Fishery EconomicsRenewable ResourcesMotivationSome terms we will useSimple Model of Fish BiologyPut growth and drag togetherInterpreting the growth-stock curve AKA: recruitment-stock; yield-biomass curvesIntroduce harvestingIntroduce humansWill stock grow or shrink with harvest?“Yield-effort curve”Introduce economicsSlide 13Open access resourceIllustration of equilibriaMechanics of solving fishery pblms (with solutions for specific functions)Example: NE Lobster FisheryFishery EconomicsThe role of economics in fishery regulationRenewable ResourcesExamplesFisheries  todayForestsCharacteristicsNatural growthCarrying CapacityMotivation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.pdfSome 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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 limitationsxStock, xttxkPut growth and drag togethertimeBiomass(x)x“CarryingCapacity” (k)xMSYxStock that gives “maximumsustainable yield”GrowthRateInterpreting the growth-stock curveAKA: recruitment-stock; yield-biomass curvesxxGrowth rate of population depends on stock sizelow stock  slow growthhigh stock  slow growthGRdx/dt = g(x)Introduce harvestingxxH1H2H3H1: nonsustainable  extinctionH2: MSY – consistent with stock size XbH3: consistent with two stock sizes, xa and xcxa is stable equilibrium; xc is unstable. Why??xcxbxaGRIntroduce humansHarvest depends on How hard you try (“effort”); stock size; technologyH = E*x*kxkEHxkELxHk = technology “catchability”E = effort (e.g. fishing days)x = biomass or stockHarvest for low effortHarvest for high effortWill 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)Where k*E*x = g(x) (1)andg(x) = H (2)x“Yield-effort curve”H(E)EGives sustainable harvest as a function of effort levelNotice that this looks likerecruitment-stock graph. This is different though it comes from recruitment-stock relation.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$TR=p*H(E)TC=w*EEMC=ACMR$/EEwRentsto thefisheryEOAE*Value of fisherymaximized at E*.Profits attract entryto EOA (open access)Open Access vs.Efficient FisheryAREMSYOpen 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 themIllustration of equilibriaXSustainableCatchMaximum Sustainable Yield (Effort EMSY)Efficient Catch (Effort E*)○○Open Access Catch(Effort EOA)○Note: efficient catchlets biology (stock)do some of the work!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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