introduction to bioeconomic models for fishery - the schaefer-gordon model

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

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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

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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

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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

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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

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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

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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

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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

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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 . . .

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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 . . .

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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 . . .

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The biological productivity curve

The Basic Biological Model . . . The Basic Biological Model . . .

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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

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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 ...

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F = qf (6)

q = catchability coefficient;

= represents the state of technical efficiency

The Fishing Effort ...

» Both nominal and effective efforts are

related by

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Y = qfP (7)

The Fishing Effort ….

» Using nominal effort we can define yield

equation for short-run as

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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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Short-run yield with diminishing returns to population

Diminishing returns to population size

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Y = qPf (8)

This gives a short-run yield equation as

Where 0 << 1

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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)

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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)

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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 . . .

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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 . . .

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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)

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Cost as a function of fishing effort

The Economics of

Fishing - CostTCf = cf

ACf = MCf

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The Bioeconomic Equilibrium The Bioeconomic Equilibrium

The open-access equilibrium

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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 . . .

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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 . . .

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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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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)

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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)

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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 )

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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