Lecture 6

Fishery Dynamics and Management

Byeong-Hak Choe

bchoe@geneseo.edu

SUNY Geneseo

October 7, 2026

🐟 Fishery Dynamics

Guiding question: How do biological growth and fishing change the stock, sustainable catch, and annual net benefit?

Plan approximately 1.5 classes (75 minutes): stock accounting (7 minutes); growth, carrying capacity, low-stock risk, and MSY (13); the simple growth rule, effort, and harvest intersections (12); the stock calculations and four time paths (12); the sustainable-catch/effort graph and transition to steady outcomes (9); annual revenue, cost, and the biological/economic targets (17); checks and a buffer (5). Use the first 50-minute meeting for biology and stock adjustment. Continue through the annual revenue/cost comparison in the first half of the next meeting, then start Fishery Management.

Use stock accounting and H=qES as the main equations. For the numerical example, evaluate the supplied growth rule without deriving the growth function. Ask students to predict each graph reveal. Emphasize that each point on the sustainable-catch curve represents a different maintained stock/effort combination, not the next year along a single stock’s time path.

🐟 A Renewable Resource Stock

• In Lecture 5, extracting a non-renewable resource reduced a fixed stock.
• A fish stock can grow and reproduce, so natural growth changes the problem.
• Harvest today affects both next year’s stock and next year’s catch.
• Our fishing experiment showed the choices. Now we will explain the stock dynamics with graphs.

Core reading: Tietenberg and Lewis, Environmental and Natural Resource Economics, 12th edition (2023), Chapter 17, “Common-Pool Resources: Commercially Valuable Fisheries.” The main diagrams are original ggplot adaptations of Figure 17.2 (printed p. 425), Figure 17.3 (p. 427), Figure 17.4 (p. 428), and Figure 17.5 (p. 429). These are printed page numbers; add 29 for physical PDF pages in the supplied file.

Suggested pacing for 2.5 classes of approximately 50 minutes: Fishery Dynamics, including the annual revenue/cost comparison, takes about 1.5 classes (75 minutes), and Fishery Management takes about one class (50 minutes). The section-divider notes provide the pacing plan. Teach the biology through graph reading without deriving the growth function. Pause at each graph and have students predict the next reveal. Keep the scallop case and EEZ example brief if time is limited.

Figure 17.6 (p. 432) was covered in Lecture 4. Recall its entry/zero-profit result when comparing targets, without repeating the marginal/average-revenue derivation. The emphasis here is biological stock dynamics and sustainable benchmarks. A full discounted optimal-control solution is outside this short lecture.

All numerical examples and plotted parameters are illustrative classroom values, not estimates of an actual fishery. The low-stock-threshold diagram and the simpler effort model use distinct growth specifications, explicitly identified on the slides.

TL, printed pp. 424–426. Emphasize that renewable means capable of regeneration, not guaranteed to recover after any harvest. Refer briefly to Classwork 3 without repeating the experiment or asserting that its fixed growth increment was a realistic biological function.

📦 Stock, Growth, and Harvest

• \(S_t\): fish stock at the start of year \(t\), measured in metric tons.
• \(G(S_t)\): net biological growth during that year, in tons per year.
  • Reproduction and growth of fish, minus natural deaths, before harvest.
  • The current stock \(S_t\) determines net growth, which can be positive, zero, or negative.
• \(H_t\): harvest during that year, in tons per year.

\[ S_{t+1}=S_t+G(S_t)-H_t. \]

TL, pp. 424–426. Annual periods have length one year, so annual growth and harvest flows contribute that year’s tonnage to the stock accounting. Net growth combines reproduction and individual growth minus natural deaths; migration can also affect stock in a particular managed area. The parentheses in G(S_t) mean that net growth depends on the stock, rather than being a fixed number of fish added every year as in our classroom experiment. A positive value adds biomass, a negative value removes biomass even without fishing, and zero means natural additions and losses balance. Subscript t identifies the year; t+1 is the following year. This is a simplified aggregate-biomass model, abstracting from age structure, seasonal timing, and migration between managed areas.

⚠️ Low-Stock Threshold and Carrying Capacity

Minimum viable stock (\(S_{\min}\))

• Below this threshold, net growth is negative.
• A very small population can have difficulty reproducing successfully.
• Even stopping fishing may not be enough for recovery.

Carrying capacity (\(K\))

• The stock the environment can support without fishing.
• At \(K\), natural additions and losses balance: net growth is zero.
• Above \(K\), net growth is negative and the stock shrinks.

A low-stock threshold is a possible risk. Both thresholds and carrying capacity depend on species and conditions.

TL, pp. 425–426. The figure includes a low-stock threshold; do not claim every fish stock has the same positive threshold. Environmental variability and species biology affect recovery. K is the natural equilibrium stock in the absence of harvest: reproduction and individual growth balance natural mortality. At stocks above K, limited food and habitat make natural losses exceed additions, bringing the stock down. Carrying capacity can change with environmental conditions and habitat quality. The next effort diagrams, like the textbook’s Figures 17.3–17.5, will use a simpler baseline without the low-stock threshold. No Allee-effect terminology or cubic-growth equation is required for students.

🌱 Stock, Natural Growth, and MSY

Adapted from TL Figure 17.2, pp. 425–426. The three reveals use the same axes and growth function. First, read the axes: horizontal is biomass stock, vertical is net annual growth. The hump is not the number of fish over time. At S_0, project up to the curve and across to read G(S_0). S_min is the minimum viable stock, and K is the natural equilibrium/carrying-capacity stock.

Second, show movement with no harvest. The sign of G determines the direction of stock change. At K, births and growth balance natural losses. A small disturbance on either side of K leads back toward K, so it is stable. Movement below S_min leads farther down and movement above it leads away toward K, so S_min is unstable. Explain stability in plain language: does a disturbance make the stock return, or move farther away?

Third, add the growth maximum. Maximum sustainable yield, MSY, is the largest annual harvest that can be maintained by matching net growth at the corresponding stock. S_MSY is the stock supporting that growth. The supplied textbook labels its biological growth maximum S-star; we use S_MSY to avoid confusing MSY with an economically optimal stock. At carrying capacity, the stock is large but net growth is zero. Harvest above current growth draws down the stock. A constant quota equal to estimated MSY leaves little protection against negative growth shocks or stock-assessment error.

🎯 Maximum Sustainable Yield: Why It Matters

• Maximum sustainable yield (MSY) is the largest annual catch that can be maintained when harvest matches natural growth.
• It occurs at the stock with the greatest net growth, rather than the largest stock.
• MSY gives a biological reference for comparing harvest levels and stock recovery.
• A catch below MSY can still reduce stock if it exceeds growth at today’s stock.
• The largest catch need not give the largest net benefit, and uncertain growth makes fishing right at MSY risky.

TL, printed pp. 425–428. Refer back to the peak of the preceding growth curve. MSY is an annual flow, while S_MSY is the stock that supports it. Few fish limit reproduction at a small stock, while crowding limits net growth at a large stock. Harvest must match actual growth at the maintained stock for that catch to be sustainable. MSY is a biological reference, not a guarantee that a fixed quota of that size is safe at every starting stock or under every environmental condition. Cost and price determine which sustainable outcome gives the largest economic net benefit.

Do not attach the later numerical values S_MSY=50 and MSY=10 to the preceding low-stock-threshold graph. Those values belong to the simpler logistic model introduced next. Keep this slide conceptual, with no maximization or differentiation required.

🧩 The Simplified Fishery Model

• Logistic growth: total growth first rises with stock, then falls as food and space become limiting.

\[ G(S)=0.4S\left(1-\frac{S}{100}\right). \]

• Here, carrying capacity is \(K=100\) tons. The value \(0.4\) is the biological growth parameter.
• This simplified rule omits the earlier low-stock threshold.
• The fish price and the cost of one unit of fishing effort are constant.

TL, p. 427. Introduce the name and intuition only after students have read the growth graph. More fish initially support more reproduction and biomass growth. As stock approaches carrying capacity, crowding and limited food slow net growth. The factor 1-S/100 captures that limit: at stock 100 it is zero. The value 0.4 is a chosen annual biological growth parameter, not a discount rate or an estimate for a real fishery. Students only need to substitute a stock into this supplied rule. No calculus, derivation of the logistic function, or solution of a differential equation is required.

Make the textbook’s simplification explicit: Figure 17.2 draws a positive viability threshold, whereas Figure 17.3 draws the ordinary growth hump beginning at the origin. We do not carry the threshold into the numerical effort model. Baseline G(S)=0.4S(1-S/100), H(S,E)=0.02ES, and K=100 model tons. Constant fish price treats this fishery as small relative to its market, not as a complete demand-and-supply model. Constant cost per effort unit does not imply constant cost per ton of fish; fewer fish per effort unit makes each ton more expensive when stock declines. At the same effort, a larger stock makes fish easier to catch. These assumptions connect stock, effort, sustainable catch, and net benefit.

⚓ Fishing Effort

• Effort is an input, such as fishing days, vessel hours, or trips.
• More effort raises catch at a given stock.
• With the same effort, a smaller stock produces a smaller catch.

\[ H(S,E)=qES. \]

• \(q\) measures how effectively effort catches fish. In our example, \(q=0.02\).

TL, p. 427, and harvest technology in the appendix. E is an annual effort index; q is held constant and converts effort times biomass into annual catch. In the illustrative calibration, one effort unit harvests 2% of the initial stock over the annual period. No real fleet or species is implied. Distinguish input E from output H. We use constant q; improving catchability and lowering the cost of an effort unit are different technological changes.

🚤 Harvest Lines and Fishing Effort

Adapted from TL Figure 17.3, p. 427. First read the axes: horizontal is fish stock, vertical is annual growth or catch. The blue curve shows G(S). The first harvest line shows H(S,E_1) for maintained effort 4. Its positive intersection is S_1=80, where growth and catch both equal 6.4. Then reveal effort 8. The steeper harvest line H(S,E_2) intersects growth at S_2=60, with growth and catch both equal 9.6. A larger effort rotates the harvest ray upward because H=qES. Ask which variable is on the horizontal axis before reading the movement to the left.

E is aggregate annual fleet effort, the sum of individual fishers’ effort. Individual fishers choose their effort; they inherit the current stock, which responds to aggregate harvest and biological growth. The full harvest line is H(S,E_i)=qE_iS; at its growth intersection, sustainable catch is Y(E_i)=H(S_i,E_i). Each line is a different maintained-effort scenario.

S_1 and S_2 label the steady stocks associated with the two maintained effort levels. Their subscripts identify scenarios, not Year 1 and Year 2. At a positive intersection, G(S_i)=H(S_i,E_i), so S_next=S_i. The stock stays there if effort and biological conditions remain unchanged. At a stock above that intersection, catch exceeds growth and the stock falls; below it, growth exceeds catch and stock rises in this simplified model.

This is consistent with the next slides: both scenarios begin at S_t=80, which already is the low-effort steady stock S_1. Under effort 8, stock then approaches S_2=60 over time. It does not jump to 60, and 60 is not the stock inherited at the start of the first high-effort year. Use the horizontal growth/harvest guides to read sustainable catch, then explain that the next slide calculates the first adjustment step. Individual fishers choose effort, whereas stock is an inherited state. The annual revenue/cost comparison later in Fishery Dynamics explains why unrestricted entry can encourage higher effort.

🔁 Catch Now, Stock Later

Both cases start with the same stock, \(S_t=80\) tons.

So both have the same natural growth:

\[ G(80)=0.4\times80\left(1-\frac{80}{100}\right)=6.4. \]

Low effort: \(E_1=4\)

\(H(80,4)\) \(=\) \(0.02\times4\times80\)

\(=\) \(6.4\)

\(S_{t+1}\) \(=\) \(80+6.4-6.4\)

\(=\) \(80\)

Higher effort: \(E_2=8\)

\(H(80,8)\) \(=\) \(0.02\times8\times80\)

\(=\) \(12.8\)

\(S_{t+1}\) \(=\) \(80+6.4-12.8\)

\(=\) \(73.6\)

Question: If each effort level is maintained, how will the two stock paths differ over time?

Numerical illustration of TL Figure 17.3, p. 427. The growth rule G(S)=0.4S(1-S/100) was introduced on The Simplified Fishery Model slide. The harvest rule is H(S,E)=0.02ES. Both columns inherit stock 80. Calculate natural growth once for that common stock. Reveal each pair of harvest and next-stock calculation lines together. Effort changes harvest immediately: 6.4 at effort 4 and 12.8 at effort 8. Stock accounting gives 80 in the low-effort case and 73.6 in the high-effort case. These are alternative scenarios, not consecutive years. Ask students to predict the two paths before revealing the next graph.

The growth and harvest calculations yield annual flows in tons per year; with one-year periods, use their tonnage in the stock equation. Explain the values 0.4 and 100 as chosen biological parameters for this classroom model, not estimates of an actual fishery. Evaluating the supplied rule does not require deriving the growth function.

The effort increase is an assumed change for this comparison, not a prediction that every fisher optimally doubles effort. Catch changes immediately, while the stock then adjusts through growth minus harvest. Hold effort at 8 during that adjustment. The immediate catch response is larger than the eventual sustainable-catch increase: at the eventual stock of 60, H(60,8)=0.02 times 8 times 60=9.6. This annual stock accounting is illustrative, not a calibrated transition for a real fishery.

📉 Stock Adjusts Over Time

Original simulation of the stock accounting rule using the illustrative baseline. Reveal four cumulative paths, all starting at stock 80. Maintained E_1=4 keeps stock at 80; E_2=8 gives next stock 73.6 and approaches 60; E_MSY=10 gives next stock 70.4 and approaches 50; E=14 gives next stock 64 and approaches 30. Each step uses S_next=S+G(S)-H(S,E). At the four steady stocks, annual catch and growth are 6.4, 9.6, 10, and 8.4 respectively. Ask why each declining path flattens: as stock declines, the same effort catches fewer fish, until harvest and growth balance. MSY effort gives the largest steady annual catch, rather than the largest remaining stock.

The high-effort label says “Approaches S_high = 30”. Its short solid horizontal leader sits near the end of the displayed curve for readability, rather than marking y=30. The stock has not yet reached its steady level within the fifteen years shown.

The last reveal is labeled high effort for now. It is the open-access benchmark for the price/cost calibration introduced later: with effort 14, sustainable revenue and cost both equal 8,400. High effort alone does not define open access. Unrestricted entry and the break-even condition explain that benchmark. Holding effort 14 fixed from the start illustrates its stock adjustment, rather than simulating the actual time path of entry. Do not claim that the open-access stock of 30 is extinction.

The horizontal axis is time. These are alternative maintained-effort paths, whereas the harvest-line and sustainable-yield graphs compare steady states. Effort is an assumed constant in each scenario, not an optimal-choice prediction or an endogenous open-access entry path. A falling stock need not imply extinction: here it approaches a lower positive equilibrium. Starting stock, the biological function, and the harvest rule determine the path.

🪞 Sustainable Annual Catch

Sustainable annual catch, \(Y(E)\), is catch maintained after stock settles, when growth equals harvest.

Annual effort \(E\)	Steady stock \(S\)	Sustainable catch \(Y(E)\)
4	80 tons	6.4 tons per year
8	60 tons	9.6 tons per year
\(E_{MSY}=10\)	50 tons	10.0 tons per year
\(E_{OA}=14\)	30 tons	8.4 tons per year

• With \(E_2=8\) held fixed, catch starts at 12.8 tons and approaches 9.6 tons as stock falls from 80 toward 60 tons.

Introduce sustainable annual catch before revealing the table. It is the annual harvest that can be maintained at the corresponding steady stock, with natural growth replacing the fish caught. During the adjustment toward that stock, annual catch can differ from Y(E). The definition and this distinction now appear together before the sustainable-catch/effort graph.

TL, p. 427. The table transfers the two harvest intersections and the extra stock-path comparisons to an effort-based view. Each row reveals separately. Y(E) means annual sustainable catch after the stock settles at the equilibrium associated with E. It is not a new growth curve and is not catch during every year of the transition. MSY effort 10 corresponds to stock 50 and catch 10. Effort 14 is the open-access benchmark under the coming price/cost calibration, with stock 30 and catch 8.4. Point ahead to the break-even revenue/cost condition rather than defining open access as simply high effort. The algebraic bridge, optional for the whiteboard, is S(E)=100-5E and Y(E)=2E-0.1E^2 for 0<=E<=20. No derivation is required in this graphical lecture.

TL, pp. 426–428. Students need the distinction because the numerical adjustment uses H(S_t,E), while the annual revenue graph uses Y(E)=H(S(E),E) at the maintained stock. No additional technical term for immediate catch is necessary. With effort 8 at initial stock 80, harvest 12.8 exceeds growth 6.4, so the next stock is 73.6. Eventually stock approaches 60 and catch approaches 9.6, equal to biological growth. The fixed-catch stable and unstable graphs remain in Fishery Management for quota risks.

A current record catch is not sufficient evidence of a healthy stock or a sustainable harvest. Biomass, growth, and effort must also be observed. A catch below MSY can still draw down stock if it exceeds growth at the current stock. The lower-catch warning compares excessive effort with effort at MSY; it does not imply that every higher-effort outcome yields less catch than every lower-effort outcome. Avoid introducing unverified current fisheries statistics; this is a model-based inference.

For the change of axes, refer specifically to the harvest-line graph: stock is on its horizontal axis, so more maintained effort moves its positive growth intersection left. The next graph places effort on the horizontal axis and compares the sustainable catches listed here. The preceding time-path graph instead has years on its horizontal axis. Keep those three different comparisons distinct.

🎣 Sustainable Catch and Effort

Adapted from TL Figure 17.4, p. 428. First transfer E_1,H_1 and E_2,H_2. Then show MSY at E_m=10, stock 50, catch 10. At E_OA=14, stock is 30 and sustainable catch is 8.4. The subscript OA identifies the open-access, break-even outcome. The revenue-and-cost graphs later in Fishery Dynamics explain why unrestricted entry leads to that effort: R=C=8400, with zero economic profit. The falling branch means that higher maintained effort reduces sustainable production because it reduces the stock supporting growth. It does not mean adding a fishing day instantly reduces the day’s catch at an unchanged stock. Each point is a different long-run stock/effort combination, not a year along a single trajectory.

Catch alone cannot rank the outcomes. At effort 4, stock is 80, sustainable catch is 6.4, and annual net benefit is 4,000 dollars. At open-access effort 14, stock is 30, sustainable catch is 8.4, and annual net benefit is zero. The extra catch uses more effort and leaves less stock. The static efficient outcome at effort 7 has stock 65, catch 9.1, and net benefit 4,900 dollars. All are illustrative classroom values.

Open access draws down the stock in this calibration but does not cause extinction: its steady stock remains positive at 30. To illustrate drawdown, optionally compare a maintained effort of 14 starting from stock 80: immediate harvest is 22.4, growth is 6.4, and next stock is 64. With that effort held fixed, stock approaches 30, where harvest and growth both equal 8.4. Such a fixed-effort time path is an illustration, not the endogenous entry path of the open-access fishery. Complete collapse would require different conditions, such as still higher maintained effort or a biological threshold; do not imply that this open-access point entails extinction.

💵 Revenue and Fishing Costs

• Let \(Y(E)\) be sustainable annual catch. Fish sell for $1,000 per ton.
• Fishing costs $600 per effort unit. Subtract cost from revenue to find annual net benefit.

\(R(E)\) \(=\) \(1{,}000\,Y(E)\)

\(C(E)\) \(=\) \(600E\)

\(\text{Annual net benefit}\) \(=\) \(R(E)-C(E)\)

TL, pp. 427–429. These prices and costs are illustrative model dollars, not observed market estimates. Constant price makes total revenue have the same shape as sustainable yield. A constant cost per effort unit creates a straight total-cost line. With price-taking fishers and no additional external harms in this simplified model, the fishery’s revenue less real harvesting cost is the annual net-benefit measure used for the static sustainable comparison. It is not a full consumer-surplus calculation for the entire fish market.

📊 Revenue, Costs, and Net Benefit

Adapted from TL Figure 17.5, p. 429, and explanation on p. 428. Revenue equals price times sustainable catch; cost equals cost per effort unit times effort. Reveal the curves, then the largest gap, then the MSY and break-even markers. Efficient effort maximizes R-C, not R alone. The tangent at E_e is parallel to the cost line: for a very small change in effort, the extra revenue matches the extra cost. Explain local slopes in words; no derivatives. In the illustrative model, R=2000E-100E^2 and C=600E, so E_e=7, R=9100, C=4200, and net benefit=4900. E_m=10 maximizes catch and revenue. At E_OA=14, R=C=8400 and net benefit is zero. Figure 17.6 adds the entry logic behind this positive zero-profit outcome; that logic was already covered in Lecture 4.

🟢 The Static Efficient Target

• Static means we compare sustainable (steady-state) outcomes only, ignoring discounting and the transition path between stock levels.
• The efficient effort level \(E_e\) maximizes annual net benefit: sustainable revenue minus total cost.
• Equivalently, \(E_e\) is where marginal revenue of effort = marginal cost of effort.
• In our example:
  • Effort: \(E_e = 7\)
  • Maintained stock: 65 tons
  • Annual catch: 9.1 tons
  • Annual net benefit: $4,900

TL, pp. 426–430. E_e is the static efficient sustainable effort, not automatically the dynamically optimal effort for a given initial stock and discount rate. Maintaining that stock requires growth to equal catch. The book calls the static criterion a zero-discount benchmark. At a nonsteady initial stock, the transition itself has benefits and costs; maximizing a steady-state annual gap alone does not solve that transition.

🔍 MSY vs. Efficient Effort

Target	Effort	Stock (tons)	Catch/year (tons)	Net benefit/year
Static efficient	7	65	9.1	$4,900
MSY	10	50	10.0	$4,000
Open access	14	30	8.4	$0

• Different goals: MSY maximizes sustainable catch; static efficiency maximizes sustainable net benefit.
• Why stop at 7? Raising effort from 7 to 10 adds $900 in revenue but $1,800 in cost.
• Why MSY still matters: Stock 50 and effort 10 are biological benchmarks. Effort above 10 lowers both catch and stock.

TL Figures 17.5–17.6, pp. 428–433. Stock/catch units are tons and tons per year. The table summarizes the same illustrative model. Do not reteach MR/AR from Figure 17.6. Entry continues when entrants can earn an economic profit, and the positive open-access steady state has R=C. Zero economic profit does not mean zero sales, unpaid fishers, or physical extinction; opportunity costs of labor and capital are included. The ordering of catch between the efficient and open-access outcomes is specific to this calibration; the robust lesson is excessive effort and dissipated rent. With positive effort cost, the static efficient effort lies below MSY effort in this benchmark.

Explain the two questions: MSY asks how many tons can be caught sustainably each year; static efficiency asks which sustainable steady outcome produces the greatest annual value after the real opportunity costs of fishing. In this fixed-price model, that economic target is also called maximum economic yield. More output has value, but fuel, labor, boats, and equipment also use scarce resources. From effort 7 to 10, catch rises from 9.1 to 10 tons and revenue from $9,100 to $10,000. Cost rises from $4,200 to $6,000, so the extra $900 of revenue costs $1,800 and annual net benefit falls by $900. Stock is 65 rather than 50 at the efficient target because lower maintained effort leaves more fish in the water. Both targets are sustainable steady states in this deterministic model.

For the policy question, prefer E_e=7 if the aim is to maximize this model’s annual net benefit under its assumptions. MSY is the 10-ton annual catch, not the effort input. Its associated effort of 10 identifies the peak of the sustainable-catch curve: maintaining effort above 10 leads to a lower steady stock and less sustainable catch in this model. Reducing that excessive effort can therefore improve both stock and sustainable catch. Moving further to effort 7 accounts for fishing costs and produces greater annual net benefit, with a stock of 65 rather than 50. MSY helps identify excessive fishing pressure; it does not tell us to choose effort 10 when effort 7 is economically better.

The stock of 50 tons that supports MSY is a biological comparison point for tracking stock condition and rebuilding progress, not a minimum viable stock or an extinction threshold. Compare actual stock and fishing pressure with these benchmarks, then adjust harvest to current growth and the desired stock path. To hold a stock constant, harvest equals growth; to rebuild it, harvest must be below growth. For example, at stock 20, annual growth is 0.4(20)(1-20/100)=6.4 tons. A catch of 8 tons is below MSY of 10 but still shrinks that stock. Catching 4 instead leaves 2.4 tons of net growth. This optional example explains why knowing MSY alone does not protect fish: monitoring and responsive harvest limits do. A stock below 50 does not by itself establish a legal overfished designation or prescribe a safe catch.

Do not equate maximized industry profit automatically with maximized social welfare: costs must reflect real opportunity costs, and ecosystem effects and other social benefits must be included. Policymakers also face uncertain biological growth and the effects of effort reductions on fishing communities. A larger stock here is a useful biological buffer, but the table alone does not quantify resilience or determine a safe real-world catch limit. Real catch limits must account for current conditions and uncertainty, rather than simply allowing the MSY amount every year.

This is a comparison of maintained annual outcomes, not a solution for the best transition from today’s stock. A forward-looking policy considers the present value of benefits and costs along that transition, biological safeguards, and distribution. Its preferred target need not equal either tabulated benchmark. Keep that caveat brief here; the next section discusses management institutions and the value of leaving fish.

Supporting sources: FAO, Management Concepts for Small-Scale Fisheries, Summary and Conclusions, on catch versus economic surplus and social objectives; NOAA Fisheries, Fish Stock Sustainability, on stock assessments, biological reference points, and rebuilding; NOAA Fisheries, Setting an Annual Catch Limit, on MSY and scientific and management uncertainty.

🎯 Why Is MSY Still Useful?

In our example, \(E_e = 7 < E_{MSY} = 10 < E_{OA} = 14\): MSY sits between efficiency and open access.

• Biological limit: Beyond \(E = 10\), more effort yields less catch and a smaller stock. This defines biological overfishing.
• Less information needed: MSY depends only on growth (\(r\), \(K\)). \(E_e\) also needs prices and costs, which shift often.
• Legal anchor: UNCLOS (United Nations Convention on the Law of the Sea) and the U.S. Magnuson-Stevens Act use MSY as the reference point for setting “optimum yield.”
• Different objectives: If the goal is food supply or jobs rather than net benefit, MSY may be the target.

⚓ Fishery Management

Guiding question: How can rules and institutions control fishing pressure and sustain the stock?

Plan approximately one class (50 minutes). Begin with the incentives created by cheaper fishing or subsidies, then briefly recall the value of leaving fish. Use the fixed-catch stability and rebuilding graphs to explain why a catch limit must fit the current stock. Continue to the race to fish, catch shares, monitoring, protected areas, and coordination across boundaries. Keep the program taxonomy, scallop comparison, and EEZ case brief. Reserve three to five minutes for the management decision and exit check. The annual revenue/cost graph and economic targets have already been covered in Fishery Dynamics.

Keep the fixed-catch stable and unstable stock slides together immediately before the rebuilding example. They apply the smooth growth curve from Fishery Dynamics to a different harvest rule. Distinguish fixed annual catch from fixed effort before showing the horizontal catch line. Recall the open-access entry result from Lecture 4 without repeating its full derivation.

🛠️ Cheaper Fishing and Subsidies

• Real savings free up resources; a subsidy may lower only the fisher’s bill.
• Policy question: Would cheaper equipment conserve fish without an enforced catch limit?

TL, pp. 428–429, provides the lower-cost comparative static. The subsidy discussion applies that incentive to the illustrative model, conditional on unrestricted entry. Distinguish a genuine saving in resources from a transfer that reduces only the cost paid by fishers. Hold q and fish price constant here; equipment that raises catchability is a separate technological change.

For a real cost reduction from 600 to 400 per effort unit, static efficient effort rises from 7 to 8, maintained stock falls from 65 to 60, catch rises from 9.1 to 9.6, and annual net benefit rises from 4,900 to 6,400. Thus better technology is not automatically harmful. Under open access, however, the positive break-even effort rises from 14 to 16, stock falls from 30 to 20, and sustainable catch falls from 8.4 to 6.4. The extra effort dissipates the potential surplus.

If a subsidy instead reduces fishers’ payment from 600 to 400 while real cost remains 600, open-access effort 16 has revenue 6,400, real fishing cost 9,600, and subsidy expenditure 3,200. Zero private profit does not imply zero social cost. Do not substitute the subsidized private cost for full social cost in a welfare calculation. An enforced total catch limit constrains the harvest expansion, although capacity, subsidy spending, and the race to fish can still matter. The policy question therefore concerns the rules and incentives accompanying support, rather than claiming every innovation or subsidy inevitably destroys the fishery.

⏳ The Value of Leaving Fish

Harvest now provides current income; leaving fish supports reproduction and future harvest opportunities and can make future catch less costly.

• Discounting compares income today with future benefits.
• Our earlier graphs compare steady annual outcomes, not the best path between them.

TL, pp. 429–431. Link to Lecture 5 without presenting the classic non-renewable Hotelling rent-growth rule as the rule for fisheries. Biological growth and stock-dependent catch costs modify the trade-off. Higher discounting can encourage more current harvest in the textbook’s simple model, but the optimal steady stock and transition depend on biological growth, costs, initial stock, and the objective. The textbook discusses possible extinction under additional assumptions, and pp.430–431 explain that efficiency and sustainability need not always coincide. Do not claim that positive discounting automatically implies extinction, or that all economically optimal fisheries lie below MSY stock. Full dynamic optimization is optional material outside the 2.5-class core.

🟢 Fixed Catch: A Stable Stock \(S_{H}\)

Graphical application of TL’s sustainable-yield definition, p. 426. Return to the smooth growth curve introduced in Fishery Dynamics. Now hold annual catch fixed at eight tons instead of holding effort fixed. First identify the higher intersection, where growth equals the annual catch of eight tons. Then consider a small disturbance below it: growth exceeds catch, so the stock rises. Finally consider a small disturbance above it: catch exceeds growth, so the stock falls. Both movements return toward the intersection, making it stable under this fixed-catch rule. The return is local: a stock far below the lower intersection will not recover under the same catch rule. These are direction-of-adjustment comparisons, not a claim that stock jumps to equilibrium in one year.

⚠️ Fixed Catch: An Unstable Stock \(S_{L}\)

At the lower intersection, growth also equals catch, but a disturbance pushes the stock away. Below it, catch exceeds growth and the stock falls farther. Above it, growth exceeds catch and the stock rises farther, eventually toward the higher stable intersection. This lower intersection is therefore unstable under the fixed-catch rule. It arises even in this model without a biological minimum viable stock: harvest itself creates the threshold for recovery. A sustainable catch is conditional on the initial stock. Actual harvest cannot exceed available biomass, so managers must reduce or stop the catch before a declining path reaches zero. This is a fixed catch, distinct from the fixed effort used in the earlier graphs.

🐟 A Catch Limit That Rebuilds Stock

Application of TL’s stock accounting, pp.424–426, and adaptive quota discussion p.442. At S=20, baseline growth is6.4. Catch8 leads to next stock18.4; catch4 leads to22.4. A positive net stock addition requires H<G(S), not simply a quota below the global growth maximum. A fixed catch can be sustainable at one stock but unsafe at another. Rebuilding requires stock assessments, catch rules suited to the depleted state, and time for growth. The graph does not assert a universal optimal catch of4 or a precise rebuilding schedule.

Reveal growth at the current stock first, then the old catch and stock decline, and finally the reduced catch and rebuilding. The two catches are alternative policies from the same starting stock, not consecutive years.

📋 A Catch Limit and the Race to Fish

• Total allowable catch (TAC): 100 tons for the whole fleet this year. Here, catch is first come, first served.
• No reserved shares: “If I wait, other boats may fill the cap before I get any catch.”
• Boats add gear and hours to catch first. Costs rise, but the fleet’s total cap stays at 100 tons.

TL, pp.435–436,438–439, and Self-Test2 p.455. This is a hypothetical aggregate-cap example, not a current fisheries regulation. A well-set and enforced cap can protect biomass while leaving the scramble for its allocation unresolved. Link to the shared-bay experiment and Lecture4 without repeating property-rights terminology at length. Do not infer that all seasonal or gear rules waste resources: some protect spawning, juveniles, habitat, or bycatch species, harms that the single-stock catch cap does not capture.

The race occurs along the rising catch segment before the cap is reached, not during the shaded closed season. Each boat tries to secure more of the common total before competing boats do. More capacity and longer hours can compress fishing into a short season without increasing the permitted annual total. The April closure is only an illustration for a different fishery with a 100-ton TAC, not a prediction or a continuation of the earlier stock calibration.

Make the institutional assumption explicit: a TAC is an aggregate limit, and it can coexist with individual catch shares. This example instead leaves allocation first-come, first-served. Suppose I delay my trip and other boats catch the remaining allowable total. The fishery then closes and I have no catch left to claim. Going sooner or fishing harder can increase my share without increasing the permitted fleet total. Thus an aggregate cap can protect stock while leaving the race unresolved. It does not follow that every catch-limit system creates a race.

Transition: could limiting boats or fishing days help? The next slide separates reducing fishing inputs from allocating the permitted catch. Catch shares then address the allocation incentive directly, before the following slide introduces program names.

⚙️ Why Effort Limits May Leave a Race

Effort limits can reduce fishing pressure by restricting boats, gear, or fishing time.

Restriction	Why the race can remain
Fewer boats allowed	The remaining boats still compete for the shared catch.
Fewer fishing days	Boats may add gear or fish harder on the allowed days.

• The missing piece: no boat has a reserved share. Catch shares change that incentive.

Effort controls can conserve fish and complement catch limits. Here the TAC remains first-come, first-served: limiting inputs does not itself allocate the catch. Even a smaller fleet can race; limiting one input may encourage greater use of another. Explain the rows as possible responses, not inevitable failures. With effectively enforced catch shares, another boat cannot exhaust my allocation by fishing first. Transferability is optional for this incentive change.

Source: FAO, Input and Output Controls, sections 2.1 and 6.1–6.2. The next slide compares catch allocation with input restrictions, rather than claiming catch shares are suitable for every fishery.

🧾 Catch Shares

• A catch share reserves a fisher’s or group’s fraction of the TAC.
• Another boat cannot take my reserved share by fishing first, so I have less need to race.
• Monitoring: record each holder’s catch and check it against their allocation.
• The TAC must fit the stock. Decide who receives shares.

TL, pp.438–442. Catch shares divide an aggregate cap; they do not make an excessive cap sustainable. An individual transferable quota (ITQ) is a catch entitlement that can be transferred among fishers. Trading can lower harvesting costs while keeping the permitted total fixed. Initial allocation and concentration affect access, equity, and who receives rents. Students need the distinction between a percentage share and fixed tonnage, not a quota-price calculation.

Return to the same 100-ton example. A secured 10% share gives me 10 tons, and another boat’s earlier trip cannot use it up. This reduces the incentive to spend more solely to catch first. I can plan trips around costs and conditions within the rules. If the TAC falls to 60 tons, the same percentage gives 6 tons, not a guaranteed 10 tons. The mechanism requires credible allocation and monitoring; transferability is not necessary to reserve a share. It is a separate feature introduced on the program-terminology slide. See NOAA Fisheries, Catch Shares FAQ.

Optional historical example, TL p.442: stock estimates for New Zealand orange roughy proved too high, making issued catch entitlements unsafe. Replacing fixed-tonnage entitlements with percentage shares allowed managers to adjust the annual TAC as stock information changed. This is the textbook’s historical account, not an assessment of current orange roughy stocks. Neither shares nor private ownership automatically resolves biological uncertainty or every ecosystem externality.

Optional detail on discards and bycatch, TL p.442 and pp.449–451: biological removal includes fishing mortality beyond marketed catch. Sales records alone can miss it. Verify reports using dock checks, observers, or cameras. Use selective gear, spatial rules, and habitat protection as complements when an aggregate single-species cap misses other harms. Connect to the experiment’s monitoring setup, but avoid claiming every release causes death.

For example, 10 tons sold and 1 ton discarded dead means 11 tons removed from the same stock. These hypothetical amounts explain mortality accounting, not a representative discard rate. Dock records alone cannot show fish discarded at sea, so vessel records, observers, or electronic monitoring provide complementary evidence.

Monitoring does not mean checking whether the entire fish stock has been removed. Managers assess fish remaining through stock surveys and other biological information, estimate fishing mortality from catch and discard records, and verify compliance with the rules. Under-recorded fishing deaths can make projections too optimistic and undermine future harvest decisions.

Bycatch identifies what was caught: species other than the intended target. Dead discards identify what happened to released catch: it did not survive. Bycatch may be kept or released, and dead discards can include either target fish or bycatch. Record and assess each species separately. The numerical example concerns one species and does not add deaths from different stocks together. Eleven tons of biological loss is not automatically a violation of a ten-ton sales or landings limit: compliance depends on what the regulation counts. Managers need reliable mortality accounting as well as checks against the actual rules.

🧾 Catch Shares and Territorial Rights

Quota-based catch shares

• IFQ (Individual Fishing Quota): a person’s portion of the TAC.
• ITQ (Individual Transferable Quota): an IFQ that can be sold or leased.
• IVQ (Individual Vessel Quota): catch allocated to a boat.
• Examples:
  • ITQs: New Zealand, Iceland, Canada.
  • U.S. IFQs: halibut, sablefish, red snapper.

Territorial rights

• TURF (Territorial Use Rights in Fisheries): exclusive access to a defined fishing area.
• Area access can be combined with catch limits and other rules.
• These arrangements do not mean owning every fish or the ocean itself.
• Examples: Japan’s co-ops; Chile’s nearshore areas.

TL, pp.438–441 and 444–445. An IFQ is the broader individual allocation category; the label alone does not say whether transfers are allowed. An ITQ is a transferable IFQ. An IVQ assigns the entitlement to a vessel and may or may not permit transfers. A TURF assigns access to a geographic area rather than a share of the catch across the entire fishery. These are harvesting/access entitlements, not ownership of all fish or the ocean itself. Territory-based approaches work more easily for resources that do not migrate far.

The examples are selected from Table 17.1 (p.439) and Table 17.2 (p.441), not an exhaustive or current count of programs. Table 17.1 lists New Zealand, Iceland, and Canada among countries using ITQs. Table 17.2 lists Alaska halibut and sablefish IFQs (1995) and Gulf of Mexico red snapper IFQs (2007). Do not infer that all IFQs have unrestricted transferability. Japan’s local fishing cooperatives and Chile’s nearshore management areas are the textbook’s TURF examples on pp.444–445.

For the distinction, the TAC sets the fleet-wide total, while quota-based catch shares allocate that total to people or vessels. Territorial rights allocate access to an area, which can be combined with catch limits and other rules. NOAA includes TURFs under its broader catch-share umbrella, but a TURF need not assign a fixed percentage of a TAC. See NOAA Fisheries, Catch Shares and Catch Shares FAQ.

🐚 Atlantic Sea Scallops: Canada and the U.S.

• Canada (1986): offshore scallop companies adopted ITQs.
• U.S. then: minimum-size rules, fishing-day limits, and area closures.
• Implication: larger stocks mean more catch per day and lower costs per ton, increasing earnings for those still fishing.

• Economic logic: quota holders keep a share of future catches, so leaving small scallops to grow can pay instead of racing to catch them. Trading can shift quota to lower-cost boats.

TL Example 17.2, pp.443–444. Primary study: Repetto, R. (2001), “A natural experiment in fisheries management,” Marine Policy, 25(4), 251–264, DOI. The trend recreates Figure 8, “Catch per Sea-day,” in the author’s original working paper, also available through Yale. The annual values are approximate digitizations of the supplied screenshot, rounded to hundredths of a ton per sea-day. They are not the original raw data. This is historical evidence, not a description of today’s management or stock conditions.

Fisheries and Oceans Canada, historical overview and Appendix 2, dates the offshore scallop enterprise allocation trial to June 1986. It became permanent in 1989. Here, “ITQ adoption in 1986” refers to this particular Canadian offshore scallop program, not to every Canadian fishery. The U.S. comparison used size, effort, and area controls.

The economic mechanism is that a durable share of future TAC lets quota holders capture part of the future benefit from leaving scallops to grow and supporting stock rebuilding. They have less reason to harvest small scallops before a competitor does, and more flexibility to choose when and how to take their quota. Transferability can move harvesting toward lower-cost operators and reduce excess fleet capacity. These gains depend on a suitable overall TAC, credible monitoring, and durable allocations; ITQs alone do not guarantee conservation. Repetto’s own 2001 explanation describes the U.S. minimum-size restrictions, later limits on days at sea and crew size, and area closures. These measures changed over the study period. Area closures also helped U.S. stocks recover, so the comparison does not show that effort or area controls can never work.

First reveal the 1985 baseline and the 1986 adoption marker. Next add Canada’s 1985–1999 path, then add the U.S. path and its management description on exactly the same axes. Reveal the implication, then the economic logic. Catch per sea-day measures fishing productivity, not total catch or stock biomass directly. Canada’s line rises overall but fluctuates, with a peak in 1997 and a subsequent decline. The U.S. line remains lower and falls through much of the 1990s before rebounding in 1999. The time series is in tons per sea-day, not an index or a country ratio. Do not infer an exact policy effect from the size of the before-and-after change.

Scallops are relatively immobile after settlement, and the fisheries used similar technologies. The Canadian case maintained greater stock abundance and reduced harvest of undersized scallops. The historical U.S. comparison had lower stock abundance and declining catch and revenue per sea-day. Use this to illustrate how stock abundance and incentives can affect catch per unit of effort. This natural comparison supports the incentive mechanism, but other policy, stock, and environmental changes can also contribute. One pre-adoption year and two country trends alone do not isolate a causal effect of ITQs.

Canadian quota holders decreased from nine to seven over 14 years, but 65% of quota remained with original holders. The study did not find the expected disadvantage for smaller holders in this particular case. Under the “lay” system, revenues after specified operating costs were split among crew, captain, and owner, allowing remaining participants to share gains. This case supports the incentive mechanism, but does not establish that quotas automatically improve every fishery or compensate everyone who leaves.

🤝 Communities and Protected Areas

A marine protected area can include a no-take marine reserve and areas allowing regulated fishing. Spillover into fishing grounds is possible, not guaranteed.

• Fishers and public authorities can share management and monitoring.
• Protecting spawning grounds and habitat can aid recovery, but who bears the costs today?

TL Example17.1 p.434, territorial use rights pp.444–446, and marine protected areas pp.449–450. Co-management means sharing responsibilities, not automatically leaving a resource open to everyone. Community success depends on cooperation, legitimate enforcement, and complementary conservation measures. A local territory cannot fully control a highly mobile stock without wider coordination.

MPA is the broad category, with protections ranging from restrictions on specific uses to full protection. A marine reserve is the fully protected/no-take version in the textbook: harvest is prohibited, and protections address other threats as well. Safeguarding spawning habitat, reducing gear damage, and protecting species interactions complement catch limits. Larger populations may support catches outside the protected boundary through spillover, but this is not guaranteed in every setting. Protection can displace fishing effort and needs monitoring. Do not guarantee that future aggregate gains compensate every current fisher. Taxes, harmful input subsidies, buybacks, and aquaculture are optional further topics if time permits.

🌊 EEZs and Russia’s “Peanut Hole”

▶ Watch: Russia’s “Peanut Hole”

• EEZ: exclusive economic zone, up to 200 nautical miles from a coastal baseline.
• High seas: waters beyond national EEZs. No country has sovereignty over them, but international law still applies.
• Peanut Hole: high-seas waters in the Sea of Okhotsk, surrounded by Russia’s EEZ.
• 1990s: foreign fleets fished for pollock in the pocket beyond Russia’s EEZ. Russia feared overfishing.
• 2014: a UN commission supported Russia’s seabed-resource claim, not a larger EEZ or exclusive rights to fish above.
• Lesson: shared fish stocks need international cooperation.

TL, p.449, introduces EEZs as the international jurisdictional dimension of fishery management. Use “exclusive economic zone,” not “economic exclusion zone.” The legal maximum is 200 nautical miles from coastal baselines, not 200 ordinary miles. Coastal states have sovereign resource rights and relevant jurisdiction in the EEZ, rather than full territorial sovereignty over every activity there.

For an introductory definition, describe high seas as waters beyond national EEZs, rather than measuring a fixed distance from a country’s coastline. UNCLOS Article 86 excludes EEZs, territorial seas, internal waters, and archipelagic waters from the high seas. Article 89 prohibits claims of national sovereignty over the high seas, while international law and flag-state jurisdiction over vessels still apply (Articles 87 and 92). The definition concerns the water column; rights over the seabed can differ.

The supplied YouTube Short is an optional geographic illustration, not the authority for the legal claim. The Peanut Hole water column lies beyond Russia’s 200-nautical-mile EEZ in the central Sea of Okhotsk. NOAA’s historical account describes international pollock fishing beginning there in 1991 and Russian concerns about another stock collapse. High seas does not mean an absence of all law: flag-state obligations and international cooperation still apply.

The Commission on the Limits of the Continental Shelf adopted its Okhotsk recommendations on 11 March 2014. The process concerns the continental shelf beyond 200 nautical miles. Russia deposited the relevant chart in 2016. UNCLOS Article 78 explicitly preserves the legal status of the waters above the shelf, so do not say the Peanut Hole was integrated into Russia’s EEZ in 2014. Shelf rights cover seabed/subsoil resources and specified sedentary species, not a general entitlement over swimming pollock in the high-seas water column.

Primary sources: UNCLOS Articles 56–57, Articles 77–78, Articles 86–92, UN Okhotsk recommendations record, UN maritime-zone notification, 2 June 2016, and NOAA historical distant-water-fleet report.