1
Handout November 2005
Natural resources
Finn R. Førsund
Fishery economics
Jens Warming 1911:
Topics:
1. Consequences of open access to fishing grounds (same fish) of different qualities
(i.e. different unit costs of catch).
Warming’s points:
•
misallocation of effort
•
most productive ground turned into most wasteful effort
•
biological overexploitation may occur at low cost of effort
•
biological regulation, e.g. closed season, restriction on gear, may prevent
overexploitation, but not economic overexploitation.
2. Regulation of fishery:
•
max MSY will not maximise total rent
•
the economic optimum. Level of effort at point where marginal revenue equals
marginal cost
•
optimal tax: difference between average and marginal revenue.
3. Warmings implicit model:
xi  fi ( Li ), i  A, B
(1)
where xi = catch at ground i, Li = labour employed at ground i.
Gear costs:
Ci  cLi , i  A, B
(2)
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Assumptions:
Fish price 1, cost coefficient c independent of grounds (may be generalised),
alternative employment (e.g. land-based industries) at market wage rate w.
Private equilibrium:
A fisherman decides whether to fish or be employed. Point of indifference:
fi ( Li )  cLi  wLi 
xi
 c  w, i  A, B
Li
(3)
The net wage earned at each ground should be equal to the market wage.
Maximum Sustainable Yield (MSY) catch: xMSY in figure 1 of biological growth.
dS/dt
xMSY
S
S
min
S
MSY
S
max
Figure 1. Fish growth curve
By assumption:
x AMSY
xBMSY

c

c
LMSY
LMSY
A
B
Warming’s concept of exploitation:
If MSY catch is defined as biological optimal equilibrium, then the best fishing
ground A will be over exploited if market wage is lower than the net wage from
fishing MSY at ground A, and fishing ground B will be under exploited if market
(4)
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wage is higher than net wage from fishing MSY at ground B. Depending on the
market wage fishing grounds may be both over- and under exploited according to
MSY, i.e. we may have catch both to the left and right of MSY stock..
Economic steady state optimum
Social planning problem:
MaxLA LB   {xA  xB  w( LA  LB )  c( LA  LB )} 
{ f ( LA )  f ( LB )  ( w  c)( LA  LB )}
(5)
Necessary first order condition:
f A '  fB '  w  c
(6)
The marginal net wage should be equal at each fishing ground and equal to the
alternative market wage. As Warming said it without explicit model:
“Marginal productivity is equal to that of other occupations, i.e. that the lastemployed worker increases the total yield by the same amount as he could have
earned elsewhere” (p.394).
Optimal tax to achieve MSY:
Payment for fishing license:
Difference between yield per man at MSY and wages plus gear costs per man:
t 
i
fi ( LMSY
)
i
LMSY
i
 ( w  c), i  A, B
(7)
Inserting in the private equilibrium condition:
fi ( Li )  cLi  t i  wLi ,
fi ( LMSY
)
fi ( Li )
i
 c  MSY
 wc  w
Li
Li
 Li  LMSY
i
(8)