Open access resource economics
Why the free market fails to protect
resources
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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/2001Group_Projects/Final
_Docs/otters_final.pdf
• Value of reforming management of spiny lobster fishery?
Abalone fishery?
• Value of “rationalizing” open access fisheries in Mexico?
2
Examples
• Worm et al, Science, 2006: All fisheries could
collapse by 2048
• Costello et al, Science, 2008: Fisheries that use
market-based regulation don’t collapse
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Some terms we will use
• Stock – total amount of critters -- biomass
• Intrinsic growth rate (recruitment) – biologic
term
• Harvest – how many are extracted (flow)
• Effort – how hard fisherman try to harvest
(economic term)
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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
5
Put growth and drag together
Biomass
(x)
Growth
Rate
time
x
6
Put growth and drag together
Biomass
(x)
Growth
Rate
time
“Carrying
Capacity” (k)
x
7
Put growth and drag together
Biomass
(x)
Growth
Rate
time
xMSY
Stock that gives “maximum
sustainable yield”
x
8
Put growth and drag together
Should we want MSY?
Biomass
(x)
Growth
Rate
time
xMSY
Stock that gives “maximum
sustainable yield”
x
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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
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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??
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Introduce humans
• Harvest depends on
– How hard you try (“effort”); stock size; technology
– H = E*x*k
H
k = technology “catchability”
E = effort (e.g. fishing days)
x = biomass or stock
Harvest for high effort
kEHx
kELx
Harvest for low effort
x
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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?
k*E*x = g(x)
 H(E) = g(x)
(1)
(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)
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“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
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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
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Two outcomes: Open Access vs. Efficient
TC=w*E
$
TR=p*H(E)
E
$/E
MR
AR
w
MC=AC
EMSY
EOA
E
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Two outcomes: Open Access vs. Efficient
Rents
to the
fishery
TC=w*E
$
TR=p*H(E)
E
$/E
MR
AR
w
MC=AC
E* EMSY
E
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Two outcomes: Open Access vs. Efficient
Rents
to the
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
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Open access resource
• Economic profit: when revenues exceed costs (not
accounting profit)
• Open access creates externality of entry.
– I’m making profit, that attracts you, you harvest fish,
stock declines, profits decline.
• Entrants pay AC, get AR (should get MR<AR)
– So fishers enter until AR = AC ( TR = TC)
• But even open access is sustainable
– 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
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Illustration of steady state outcomes
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
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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)
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Example: NE Lobster Fishery
• Bell (1972) used data to determine catch (lb. lobsters) per unit
of effort (# traps), using 1966 data
– H(E) = 49.4 E - 0.000024E2
• 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
– E=1,000,000 traps; H=25.5 million lbs.
• Efficient equilibrium
– E=443,000 traps; H=17.2 million lbs.
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