Slide 1Static-efficient sustained yieldAssumptions, part 1:Slide 4Slide 5Start with yield-effort relationship (Kahn, Figure 10.6)Slide 7Step 3: compute total revenueStep 4: add total cost to find E*Summary of static-efficient sustained yield modelApplication #1: Technology changeCost-reducing technology effort increases, catch rises, population fallsApplication #2: open accessOpen accessAGEC/FNR 406 LECTURE 27 Fisheries, Part IIStatic-efficient sustained yield Gordon model (simplest approach)Goal: determine a catch level that provides the largest net benefitSolution: find output level where marginal cost and marginal benefit are equal (i.e. where the distance between total revenue and total cost is at a maximum)Assumptions, part 1:Benefits:Benefit determined by total revenue: TR = P * QP = PriceMarket price reflects value to societyPrice per unit of catch is constant (fishery represents small portion of the overall market)Q = QuantityCatch per unit of fishing effort is proportional to populationCosts:Cost determined by total cost: TC = FC + VC(But here we ignore fixed cost (FC) which is a “sunk” cost)Variable cost (VC) determined by “fishing effort” VC = labor + equipment + fuel + depreciation, etc. Total cost proportional to effort.For given amount of effort, yield (Y) is proportional to population (X)Assumptions, part 2:1. Map the effort-catch relationship2. Convert sustainable yield function to effort-based relationship3. Create total revenue (benefit) function by multiplying catch*price4. Combine total revenue and total cost to find optimal level of effort (MB=MC)Four steps required:Start with yield-effort relationship(Kahn, Figure 10.6)Fish population (X)Catch (C)YE3YE1YE2E3 > E2 > E1Catch rises with effort and pop.Step 1: map pop & effort into catchStep 2: effort and sustainable yieldE2C2Fishing effort (E)Catch (C)C1E1E3C3As effort increases…catch rises then falls.Why? Higher catch reduces pop growth.Compare with Logistic Growth Function(Kahn, figure 10.1)Same shape, but x-axis is reversedKX2G2Fish population (X) increasing Growth of population (G)G1X1Effort (E) increasingStep 3: compute total revenue Total Revenue = Catch x PriceFishing effort (E)Catch (C)E2C2C1E1E3C3TRStep 4: add total cost to find E* Total Revenue = Catch x PriceCatch (C)TCFishing effort (E)E* C*TR}TR-TCSummary of static-efficient sustained yield modelEfficient catch occurs where MC = MRMC is slope of cost curveMR is slope of revenue curveObservationsEfficient catch less than maximum sustainable catch(exception is where MC = 0)Efficient catch leads to larger population level than maximum sustainable catch.Application #1: Technology changeRead “The Fish Crisis”Impact of better fishing technology? Drives down the cost of fishing. Impact on level of catch? Impact on population?Cost-reducing technology effort increases, catch rises, population falls Fishing effort (E)Catch (C)E* C*TRTCE** C**Application #2: open accessWhat does “open access” mean?Fishery open to all who “can afford to fish”Someone can afford to fish as long as TR equals or exceeds TCMaximum total effort is where TC = TREconomic rent (profit) dissipated at this pointThis level of effort is greater than efficient level where MC = MR(Relate “Fishy Economics” to the graph)Open access As long as TR>TC, new fishermen enter fishery…Result: effort increases, catch falls, population fallsCatch (C)TCFishing effort (E)E* C*TRTR =TCE**