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Commerce · IV.04 · MMXXVI · daylight
ASSESSMENT · Chapter IV.04 — Manufacture at Biological Rates
Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.
THE QUIZ — ten points
Four on recall.
1. Define the harvest-to-increment ratio and state the threshold that matters.
Planned annual draw divided by verified annual increment. At or below 1.00 the standing stock holds or builds; above it the stock falls, and so does next year's increment. One mark for the definition, one for naming 1.00 as the threshold and explaining that the increment is a rate on the stock, so the penalty compounds.
2. Menominee Tribal Enterprises mills about 14,000,000 board feet of sawtimber a year against an increment of 24,000,000. What is the ratio, and what sets the mill's capacity?
0.583. The capacity is set by the forest's increment and then deliberately set below it — not by the order book. Credit any answer that names the statutory allowable cut of 20,000,000 board feet as the intermediate constraint.
3. Why is the Collins Almanor figure described as a measurement rather than a model?
Because the standing inventory was 1,500,000,000 board feet in 1941 and 1,500,000,000 in 2000. When the stock at the end equals the stock at the start, the mean annual removal is the mean annual net increment — 33,898,305 board feet a year — with no growth-and-yield assumption in it.
4. Name the two capacity plates the chapter asks a plant to carry.
What the line can do in an hour, and what the catchment can renew in a year — the second with its measurement date and its confidence interval beside it.
Four on application.
5. A mill buying logs on the open market proposes to hold its own draw below the local increment. Diagnose the proposal.
It will not work as a conservation mechanism and may work as a commercial one. Restraint by a buyer with no control of the catchment transfers the cut to a competitor rather than leaving it standing. Both working cases in the chapter — Menominee and Collins — own their forest. Full marks require naming Ostrom's conditions: defined boundaries, monitoring by accountable people, graduated sanctions. Credit an answer that notes the firm-supply premium may still be available even where the conservation claim is not.
6. Your board is shown that the United States grows 25,000,000,000 cubic feet of timber a year and removes 13,000,000,000, and concludes that supply is not a constraint on a new mill. What is missing?
A plant does not buy from a nation, it buys from a haul radius. The national growth-to-removals ratio of 1.923 is compatible with a catchment ratio well below one. The stronger answer notes that this is a denominator problem: the figure is true and it is being asked a question it cannot answer.
7. A property team has shortlisted two sites for a beverage plant on labour cost and road access. What do you tell them, and why is the order of decisions wrong?
That for a plant on a renewing input, siting is the capacity decision. High Plains recharge runs from 0.024 inches a year to 6.000 inches — 250 times — so two sites with identical capital can differ by two orders of magnitude in sustainable throughput. Site, then rate, then ratio, then plant. Credit any answer that observes no process improvement recovers 250×.
8. Eastern Bering Sea pollock survey biomass fell 30.9 percent in a year while the total allowable catch fell 1.01 percent. What does that tell a processor sizing a plant to the quota?
That it is sizing to a management smoothing rule rather than to a fish population. The implied exploitation rate rose from 25.3 percent to 36.2 percent of survey biomass — 10.9 points — without anyone deciding to fish harder. The strongest answers note that survey index tonnes are not the assessment's age-structured biomass, so the ratio is indicative, and that this caution does not change the direction.
Two that require the arithmetic to be done.
9. A mill runs at 60,000,000 board feet a year on a forest with 1,500,000,000 board feet standing and a biological rate of 2.260 percent. The operable floor is 30 percent of the opening inventory. How long does it run at full rate, and what is the sustainable rate afterwards? Show your working.
K = H/i = 60,000,000 / 0.0226 =2,655,000,000 board feet — the stock that throughput would need.V(t) = K + (V0 − K)e^{it}, sot = ln((K − V_min)/(K − V0)) / i = ln(2,205,000,000 / 1,155,000,000) / 0.0226= 28.61 years. Afterwards the sustainable rate isi × V_min = 0.0226 × 450,000,000 =10,169,492 board feet a year, which is 30.0 percent of where it started. The point of the question is the last sentence: overshoot does not end the harvest, it permanently lowers the coupon.
10. Over a sixty-year appraisal the rate-matched mill overtakes the market-sized one below a discount rate of 1.974 percent on cash flows alone. Counting 262,500,000 dollars of standing timber at the horizon moves that crossover to 5.172 percent. Pricing the demand-spike concession moves it to 4.552; selling 60.0 percent of output firm at an 8.0 percent premium returns it to 5.145. A firm with a 9 percent WACC asks what the arithmetic tells it to do. Answer, with the numbers.
That the arithmetic does not clear its hurdle, and that saying so is the correct answer. 5.145 percent is the crossover with everything counted, and 9 percent is above it — so the rate-matched design is a decision about duration, balance-sheet composition and supply reliability, not an NPV decision, and it should be presented that way. Full marks require naming the largest single lever, which is the accounting treatment: putting the standing stock on the balance sheet is worth 3.198 points, more than the spike concession (0.620) and the firm-supply book (0.593) combined. Credit an answer that also notes the sixty-year horizon is itself an assumption and that a longer horizon moves the crossover further in the rate-matched plant's favour.
REFLECTION — eight questions, for one person and a pen
These are not for a room. Write the answers by hand if you can; the slowness is the point.
- What is the renewal rate of the thing your own work draws on most heavily? Answer in a quantity per unit of time before you answer in words.
- Where have you taken volume you could serve rather than volume you could keep serving — and what did the difference turn out to cost?
- Think of a stock you have on a balance sheet somewhere and a stock you do not. What decided which was which, and was it ever decided at all?
- When was the last time you were sold out and could not supply? What did you feel, and how much of that feeling was about the money?
- What measurement about your own capacity have you been running on an estimate somebody made years ago? What would it cost to remeasure it this month?
- Where in your life are you designing to a point estimate rather than a lower bound, and what is the confidence interval you have never written down?
- Recall a decision about where something would happen that turned out to determine what was possible. Who made it, and what were they optimising?
- If you could promise one person one thing you could not fail to deliver, what would it be — and what would you have to give up to make that promise true?
ESSAY PROMPTS — five
Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.
1. The accounting treatment, not the biology. The chapter finds that capitalising the standing stock is worth 3.198 points of crossover — more than every operational lever in the chapter combined. Argue either that the case for rate-matched manufacture is fundamentally an accounting reform, and should be pursued through standard-setters rather than through firms, or that a treatment which only pays off at a sixty-year horizon will always be gamed. Use the chapter's Collins material, and one source on biological-asset accounting or fair-value measurement that the chapter does not cite.
2. An epitaph, or an obituary? Larkin's 1977 epitaph for maximum sustained yield argued the concept was conceptually bankrupt; the Bering Sea pollock figures in this chapter show a quota moving 1.01 percent while the survey moved 30.9. Argue whether modern harvest control rules answer Larkin's objection or merely postpone it. Engage Larkin directly, and at least one post-2000 stock-assessment source the chapter does not cite.
3. The spike you let go past. The chapter prices the demand-spike concession at 4,837,339 dollars and 0.620 points of crossover, and argues it is recoverable through firm supply. Argue the opposite case: that permanent share loss in a spike is under-modelled — that customers acquired by a competitor during a two-year shortage are lost at a rate far above 0.600 percent of margin, and that the chapter's parameter is the weakest number in it. Use the chapter's own model, and one empirical source on customer switching or stockout behaviour that it does not cite.
4. Ownership as the precondition. Both working cases own their catchment outright. Argue whether rate-matched manufacture is available to a firm that buys its inputs on an open market — and if so, through what mechanism: long-term contracts, cooperative purchasing, certification, vertical integration, or something else. Ostrom is the starting point; find at least one account of a contract-based or certification-based scheme that succeeded or failed, that the chapter does not cite.
5. Siting, and who decides. The chapter's sharpest figure is that identical plants on identical capture zones differ by 250 times in sustainable throughput depending on where they stand. Argue either that industrial siting should be governed by renewal capacity the way it is already governed by zoning and emissions, or that such a regime would simply relocate extraction to wherever measurement is weakest. Use the USGS recharge material, and one source on industrial location theory or water allocation policy that the chapter does not cite.