1 open access resource economics why the free market fails to protect resources
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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?
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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– With constant growth rate, r: – = rx x=aert
• 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
Stock, x
t
t
xk
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Put growth and drag together
time
Biomass(x)
x
xGrowthRate
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Put growth and drag together
time
Biomass(x)
x
“CarryingCapacity” (k)xGrowth
Rate
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Put growth and drag together
time
Biomass(x)
xxMSY
x
Stock that gives “maximumsustainable yield”
GrowthRate
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Put growth and drag together
time
Biomass(x)
xxMSY
x
Stock that gives “maximumsustainable yield”
GrowthRate
Should we want MSY?
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Interpreting the growth-stock curveAKA: recruitment-stock; yield-biomass curves
x
xGrowth rate of population depends on stock size
low stock slow growthhigh stock slow growth
GR
dx/dt = g(x)
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Introduce harvesting
x
xH1
H2
H3
H1: nonsustainable extinctionH2: MSY – consistent with stock size Xb
H3: consistent with two stock sizes, xa and xc
xa is stable equilibrium; xc is unstable. Why??
xc xbxa
GR
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Introduce humans
• Harvest depends on – How hard you try (“effort”); stock size; technology– H = E*x*k
x
kEHx
kELx
H
k = technology “catchability”E = effort (e.g. fishing days)x = biomass or stock
Harvest for low effort
Harvest for high effort
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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?
• 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)
k*E*x = g(x) (1) H(E) = g(x) (2)
x
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“Yield-effort curve”
H(E)
E
Gives sustainable harvest as a function of effort level
Notice that this looks likerecruitment-stock graph. This is different though it comes from recruitment-stock relation.
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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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$
TR=p*H(E)
TC=w*E
E
MC=AC
MR$/E
E
w
EOA
AR
EMSY
Two outcomes: Open Access vs. Efficient
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$
TR=p*H(E)
TC=w*E
E
MC=AC
MR$/E
E
w
Rentsto thefishery
E*
AR
EMSY
Two outcomes: Open Access vs. Efficient
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$
TR=p*H(E)
TC=w*E
E
MC=AC
MR$/E
E
w
Rentsto thefishery
EOAE*
Value of fisherymaximized at E*.Profits attract entryto EOA (open access)
AR
EMSY
Two outcomes: Open Access vs. Efficient
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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
X
SustainableCatch
Maximum Sustainable Yield (Effort EMSY)
Efficient Catch (Effort E*)○
○
Open Access Catch(Effort EOA)
○
Note: efficient catchlets biology (stock)do some of the work!
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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.