La Bourse / Volume I / Nº I.10 / Quiz, reflection, essays

A kitchen counter of pale wood with a cutting board, knives and cut vegetables, morning light from the windows beyond. — Plate I.10 · Quiz, reflection, essaysThe Fortieth Kitchen.A thing has scaled when the fortieth person does it right without being watched, and cannot quite tell you why.

ASSESSMENT · Chapter I.10 — Scaling Without Losing the Thing

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. Name the four instruments of scale and state, for each, who holds the unit's residual.

Replication — you. Franchise — the local operator. Federation — each member, who also part-owns the centre. Licence — the licensee entirely. One mark for the four names, one for getting the residual right in all four. The residual is the variable that distinguishes them; brand and fee structure are consequences of it.

2. Write the fidelity expression and say what each term is.

F(k) = φ^k. φ is the fraction of the thing that survives one teaching hop; k is the number of hops between the source and this unit. Credit any answer noting that the loss is exponential in k and only linear in φ, which is why reducing hops beats improving documentation.

3. Why does shared benefit saturate while coordination cost does not?

Shared benefit — purchasing power, back office, risk pooling, brand — is mostly captured by the first dozen members and approaches a ceiling. Coordination in a mesh of peers grows as n(n−1)/2 relationships, so each member's share grows as (n−1)/2 and never flattens. One curve stops, the other does not.

4. What is the portable organ, and when is it built?

The small piece of structure that makes the next unit possible without making it dependent — Caja Laboral, a CUSO, a ground lease with a resale formula, an operations manual with a residual claim attached. Built at unit three, not unit thirty: at unit three you can still see all of it, and later means building it while it is load-bearing.

Four on application.

5. A franchisor is puzzled that quality is falling across the network while unit revenues are healthy. The royalty is 7 percent of gross plus a 2 percent ad fund. Diagnose it.

The wedge. The royalty is on revenue and quality spending comes out of profit, so the franchisor gains from any revenue-raising spend at zero cost while the operator must clear a break-even lift before they gain at all. Quality investment is being correctly declined by rational operators. The strong answer names a counter-mechanism: co-funded quality investment, a royalty holiday on specified upgrades, or a royalty on gross profit rather than gross revenue.

6. A trade association of 140 independent members is told by its board that it needs to grow to 300 to be viable. What is wrong with that argument, and what should be measured instead?

Benefit saturates; coordination does not. At 140 peers the association is almost certainly already past the point where the mesh costs more than it returns, and doubling the membership makes it worse, not better. What should be measured is B, k and c for this association, and the answer is very likely to be cluster, not grow. Full marks note that the fix is topology, not size.

7. A network has 60 units and a founder who still personally trains every one. What has actually been scaled, and what is the first structural move?

Nothing has been scaled; one person has been spread thinner. Fidelity is excellent and the mechanism is a bottleneck with a pulse. The first move is to convert the founder's training into an organ — a training function with its own staff, budget and standard — accepting a one-hop fidelity loss in exchange for a transmission mechanism that survives a holiday.

8. Why does the chapter insist that exit from a federation be cheap, and that data leave with the departing member?

Because a member who cannot leave is a hostage, and hostages do not contribute. A federation held together by switching costs has stopped being a federation and become a captive supplier relationship — which destroys the voluntary quality that made shared governance work in the first place. Credit any answer noting that cheap exit is also the only honest test of whether the organ is delivering.

Two that require the arithmetic to be done.

9. A federation measures its own parameters: shared benefit saturating at £90,000 per member per year, with k = 10, and coordination costing £3,500 per relationship held per year. Compute the optimum membership and the size above which the federation is net-negative. Show your working.

Optimum: n = k·ln(2B/kc) = 10 · ln(180,000 / 35,000) = 10 · ln(5.1429) = 16.38 — sixteen members. Net: B(n) − c(n−1)/2 with B(n) = 90,000(1 − e^(−n/10)); this turns negative at n = 53. Credit any method reaching 16 and low fifties. The point of the question is that both numbers are far smaller than a federation's usual ambition, and both are computable from figures it already has.*

10. A network transmits at 85 percent fidelity per hop and holds a floor of 70 percent. How many hops may it allow before retraining, and how large can the network be at that depth if each unit trains four others a year? Show your working.

k_max = ln(0.70) / ln(0.85) = −0.3567 / −0.1625 = 2.19 — two hops, since the third would sit at 0.614, below the floor. At four trained per unit, the network within two hops is 1 + 4 + 20 = 25 units. The stronger answer notes what this implies: at 85 percent fidelity you owe a retrain after twenty-five units, and lifting φ from 0.85 to 0.90 moves that to eighty-five — which is the cheapest scale available to the organisation.

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 in your work is currently working only because you are standing there? Write it down before you decide whether that is a problem.

How many hops are there between you and the most distant person doing the thing you started? Guess first, then find out. What is the gap between the guess and the answer telling you?

Recall something you were taught by someone who was taught by someone. What part of it arrived with a reason attached, and what part arrived as a rule nobody could explain?

Which of the four instruments have you been unconsciously assuming? Would you defend that choice if someone asked you to, out loud, today?

What do you currently do twice that you could do once? You have known the answer for about a year. Why has it not been built?

What would have to be true for you to be genuinely glad that a distant unit was better at this than you are now? Answer honestly before answering generously.

Think of a group you left, or wanted to leave, and could not do so cheaply. What did that cost you, and what did it cost them?

If you had to write the number into your own constitution — the size at which you stop admitting — what would it be, and what does the reluctance to write it down tell you?

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 ceiling and the clause. The chapter computes a federation of pure peers turning net-negative at eighty-seven members and proposes writing the ceiling into the constitution. Argue either that a self-imposed size limit is a mature governance instrument, or that it is an unenforceable pre-commitment that no growing organisation will honour when the moment arrives. Use Ostrom's design principles, and one source on organisational pre-commitment or constitutional rules the chapter does not cite.

2. Does the residual claim explain it? Rubin's argument is that franchising exists to buy unobservable effort. Take a position on whether this fully explains the franchise contract, or whether it under-weights brand capital, financing constraints on the franchisor, and the transfer of risk. Engage Rubin directly and at least one later treatment — Klein, Lafontaine, or the empirical franchising literature.

3. Mondragón did not cross the border. The great majority of Mondragón's plants outside Spain are ordinary subsidiaries with ordinary employees. Argue this as evidence that the cooperative form is locally contingent rather than generalisable — then write the strongest rebuttal, which must engage what the federation was actually trying to protect when it made that choice. Errasti et al. (2003) is the starting point; find at least one account written after 2015.

4. The second tier. The chapter's central move is that raising the ceiling requires adding a tier, and that the added tier is the one that fails. Argue whether the 2009 corporate credit union failures are an indictment of tiered federation or an indictment of how that particular tier was capitalised and supervised. Use NCUA material and one source on financial intermediation or systemic risk the chapter does not cite.

5. Retention against addition. The community land trust scales a clause rather than an organisation, and retains a subsidy rather than spending it. Argue the counter-case: that resale restrictions transfer wealth-building away from exactly the households the subsidy was meant to serve, and that five families each capturing a quarter of the appreciation is not obviously better than one family capturing all of it. Use Davis and Stokes (2009), and one source on housing wealth accumulation and intergenerational transfer the chapter does not cite.