The economics of fishery management
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Transcript The economics of fishery management
Fishery Economics
The role of economics in fishery
regulation
Renewable Resources
Examples
Fisheries today
Forests
Characteristics
Natural growth
Carrying Capacity
Motivation
Group Project: Otters eating lots of
shellfish, south of Pt. Conception. Marine
Fisheries Service considering removing
otters, and you are doing a CBA on the
policy. What is the damage the otters are
causing and thus the value of restricting
them to the north of Pt. Conception?
See
http://www.bren.ucsb.edu/research/2001Gro
up_Projects/Final_Docs/otters_final.pdf
Some terms we will use
Stock – total amount of critters -- biomass
Natural growth rate (recruitment) – biologic
term
Harvest – how many are extracted (flow)
Effort – how hard fisherman try to harvest
(economic term)
Simple Model of Fish
Biology
Exponential growth
Stock, x
With constant growth rate, r:
= rx x=aert
t
Crowding/congestion/food limits (drag)
Carrying capacity: point, k, where stock
cannot grow anymore: x ≤ k
As we approach k, “drag” on system
keeps us from going further
Resource limitations, spawning location
limitations
k
x
t
Put growth and drag
together
Biomass
(x)
Growth
Rate
time
“Carrying
Capacity” (k)
xMSY
Stock that gives “maximum
sustainable yield”
x
Interpreting the growth-stock curve
AKA: recruitment-stock; yield-biomass curves
GR
Growth rate of population
depends on stock size
low stock slow growth
high stock slow growth
dx/dt = g(x)
x
Introduce harvesting
H1
GR
H2
H3
xc
xb
xa
x
H1: nonsustainable extinction
H2: MSY – consistent with stock size Xb
H3: consistent with two stock sizes, xa and xc
xa is stable equilibrium; xc is unstable. Why??
Introduce humans
Harvest depends on
H
How hard you try (“effort”); stock size; technology
H = E*x*k
k = technology “catchability”
E = effort (e.g. fishing days)
x = biomass or stock
Harvest for high effort
kEHx
kELx
Harvest for low effort
x
Will stock grow or shrink
with harvest?
If more fish are harvested than grow, population
shrinks.
If more fish grow than are harvested, population grows.
For any given E and k, what harvest level is just
sustainable?
Where k*E*x = g(x) (1)
and
g(x) = H
(2)
This can be solved for the sustainable harvest level as
a function of E: H(E)
Solve (1) first for x(E)
Substitute into (2) to get H(E)
“Yield-effort curve”
H(E)
Gives sustainable harvest
as a function of effort level
Notice that this looks like
recruitment-stock graph. This
is different though it comes
from recruitment-stock relation.
E
Introduce economics
Costs of harvesting effort
TC = w•E
• w is the cost per unit effort
Revenues from harvesting
TR = p•H(E)
• p is the price per unit harvest
Draw the picture
Rents
to the
fishery
Open Access vs.
Efficient Fishery
TC=w*E
$
TR=p*H(E)
E
$/E
Value of fishery
maximized at E*.
Profits attract entry
to EOA (open access)
MR
w
AR
MC=AC
E* EMSY EOA
E
Open access resource
Economic profit: when revenues exceed costs (not
accounting profit)
Open access creates externality of entry.
Entrants pay AC, get AR (should get MR<AR)
So fishers enter until AR = AC ( TR = TC)
But even open access is sustainable
I’m making profit, that attracts you, you harvest fish,
stock declines, profits decline.
Though not socially desirable
What is social value of fish caught in open access
fishery?
Zero: total value of fish = total cost of catching them
Illustration of equilibria
Maximum Sustainable Yield (Effort EMSY)
Sustainable
Catch
○
○
○
Open Access Catch
(Effort EOA)
Efficient Catch (Effort E*)
Note: efficient catch
lets biology (stock)
do some of the work!
X
Mechanics of solving fishery pblms
(with solutions for specific functions)
Start with biological mechanics:
G(X) = aX – bX2 [G, growth; X stock]
Harvest depends on effort: H=qEX
Sustainable harvest when G(X) = H
First compute X as a function of E
Then substitute for X in harvest equation to yield H(E) which will
depend on E only
Costs: TC = c E
Total Revenue TR=p*H(E) where p is price of fish
Open access: find E where TC=TR
Efficient access: find E where
Marginal revenue from effort (dTR/dE) equals
Marginal cost (cost per unit of effort)
Example: NE Lobster Fishery
Bell (1972) used data to determine catch (lb. lobsters)
per unit of effort (# traps), using 1966 data
Price is perfectly elastic at $0.762/lb.
Average cost of effort: $21.43 per trap
Open access equilibrium: TC = TR
E=891,000 traps; H=25 million lbs.
Compare to actual data: E=947,000;H=25.6 million lbs.
Maximum Sustainable Yield
H(E) = 49.4 E - 0.000024E2
E=1,000,000 traps; H=25.5 million lbs.
Efficient equilibrium
E=443,000 traps; H=17.2 million lbs.