Haute Lumière
Commerce · II.02 · MMXXVI · daylight
ASSESSMENT · Chapter II.02 — Markets as Living Systems
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 three questions that live inside the word "equilibrium", and state which of them Arrow and Debreu (1954) answered.
Existence, uniqueness, and attainment. Arrow and Debreu answered existence only — under stated conditions a market-clearing price vector exists. Uniqueness does not follow, and attainment was answered in the negative by Scarf (1960). One mark for the three, one for identifying which was proved.
2. Which three properties of individual demand survive aggregation, under Sonnenschein–Mantel–Debreu, and which three do not?
Survive: continuity, Walras's law, homogeneity of degree zero. Do not survive: uniqueness, stability, comparative statics. Full marks require the consequence: individual rationality places almost no restriction on aggregate behaviour, which is why the representative agent is a substitution rather than a simplification.
3. What is the measured Pareto exponent of US firm sizes, and what does it imply about the mean and the variance?
α = 1.059 (Axtell, 2001, on roughly 5.5 million firms). The mean is finite, because that requires α > 1. The variance is infinite, because that requires α > 2. A distribution with infinite variance has no typical member.
4. State May's criterion and say what it predicts.
σ·√(S·C) > 1 implies a randomly assembled community of S species with connectance C and interaction strength σ is almost surely unstable. It predicts that adding species and connections makes such a system less stable, not more.
Four on application.
5. A colleague argues: "Markets find the efficient allocation — that is what equilibrium theory shows." What is the precise correction?
Equilibrium theory shows such an allocation exists under stated conditions. It does not show that any adjustment process reaches it, and Scarf's example is a three-good, three-consumer economy with textbook preferences in which tâtonnement orbits permanently. Credit any answer that distinguishes existence from attainment without overclaiming — the theorem is not wrong, it is narrower than the sentence quoted.
6. Your operations director says the new network is "more diverse and more connected, so it will be more resilient." Diagnose this using the chapter.
It is the inference the chapter explicitly refuses. May's criterion says diversity and connectance both raise σ·√(S·C), pushing toward instability, and Haldane and May (2011) carried exactly that result into banking. The stronger answer distinguishes the regimes: connection is risk-sharing at low stress and contagion at high stress, so the correct move is to measure S, C and σ rather than to assume either direction.
7. Why does the chapter argue that the economy is an ecosystem rather than an organism, and what turns on the distinction?
Because the scaling exponents have opposite signs relative to one: biological metabolism at β ≈ 0.75 is sublinear, urban socioeconomic output at β ≈ 1.15 is superlinear. An organism has one genome, one objective, a bounded life and a target adult size; an ecosystem has none of these. Full marks note what turns on it: the ecosystem analogy licenses inferences about diversity, adaptation and no target size; the organism analogy licenses claims about a single objective function and an optimal scale, and those claims are unsupported.
8. The Santa Fe artificial market converged toward rational expectations in some runs and not others. Why is this the chapter's strongest result rather than an embarrassment?
Because it locates the neoclassical model rather than refuting it. At slow learning rates the homogeneous rational-expectations equilibrium is found; at faster rates the complex regime appears with the realistic statistics. The orthodox model is the low-adaptation limit of the larger one. A theory that contains its predecessor as a special case is in a much stronger position than one that contradicts it.
Two that require the arithmetic to be done.
9. A metropolitan area triples in population, from 1.2 million to 3.6 million. Using β = 1.15 for wages and output, by what factor does total output rise, and what happens per head? Show your working. Then state the factor for a biological system at β = 0.75 and explain the sign difference.
Total output rises by 3^1.15.
ln 3 = 1.0986;1.15 × 1.0986 = 1.2634;e^1.2634 = 3.537. Total output rises 3.54× on a 3× population. Per head: 3^0.15 = 1.179, so output per head rises 17.9 percent. At β = 0.75 the per-unit factor is 3^(−0.25) = 0.760, a 24 percent fall. The mark is for the sign: superlinear means per-unit rises with size, sublinear means it falls, and the two systems are therefore not analogues.
10. Your treasury holds a £40 million liquidity buffer sized on a 99 percent Gaussian Value at Risk. The chapter's buffer multiple is k = ES(cubic, 99%) / VaR(Gaussian, 99%) = 1.74. (a) What is the tail-sized buffer? (b) By what percentage is the existing buffer short of the average loss in the tail it was built for? (c) Under what measured condition should you not make this change?
(a) £40m × 1.74 = £69.6 million. (b)
1 − 1/1.74 = 0.425, so the existing buffer is 42.5 percent short of the tail's average loss. (c) If the tail exponent estimated on your own series comes back above about 4, k falls close to 1 and the change is not worth its commitment fee. The third part carries the most credit. An instrument whose own test can tell you not to buy it is the only kind worth proposing.
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.
- Where have you used an average this year to describe something you privately knew had no typical member? What did the average let you avoid deciding?
- Think of a time you correctly anticipated something the official model missed. What were you attending to that the model was not, and could it have been written down?
- What in your working life is currently at high relative ascendency — highly optimised, single-path, no slack — and what would it cost you to be wrong about it?
- Which of your own beliefs about how markets work would you least like to see tested against a tail exponent? Write it out as a claim that could fail.
- Recall a standard, tool or supplier you use that you believe is inferior to an alternative that lost. What locked it in, and when was that decided?
- When have you watched an efficiency programme make something faster and then make it brittle? At what point could you feel the turn, and what did you say?
- What is the largest thing that could happen to your organisation that does not appear anywhere in its planning? Why is it absent — because it is unlikely, or because the model used cannot represent it?
- Where are you currently reasoning from a metaphor you could not convert into a theorem? Name it. Then write the one measurement that would tell you whether the metaphor is carrying weight or decorating a conclusion.
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. Does Sonnenschein–Mantel–Debreu actually damage macroeconomics? The theorem is frequently cited as fatal to representative-agent modelling and frequently answered with the claim that restrictions on preferences and endowments recover well-behaved aggregates. Take a position. Engage Kirman (1992) directly, and at least one defence of aggregation written by someone who takes the theorem seriously and is not persuaded by the conclusion drawn here.
2. Is agent-based modelling science yet? Farmer and Foley (2009) argued in Nature that the economy needs agent-based modelling; Fagiolo and Roventini (2017) treat calibration and validation as unsolved. Argue either that the method has met a defensible empirical standard — the Long House Valley validation and the Bank of England housing model are your best cases — or that its degrees of freedom make it unfalsifiable in practice. Use at least one methodological source on model validation the chapter does not cite.
3. Diversity, stability, and which discipline is right. May's random-matrix result says diversity destabilises. A substantial empirical ecology literature finds that diverse communities are more stable in practice — the portfolio effect, compensatory dynamics, non-random interaction structure. Argue which body of work should govern economic policy on concentration, and what would have to be measured to settle it. Use May (1972) and Haldane and May (2011), plus one empirical diversity-stability paper the chapter does not cite.
4. The organism and the ecosystem. The chapter rejects the metabolic metaphor on the evidence of the scaling exponents. Write the strongest defence of the organism analogy that survives Bettencourt et al. (2007) — for instance, that firms, unlike cities, may scale sublinearly, or that superlinear scaling is a transient of an innovation-driven phase. Then write the rebuttal. Conclude with which you find more persuasive and what evidence would change your mind. Find at least one study of scaling in firms rather than cities.
5. Where complexity economics should not be used. The chapter names five questions where neoclassical tools remain the better instrument — single-market analysis, auction design, matching, tax incidence, index numbers. Argue either that this list is too generous, or that it is too short and complexity economics has been oversold beyond a narrower domain than its advocates claim. Use Milgrom (2004) or Roth and Peranson (1999), and one critique of complexity or agent-based economics that the chapter does not cite.