La Bourse / Volume III / Nº III.08 / Quiz, reflection, essays

Four colleagues standing together talking among plants, late sun coming through the glass behind them. — Plate III.08 · Quiz, reflection, essaysThe Third Round.One of those notes came in this morning from the flour merchant's daughter, went out at noon to the greengrocer, and will be back on this street before Thursday. Nobody has ever measured that at the level of a country. It is measured here every evening, by hand, in a book.

ASSESSMENT · Chapter III.08 — Velocity, Circulation, and Health

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. Write the income form of the quantity equation, the Cambridge form, and say which term is measured by no independent procedure.

M · V = P · Y = nominal GDP, and M = k · P · Y with k = 1/V. P, Y and M each come from a measurement procedure — a price index, the national accounts, the monetary aggregates. V comes from none. It is defined as nominal GDP divided by M. One mark for the two forms, one for naming V as the residual.

2. What does the income form of velocity exclude, and why does that matter?

It divides by nominal GDP, which counts only final output. Intermediate trade, second-hand goods, house purchases and all financial transactions are outside it. So V is not the number of times a dollar was spent — it is the number of times a dollar was spent on things the national accounts count.

3. State the three closed forms for local income per pound at a uniform retention rate r: after n rounds, in the limit, and the share that three rounds capture.

L(n) = (1 − rⁿ)/(1 − r); L = 1/(1 − r); and L(3)/L = 1 − r³. LM3 is the case n = 3, that is 1 + r + r².

4. What happened to M1 between the first and second quarters of 2020, and what caused it?

M1 rose from 4,002.0 to 16,206.0 billion dollars because the Federal Reserve amended Regulation D on 24 April 2020, removing the six-per-month transfer limit on savings deposits, after which savings deposits were reported inside M1. M1 velocity fell from 5.382 to 1.229 — 77.2 percent — with the great majority of the fall attributable to the redefinition.

Four on application.

5. A newspaper reports that "money is barely circulating — velocity has halved since 1997." Restate the same fact in a way that invites a useful question, and say what the useful question is.

Restate it as a holding period: the economy held about 5.5 months of its income as money in 1997 and about 10.9 months of it in mid-2020. The useful question is what are households and firms insuring against, and is that reasonable? — because the second phrasing describes a decision with reasons and the first describes a disease with none. Full marks require noticing that the two statements are the identical measurement.

6. A council proposes a local-sourcing policy on the grounds that the local multiplier is higher. Name the two questions you would ask before the vote.

First: what is the boundary, and what is the rule for a counterparty with several addresses? A retention figure without a published boundary can be produced to order. Second: what is the efficiency penalty on the local basket, and how does it compare with the breakeven p? Credit any answer that also asks whether round two was measured or modelled.*

7. Your colleague argues that a demurrage currency is healthier because it circulates faster. Using the cardiac identity, say precisely what is wrong with the inference — and what is right about the underlying instinct.

Cardiac output is rate × stroke volume: 60 × 70 and 100 × 42 both give 4,200 ml/min, so a 66.7 percent higher rate at 40.0 percent lower stroke volume delivers exactly the same flow, and a clinician calls that compensated shock. The health variable is output, not rate. What is right in the instinct is that a closed ledger can measure turnover honestly, which a national aggregate cannot — so the scrip's figure is real even though the inference from it is not.

8. Why should an early-payment facility be offered to your smallest suppliers before your largest?

Because the gain is the spread between their cost of funds and yours, and that spread is widest for small, thinly-capitalised counterparties. Paying your largest supplier early transfers cash at little or no spread — a gift with no arithmetic behind it. The stronger answer notes that the facility's viability is decided by the spread net of running cost, not by volume.

Two that require the arithmetic to be done.

9. A parish measures a retention rate of r = 0.35. Compute LM3, the multiplier in the limit, and the share of the true multiplier that three rounds capture. Then state the local income generated over three rounds by £250,000 of anchor spend.

LM3 = 1 + 0.35 + 0.1225 = 1.4725. In the limit, 1/(1 − 0.35) = 1.5385. Captured share = 1 − 0.35³ = 1 − 0.042875 = 95.71 percent. Local income over three rounds = 250,000 × 1.4725 = £368,125. The point of the question is the third figure: at a modest retention rate the truncation costs almost nothing, which is exactly why LM3 is safe for a parish and misleading for a high-retention circuit.

10. Nominal GDP is 30,331.0 billion dollars and M2 is 21,900.0 billion. Compute velocity, express it as a holding period in months, and decompose the change since 1997Q3, when nominal GDP was 8,542.2 and M2 was 3,897.0.

V = 30,331.0 / 21,900.0 = 1.3850, and 12 / 1.3850 = 8.66 months of income held as money. The decomposition: ln(PY ratio) = 1.2672 against ln(M ratio) = 1.7263, so ln(V ratio) = −0.4591 and the V ratio is 0.6318 — a fall of 36.8 percent from the 2.192 peak. Full marks require the final sentence in the right register: nothing about speed was observed. Nominal income roughly tripled and the money stock rose by rather more.

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.

Think of a number you have quoted more than once that you have never computed yourself from its inputs. What would it cost you, in hours, to compute it this week?

Where do you personally hold more money than you need, and what are you actually insuring against? Answer it as a decision with reasons rather than as a habit.

When did you last describe something as slow when the honest description was that somebody had chosen to wait? What changed in your own view when you made that substitution?

Whose money are you holding right now by paying later than you could — and what is that costing them at their cost of capital rather than yours?

What boundary do you draw around the word local in your own life? Write it down precisely, including the awkward cases, and notice what the precision does to the idea.

Recall an argument you lost because your evidence was a model presented as a measurement. What would it have cost to state which it was?

Where in your work are you optimising a rate when the thing that matters is an output? Name both, in their own units.

What have you been busy at that has not, on inspection, delivered more? Sit with that without correcting it, and then write one sentence about what the busyness was doing for 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. Is velocity a concept worth keeping? The chapter argues that V is a residual with one degree of freedom and no independent observation, and that the largest recorded collapse in a velocity series was substantially a change in the definition of M1. Argue either that velocity should be retired from serious monetary discussion in favour of the Cambridge k, or that a residual can still be an informative summary statistic and the fault lies in its interpretation rather than its construction. Engage Friedman (1956) directly, and at least one post-2008 empirical paper on money demand that the chapter does not cite.

2. The Divisia argument. William Barnett has argued for four decades that simple-sum monetary aggregates add imperfect substitutes at equal weight and are therefore the wrong denominator for any monetary ratio. Take a position on whether a Divisia aggregate would have made the 2020 M1 discontinuity smaller, larger, or simply different in kind. Use Barnett (1980 or 2012), and at least one source published by a central bank or statistical agency defending the simple-sum construction.

3. LM3 and the model-measurement boundary. The chapter shows that backing a uniform retention rate out of a published LM3 of 2.50 implies 82.3 percent retained at every round, far above any measured single-round rate — and concludes that the two methods are not interchangeable. Argue either that LM3's value lies precisely in being cheap enough for a parish to run, imprecision included, or that a measure whose assumptions cannot survive inspection does more harm than good in a political setting. Use Sacks (2002), and one source on measurement quality or evaluation standards in local economic development that the chapter does not cite.

4. The threshold, applied to a real place. The chapter computes a breakeven efficiency penalty of 47.5 percent, above which a higher local multiplier delivers less circulation per unit of goods delivered. Take a real community wealth programme — Preston is the obvious choice, but it need not be — and argue whether the threshold is a genuine constraint in practice or a theoretical one. Use the CLES Preston material, and at least one critical or sceptical evaluation of community wealth building that the chapter does not cite.

5. What the bloodstream metaphor cost. Money has been described as the blood of the economy since at least William Harvey's contemporaries, and the metaphor is doing work in almost every claim about circulation health. Argue either that the metaphor has been a productive research heuristic that happened to be misapplied in this one case, or that biological metaphors in economics systematically import a normative direction — faster, richer, more — that the biology itself does not support. Use the cardiac arithmetic in this chapter and Stodder's WIR work, and at least one history or philosophy of economics source on organic metaphor that the chapter does not cite.