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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.