Manufacture at Biological Rates

Volume IV — Production and Regeneration

Nine movements, one increment.

THE PLATE

A man in a dark suit writing in an open book at a library desk, lamps lit among the shelves. — Plate IV.04The Scaler's Book.Every plant has a capacity plate riveted to its frame. Very few have the other one — the number the ground will hand over, year after year, without being asked twice.

THE LETTER

There is a sentence that gets said in every capital approval meeting for a processing plant, and it is said so naturally that nobody hears it as a claim. We'll size it to the market.

It is the right sentence for a plant that runs on steel, or on polymer, or on anything that arrives on a truck from somewhere with its own supply curve. It is the wrong sentence for a plant that runs on wood, water, fibre, fish, hide, latex, sap or soil — because those inputs do not have a supply curve in the short run. They have a rate. A quantity per unit of time, set by biology and by the ground, which can be measured, which can be raised by a few percent over decades with real work, and which cannot be negotiated.

This chapter is about designing manufacture against that rate. Not about restraint, and not about doing less — about a different engineering problem, which turns out to be a harder one than the problem it replaces and a more interesting one. You are used to sizing a plant against a demand forecast and an IRR hurdle. You are being asked to size it against a renewal rate with a confidence interval, hold it there through the years when the market would pay you handsomely to exceed it, and finance the whole thing on a balance sheet that currently has no line for the asset you are protecting.

Three things are true at once and the chapter holds all three. Rate-matched manufacture is done, at scale, profitably, and has been for a century and a half. On a cash flow statement alone, over sixty years, it loses to the market-sized plant at every discount rate above about two percent. And the whole case turns on one accounting question — whether the standing stock is an asset — which moves the crossover to five point two percent the moment it is answered the way an auditor would answer it about any other inventory.

We will do all of that arithmetic. And we will price, properly and in dollars, the thing this design genuinely costs you: the demand spike you will watch go past, every twelve years or so, permanently.

— The Editors

DISCOVERY

What is already working

Neopit, Wisconsin. The Menominee reservation is 235,000 acres of northern forest, and it has been under sustained-yield management since 1854, which makes it one of the longest continuous industrial experiments of any kind on the continent. When the boundary was drawn, the standing sawlog volume was estimated at 1,200,000,000 board feet. Since then the tribe has removed 2,300,000,000 board feet — close to twice the original forest — and the standing volume today is 1,900,000,000 board feet. The stock is 58.3 percent larger than it was at the start, after being cut through nearly twice. Counted properly, the original inventory has been turned over 3.50 times and is still there.

The number that makes this a manufacturing chapter rather than a forestry one: the Menominee forest grows about 24,000,000 board feet a year, the statutory allowable cut is 20,000,000, and Menominee Tribal Enterprises actually mills about 14,000,000 board feet of sawtimber a year alongside 75,000 cords of pulpwood, employing around 300 people. The mill's capacity was not set by the order book. It was set by the increment, and then set below it. The harvest-to-increment ratio on the milled sawtimber is 0.583.

Chester, California. The Collins Almanor Forest is 94,000 acres of mixed Sierra conifer. Harvesting began in 1941 against a standing inventory of 1,500,000,000 board feet. By 2000 the company had cut its two billionth board foot — 2,000,000,000 removed over 59 years — and the standing inventory was still 1,500,000,000 board feet. In 1993 it became the first privately owned forest in the United States to hold a Forest Stewardship Council certificate.

That pair of identical inventory figures is the cleanest measurement in this chapter, and it is worth saying exactly why. If the stock at the end equals the stock at the start, then the mean annual removal is the mean annual net increment. No model, no growth-and-yield table, no assumption. Collins removed 33,898,305 board feet a year on average, which is 360.6 board feet per acre per year, which against a standing stock of 1.5 billion is a biological rate of 2.260 percent a year.

Hold those two sites beside each other. Menominee's increment is 102.1 board feet per acre per year; Almanor's is 3.53 times that. Same discipline, same century, radically different number — because site index, species mix, rainfall and elevation set the rate, and intention does not. The renewal rate is a property of the ground. What management supplies is the decision to stay under it.

The sea. Marine Stewardship Council certified units of certification now land about 14,000,000 tonnes a year, roughly 19.0 percent of the global marine catch — including some 3,100,000 tonnes of tuna. Of that certified landing, about 1,500,000 tonnes reaches a consumer carrying the label, worth around 1,600,000,000 dollars at retail, which is about 1,067 dollars a tonne and about 10.71 percent of the certified volume. The certification has spread far faster than the label has, which is a fact about supply chains rather than about fisheries, and it means the rate-matching in the water is currently much larger than the rate-matching visible in a shop.

The national frame. United States timberland grows about 25,000,000,000 cubic feet a year net and gives up about 13,000,000,000 to harvest and clearing: a growth-to-removals ratio of 1.923, or 92.3 percent of headroom before the national ratio reaches one. That is a real and encouraging figure and it is also the single most misused figure in this field, because no plant buys from a nation. It buys from a haul radius. The aggregate can sit at 1.92 while the catchment around your mill sits at 0.7, and the aggregate will tell you nothing about the day your log supply gets short.

Four findings, and one shape underneath them: in every case somebody measured a rate first and sized the equipment second. That inversion is the entire discipline, and everything below is what it costs and what it returns.

THE ARITHMETIC

What works, what does not, and where the crossover sits

Take the Almanor measurement as the input, because it is measured rather than modelled, and build two mills on it.

  V0   standing inventory              1,500,000,000 bf
  i    biological rate                         2.260 %/yr
  H_B  rate-matched throughput            33,898,305 bf/yr
  H_A  market-sized throughput            60,000,000 bf/yr   = 1.770 x H_B

Mill B is sized to the increment. Mill A is sized to the market, at 1.770 times the increment — which is not a reckless number; it is the ratio you get from a perfectly ordinary demand study. Capital runs at 1,200,000 dollars per million board feet of annual capacity, so A costs 72,000,000 dollars and B costs 40,677,966. Contribution margin is 150.00 dollars per thousand board feet. All three of those are the chapter's own parameters and are labelled as such in the computation; the biology is measured, the plant is illustrative.

First, what happens to the stock. With V(t) = K + (V0 − K)e^{it} where K = H_A / i = 2,655,000,000 board feet — the standing stock A's throughput would need in order to be sustainable — A draws the inventory down to the operable floor of 450,000,000 board feet in 28.61 years. It consumes 1,050,000,000 board feet of standing timber to buy those years.

Then the part that is not intuitive. A does not stop. It carries on at i × V_min = 10,169,492 board feet a year — 30.0 percent of the rate that was available to it on day one. The penalty for overshoot is not an ending. It is a permanent reduction in the coupon, because the increment is a rate on the stock, and a smaller stock pays a smaller rate forever.

Second, the NPV, run the way it is normally run. Sixty-year horizon, cash flows only, A rebuilding a 12,203,390 dollar mill at year 29 when the big one is stranded:

    d       NPV A          NPV B          B - A
  2.0%   137,266,877    136,984,522       -282,355
  4.0%    86,162,507     74,908,735    -11,253,773
  6.0%    52,734,100     41,752,227    -10,981,873
  8.0%    29,635,676     22,358,279     -7,277,397

The crossover sits at 1.974 percent. That is the first honest negative and it is a large one. Below a discount rate of roughly two percent the rate-matched mill is worth more in cash; above it, it is not — and 0.87 times the forest's own biological rate is below the cost of capital of every firm that will ever read this. On the cash flow statement alone, run over sixty years, the market-sized mill wins, and it wins by eleven million dollars in the middle of the range. Any argument that pretends otherwise will be taken apart in the first ten minutes of a capital committee, and should be.

Third, run it the other way. A sixty-year appraisal that ignores what the two mills own at the end is not a conservative appraisal; it is an incomplete one. Standing timber has a market price — call it 250.00 dollars per thousand board feet of stumpage, well inside the observed range. At year sixty, A stands on 112,500,000 dollars of timber and B stands on 375,000,000. The difference, 262,500,000 dollars, is the asset A converted into thirty years of extra throughput.

    d       NPV A          NPV B          B - A
  2.0%   171,151,226    249,932,352     78,781,126
  4.0%    96,368,277    108,927,967     12,559,690
  5.0%    73,412,713     74,624,008      1,211,295
  6.0%    55,808,019     51,998,623     -3,809,396

The crossover moves to 5.172 percent — 3.198 points, and 2.29 times the forest's biological rate. That is the capital consequence of this chapter, stated exactly: rate-matched manufacture is not a cash flow argument and it never was. It is a balance sheet argument, and it is won or lost on whether the standing stock is carried as an asset. Nothing about the physical plant changed between those two tables. One line of accounting treatment changed, and it was worth three and a fifth points of discount rate.

Fourth, the concession, priced. Mill B cannot serve a demand spike. Not "struggles to" — cannot, by construction. Put numbers on it. A spike arrives about once every 12.0 years, lasts 2.0 years, brings 40.0 percent more volume demanded and 25.0 percent more margin on each unit sold. A, built at 1.77 times the increment, can surge 25.0 percent on inventory and serve the whole of it. B cannot serve any of it.

  margin in a spike                187.50 $/1000bf
  volume B is asked for            13,559,322 bf/yr
  forgone margin, one spike         5,084,746 $
  scarcity rent B does capture      2,542,373 $
  net cost, one spike               2,542,373 $
  expected annual cost                211,864 $/yr   =  4.17 % of contribution

Two things are usually got wrong here and both matter. The first is that a sold-out plant is not a plant with no upside: the 25.0 percent uplift lands on every unit B sells, so B captures 2,542,373 dollars of scarcity rent per spike and the net loss is half the gross. The second is that the loss does not end when the spike does. Assume 0.600 percent of B's margin is permanently lost to customers who found another supplier and stayed there. As a continuous decay that is 5.02 basis points a year, leaving 97.04 percent of the margin after sixty years.

Priced in full, the concession costs B 4,837,339 dollars at a 5 percent discount rate — 6.48 percent of its NPV — and moves the crossover down by 0.620 points, from 5.172 percent to 4.552 percent. That is the honest size of it. It is a real cost, it is not the cost that decides, and it belongs in the paper as a number rather than in the room as an objection.

It is also recoverable, and this is the part the defensive version of this argument misses. A plant that cannot surge is a plant that cannot fail to deliver. Sell 60.0 percent of B's output on firm multi-year supply at an 8.0 percent premium and that is 244,068 dollars a year against an expected spike cost of 211,864 — a cover ratio of 1.15 times, and the crossover comes back to 5.145 percent. Reliability is the one product the flexible competitor structurally cannot sell, because in the spike he is selling his inventory to somebody else.

Fifth, the negative that has no workaround: the rate is an estimate. Eastern Bering Sea pollock survey biomass fell from 5,500,000 tonnes to 3,800,000 in one year — -30.9 percent. Acceptable biological catch went from 2,400,000 to 2,000,000 tonnes, -16.7 percent. The total allowable catch went from 1,389,000 to 1,375,000 tonnes: -1.01 percent. Read those three lines together. TAC as a share of survey biomass rose from 25.3 percent to 36.2 percent — 10.9 points — and nobody decided to fish harder. (Survey index tonnes are not the assessment's age-structured biomass, so treat the ratio as indicative; the direction is the point.) A processor sized to the quota is sized to a management smoothing rule, not to a fish population.

So size inside the error bar. At a coefficient of variation of 20.0 percent on the increment estimate, a 90 percent one-sided design point is 1 − 1.2816 × 0.20 = 74.4 percent of the point estimate: 25,209,492 board feet rather than 33,898,305. That gives up 8,688,814 board feet of capacity, 10,426,576 dollars of capital, 1,303,322 dollars of annual contribution, and 1.677 points of crossover — down to 3.467 percent, which is below most firms' cost of capital. This is the threshold at which the design fails: if you cannot measure your renewal rate better than a 20 percent CV, rate-matching is a values decision and should be presented as one.

Which is an argument for measuring better, and the payback is absurd. Halve the CV to 10 percent and the design point rises to 87.2 percent, buying back 4,344,407 board feet and 651,661 dollars a year of contribution. An independent inventory cruise costs about 45,000 dollars. That is a payback of 0.83 months.

And now the cut. Every number above treats the plant's location as given. Take the same argument to water and it does not survive. Recharge to the High Plains aquifer runs from 0.024 inches a year in the Southern High Plains of Texas — 0.6096 millimetres — to 6.000 inches in south-central Kansas, 152.40 millimetres. Put an identical plant on an identical 50.0 square kilometre capture zone in each place. Texas sustains 30,480 cubic metres a year, which is 83.5 cubic metres a day; Kansas sustains 7,620,000, or 20,876.7 a day. At 3.50 litres of water per litre of product, the Texas plant is a 74,212 barrel craft brewery and the Kansas plant is an 18,552,876 barrel national one.

Same drawings, same capital, same engineers, and two hundred and fifty times the sustainable throughput. Siting is normally decided by logistics, labour cost and incentives, by a property team, months before the process engineers are asked to size anything. For a plant that runs on a renewing input, siting is the capacity decision, and it is currently made by the people in the building least equipped to make it.

DREAM

What becomes ordinary

In the plant that has made this transition, there are two capacity plates on the wall of the control room and everyone knows both numbers. One is what the line can do in an hour. The other is what the catchment can hand over in a year, with the date of the last measurement and the confidence interval printed beside it. Nobody finds the second plate unusual. It is checked the way a pressure vessel certificate is checked.

Capital papers open with a rate, not a forecast. The first exhibit is the renewal rate of the primary input, how it was measured, by whom, when, and how wide the interval is — and the plant's nameplate is quoted as a fraction of it. A ratio above one is not forbidden; it is simply shown with the years of stock drawdown it implies and the reduced rate that follows, so that the committee is choosing knowingly rather than discovering later.

The standing stock is on the balance sheet, carried at a defensible value, tested annually against a cruise or a survey or a piezometer network. The controller can show you the increment as a line, and the harvest as a line, and the difference between them is read every quarter the way a covenant is read. When the difference goes the wrong way, someone asks about it that month rather than in three years.

Procurement writes firm supply because the plant can promise it. The sales book has a reliability tier that the spot market cannot match, and customers pay for it, and the premium is a recognised line rather than a rounding. In the spike, the sales director does not apologise for being sold out. She takes orders for the year after next.

And the plant is old. It is unfashionable to say so, but a plant designed at the rate of its catchment is a plant whose catchment is still there when the second generation of equipment goes in, and that is why these businesses look the way they do: a century and a half in one case, eighty years in another, the same families, the same ground, the same saw kerf getting thinner as the technology improves. The throughput is modest and the duration is not, and duration is the variable nobody puts in the model.

DESIGN

The structure that gets there

One. Measure the rate before you specify the equipment. Not from a literature value and not from the national figure. From your catchment, by an independent party, with a stated confidence interval. Forest: an inventory cruise with growth plots remeasured on a five-year cycle. Water: abstraction metering plus a piezometer network and a recharge estimate for your own capture zone, not the basin. Fibre: contracted hectares with measured yields. Fishery: the assessment, read in full, including the retrospective pattern.

Two. Quote every capacity as a ratio. The harvest-to-increment ratio — the draw divided by the renewal — is the one number this whole discipline runs on. Menominee mills at 0.583. Collins ran at 1.000 for fifty-nine years. The market-sized mill starts at 1.770 and ends at 0.300 of the rate it began with. Put that ratio on the front page of the capital paper and most of the argument becomes arithmetic instead of temperament.

Three. Design to the lower bound, and then buy the error bar down. Size to the 90 percent lower bound, accept the 8,688,814 board feet you give up, and fund better measurement out of the contribution it returns. The cruise pays back in 0.83 months. This is the rare case where the conservative choice and the profitable choice are the same choice, and it is only visible if you have priced the interval.

Four. Put the stock on the balance sheet. This is the load-bearing structural move and it is an accounting conversation, not a philosophical one. Standing timber, breeding stock, aquifer storage and soil carbon are inventories with observable market prices or defensible valuation methods. Capitalise, value annually against the physical measurement, and let the increment appear as what it is. It is worth 3.198 points of discount rate, which is more than any efficiency programme you will run this decade.

Five. Sell the inflexibility. Convert the thing the design costs you into a product. Firm supply, multi-year, at a premium, at 60.0 percent of output. A rate-matched plant is the only credible counterparty for a buyer whose own line stops when a delivery is late.

Six. Write the overshoot rule before you need it. Define, in advance and in the board minute, the conditions under which the ratio may exceed one, by how much, for how long, with what repayment schedule to the stock, and who signs. Every rate-matched business that has held has had this rule, and every one that failed discovered it needed one during the spike, which is the one moment it cannot be written honestly.

Seven. Sequence it: site, rate, ratio, plant, book. In that order, and the first two before the property team signs anything. Reversing the first two costs two orders of magnitude of capacity and cannot be recovered by any amount of process engineering afterwards.

DESTINY

How it holds when nobody is pushing

It holds when the ratio is in the monthly pack. A number reviewed monthly survives a change of management; a number reviewed by exception does not survive the first quarter it is inconvenient.

It holds when the measurement is done by someone who does not report to operations. Menominee's constraint is statutory and tribal; Collins's is a third-party certificate re-audited on a cycle. In both cases the number that sets the plant's capacity is produced outside the plant, which is the whole mechanism. A self-measured increment drifts upward by about the amount the order book is short.

It holds when the stock is on the balance sheet, because then drawing it down shows up as what it is — a disposal — rather than as a strong quarter.

Now the failure modes, named. It fails in the spike, and it fails there because the spike is the moment when every incentive in the building points one way and the only thing pointing the other way is a rule written when times were quiet. That is why the rule is written in advance, with a signature attached.

It fails when the catchment is not owned or contracted. Both of the working cases in this chapter own their forest. A mill buying on the open log market cannot rate-match, because its restraint simply transfers the cut to a competitor — which is the tragedy Ostrom spent a career specifying, and her conditions apply here without modification: defined boundaries, monitoring by accountable people, graduated sanctions.

It fails when the rate is measured badly, and at a 20 percent CV it fails quietly, because a plant sized to an over-estimate looks exactly like a plant running well for about a decade.

And it fails when it is argued philosophically before it is argued numerically. The crossover is 5.145 percent with everything counted. If your weighted average cost of capital is above that, say so plainly, present it as the balance-sheet and duration decision it is, and let the committee decide knowingly. A committee that is told the truth about a 5.145 percent crossover will sometimes say yes. A committee that suspects it is being managed will always say no.

DELIGHT

What it feels like

There is a particular quiet in a mill that is running at the rate of its own ground. It is not the quiet of underuse. It is the quiet of a machine that is never being asked for the extra ten percent — no chronic overtime, no maintenance deferred into the next shutdown, no arguments about whether the line can hold together until the order clears.

And there is the scaler's book. Somebody walks the deck, measures what came in, writes it down, and the number goes into a column that is compared each year against a number the forest produced. The comparison is legible to everyone who works there. You can stand in the yard and know whether the year went well in a sense deeper than the P&L, because the two numbers are on the same page and one of them is about whether your grandchildren have a mill.

The best of it is the second decade. A plant sized to the market spends its second decade discovering constraints it did not know it had. A plant sized to its catchment spends its second decade doing exactly what it did in the first, only better, because every improvement in yield and kerf and drying is an improvement in what the same increment can be turned into. The ceiling stops being a fight and becomes a design brief, and that is a far better thing to have on a wall than a target.

OPERATIONALIZE THIS

At the level of finance

The instrument: an increment-based borrowing base — an IBB facility.

Reserve-based lending in oil and gas sets a borrowing base against a depleting reserve, certified annually by an independent engineer. The IBB inverts it. The borrowing base is indexed to the verified annual increment of the stock, not to the stock itself — so the facility grows when the asset is managed above replacement and contracts when it is not, automatically, without a covenant breach negotiation.

The mechanics.

Base. A multiple of verified annual increment valued at stumpage or its equivalent — for Almanor, 33,898,305 board feet at 250.00 dollars per thousand is 8,474,576 dollars a year of increment value. A 4× base is 33,898,305 dollars of facility, which funds most of a 40,677,966 dollar rate-matched mill.
Certification. Independent cruise, survey, or metered abstraction, annual, by a party that does not report to operations. Budget 45,000 dollars for the cruise, 12,000 for metering, 8,000 for assay — 65,000 dollars in total, or 0.160 percent of the plant's capital cost.
The governing covenant. Harvest-to-increment ratio ≤ 1.00, tested annually on a three-year rolling mean so that one bad survey does not trip it. Breach triggers a base reduction, not an acceleration: the lender's security is the increment, so shrinking the base is the correct and self-healing remedy.
Pricing. Price the facility against the certified ratio in steps. A borrower at 0.583, as Menominee mills, is a materially better credit than one at 1.000, and there is no instrument in the market today that says so.
Term. Fifteen to twenty-five years, which is available precisely because the security does not deplete. That is the second reason to write the facility this way: an undepleting security supports a longer tenor, and tenor is where the cost of capital actually lives.

The balance-sheet treatment. Capitalise the standing stock as biological inventory and revalue it against the annual physical measurement. Depreciate the plant over the catchment's supportable life rather than a conventional asset life. This is the move worth 3.198 points of crossover, and it is a conversation with your auditors about measurement and useful economic life — one they have every year about other things.

The counterparty. Farm credit institutions, timberland investment management organisations, and the agricultural desks of the commercial banks already lend against standing timber and already commission the cruise. They have the collateral machinery and no product pointed at the increment. Start there, with one internally documented facility behind you.

The hedge for the concession. Sell 60.0 percent of output as firm multi-year supply at an 8.0 percent premium — 244,068 dollars a year against an expected spike cost of 211,864, a 1.15 cover — and disclose both sides in the paper.

The number that decides it. One figure, on the front page:

     verified annual increment
  ------------------------------  >=  1.00
       planned annual draw

and beneath it the crossover, computed for your own catchment and your own plant, stated beside your WACC. For the worked mill in this chapter it is 5.145 percent with everything counted, 4.552 with the spike concession and no firm-supply book, 3.467 if you design to the 90 percent lower bound, and 1.974 if you refuse to put the stock on the balance sheet. Four numbers, one decision, and the accounting treatment moves it more than the biology does.

The first ninety days.

Day	Action	Artifact
1–15	Define the catchment; name the primary renewing input	Catchment map
16–30	Commission the independent measurement	Cruise / survey scope
31–45	Compute the increment and its confidence interval	The rate, with its CV
46–60	Compute the harvest-to-increment ratio for every line	Ratio schedule
61–75	Run the NPV both ways; find your crossover	Crossover memo
76–90	Take the ratio and the crossover to the capital committee	One page, two numbers

APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

Where in this business do we already know the renewal rate of something we depend on — and who is the person who knows it?
Which of our lines has run at the same throughput for a decade or more, and what has that steadiness quietly bought us that we have never costed?
When have we turned down volume we could have taken, and what did it protect?

Dream — what becomes possible

If the renewal rate of our main input were printed beside the nameplate capacity in the control room, what conversation would start that is not happening now?
What could we promise a customer that no competitor could credibly promise, if our supply genuinely could not fail?
If the standing stock appeared on our balance sheet at a defensible value, what would we do differently in the first week?

Design — what we build

What would it take to have our increment measured by someone who does not report to operations, starting this year?
What is the ratio — draw over renewal — for our largest input, and what would we have to do to be able to answer that question in a week rather than a quarter?
What is our overshoot rule, who signs it, and when is the right moment to write it?

Destiny — how it holds

Which of our decisions about where to put a plant were made before anyone asked what the site could renew, and what would we do differently next time?
What would we want still running here in eighty years, and what is the first measurement that makes that possible?
Who would notice first if our draw quietly crossed our renewal — and does that person have anywhere to say so?

WORKS CITED

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Collins Companies. The Collins Almanor Forest. Company record, Chester, California; and BuildingGreen newsbrief, "Collins Pine Harvests 2 Billionth Board Foot," 1 November 2000.

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North Pacific Fishery Management Council / National Marine Fisheries Service. Bering Sea and Aleutian Islands Groundfish Harvest Specifications, 2025, 2026 and 2027. Federal Register, 18 March 2025 and 16 December 2025.

Ostrom, E. (1990). Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press.

Pearce, D. W. and Turner, R. K. (1990). Economics of Natural Resources and the Environment. Johns Hopkins University Press.

Schaefer, M. B. (1954). "Some aspects of the dynamics of populations important to the management of the commercial marine fisheries." Bulletin of the Inter-American Tropical Tuna Commission, 1(2), 27–56.

United States Department of Agriculture, Forest Service. Forest Inventory and Analysis: net annual growth and removals on timberland. Successive national reports.

United States Geological Survey. Ground Water Atlas of the United States, HA 730-C and HA 730-E: High Plains aquifer. Reston, Virginia.

Note on figures. Every figure in this unit is computed in lib/verify/IV_04.py and printed with its inputs, its units and its source. Inputs marked [PLANT] — capital per unit of capacity, contribution margin, stumpage, the operable-inventory floor, spike frequency and depth, and the appraisal horizon — are the chapter's own stated parameters and are labelled as assumptions, not measurements. The biology, the landings, the quotas, the recharge rates and the yields are measured, and each carries its source in the module.