs in a fishery
May 2000
Overview of Models Overview of Models
Market equilibrium of fishery sector in a supply-demand model
May 2000
Overview of Models Overview of Models
Gordon-Schaefer Model
Sustainable a) biomass, b) yield and c) total sustainable revenues (TSR) and costs (TC).
May 2000
Overview of Models Overview of Models
Population logistic growth model for K = 3.5 million tonnes and r = 0.36
May 2000
Overview of Models 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
May 2000
Gulf of Thailand Gulf of Thailand
Market equilibrium of fishery sector in a supply-demand model
Demersal catch and Catch per unit effort(CPUE),1966-1995
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
year
tons
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00kg/hr
Demersal Catch (tons)
CPUE (kg/hr)
May 2000
Gulf of Thailand Gulf of ThailandCatch per unit effort(CPUE) (kg/hr)and Standard fishing
effort, 1966-1995
0
20
40
60
80
100
120
140
160
Standard fishing effort (St hrx10^6)
CPUE(kg/hr)
May 2000
Gulf of Thailand Gulf of Thailand
Fig.1 Fixed price model applied to demersal fisheries (demersal fish including trash fish) in the Gulf of Thailand
MSY
MEYActual (1995)
61.0856.8827.7821.18
TC = c.fi
4,612
TR = P.Y
6,4156,201
4,259 Open access
0Standard fishing efforts (St hr x 106)
Reve
nu
es
& C
ost
s (B
ah
ts x
10
6 )
May 2000
Gulf of Thailand Gulf of Thailand
Comparison of catch, revenues, costs and profits at differentlevels of effort based on a fixed price model and 1966-
1995 data, Gulf of Thailand.
Items Effort(St hr x 106)
Catch(Tonsx 103)
Revenues(Bahts x 106)
Costs(Bahtsx 106)
Profits(Bahtsx 106)
MSY 22.78 959 6,415 1,937 4,478MEY 21.18 927 6,201 1,477 4,724
Open assess 61.08 637 4,259 4,259 0Actual (1995) 56.88 690 4,612 3,966 347