La Bourse / Volume IV / Nº IV.05 / Quiz, reflection, essays

A watercolour of rolling hills in late summer, a farmhouse and a line of trees on the far ridge. — Plate IV.05 · Quiz, reflection, essaysThe Ten Thousandth.The ten thousandth panel costs less than the first. Nobody economised. Ten thousand people each learned something small and none of them could tell you what.

ASSESSMENT · Chapter IV.05 — Energy Systems That Compound

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. State Wright's law, define every term, and give the relationship between the learning rate and the learning exponent.

C(Q) = C0 · (Q/Q0)^(−b), where Q is cumulative units ever produced, C is cost per unit and b is the learning exponent, with b = −log2(1 − LR). One mark for the expression, one for naming Q as cumulative production rather than annual output — that is the substitution the whole chapter turns on.

2. Give the fitted learning rate for solar photovoltaic modules from the chapter's regression, with its interval, and say what a second route gives.

22.5 percent per doubling, 95 percent interval 19.1 to 25.7 percent, from an ordinary least-squares fit on eleven published points, R² = 0.9534. An endpoints-only route sharing none of the regression's assumptions gives 25.6 percent, a disagreement of 3.1 points. Full marks require the interval; a point estimate alone is half the answer.

3. Name three costs that a levelised cost of energy figure does not contain.

Transmission to demand; balancing, reserves and frequency control; curtailment; firming — the cost of moving a kilowatt-hour to a later hour. Any three. Credit also grid-connection queue costs and system-strength services.

4. What did the French pressurised-water reactor programme measure, and why is it in this chapter?

Across 5.86 doublings — 58 reactors, largely to a small number of designs, by one utility — real overnight construction cost rose by a factor of about 3.5: a learning rate of −23.8 percent. It is in the chapter because it establishes that cumulative production is not a cause of cost reduction, only an opportunity that a particular manufacturing architecture can take.

Four on application.

5. A colleague presents a slide showing that onshore wind has a learning rate of 39.4 percent. What has probably happened?

They have computed it from LCOE rather than capital cost. The chapter's decomposition: capital cost fell to a ratio of 0.5324 over 2.42 doublings while the global weighted-average capacity factor rose from 27 to 36 percent, a ratio of 0.7500. The capital-cost learning rate is 23.0 percent and the published turbine figure is about 12 percent. The stronger answer notes that a global weighted average also carries a composition effect as the country mix shifts, so even 23.0 percent is not a pure learning measurement.

6. Your board asks for a single-number forecast of solar cost in 2040. What do you give them, and what do you tell them the answer is sensitive to?

An interval, not a number, with the deployment assumption stated. Across the measured learning interval the answer at 16,000 GW moves by 1.30×; across a deployment range of 4,000 GW to 16,000 GW it moves by 1.67×. Full marks require the conclusion: an argument about the learning rate is usually a displaced argument about deployment policy, and should be conducted as one.

7. A supplier offers a fifteen-year fixed-price contract for a component you buy in growing volumes. What should you ask for instead, and why?

A volume commitment against a price path indexed to cumulative production, with the implied learning rate stated. Volume is the input to the exponent and price is the output; negotiating the output negotiates the wrong variable. Credit any answer naming a collar, a public index, or a periodic re-fit.

8. Residential solar costs about $3.00/W installed in the United States and about $1.00/W in Australia, with the same panels. What does that ratio measure, and what does it imply about where the remaining work is?

A ratio of 3.0× that measures soft cost — permitting, inspection, interconnection, customer acquisition, licensing — because the hardware is a world price. It implies the remaining work is institutional rather than technological. The stronger answer connects it to the module share: a module at $0.15/W inside a $0.758/W utility system is 19.8 percent of the cost, so free modules would still leave $0.0353/kWh standing.

Two that require the arithmetic to be done.

9. Cumulative world solar stands at 1,865 GW and modules are $0.15/W. Project the module price at 7,460 GW at the bottom and the top of the measured learning interval. Show your working, and say which of the two inputs you are less sure of.

Doublings: log2(7,460 / 1,865) = 2.00. At 19.1 percent: 0.15 × 0.809² = 0.15 × 0.6545 = $0.0982/W. At 25.7 percent: 0.15 × 0.743² = 0.15 × 0.5520 = $0.0828/W. At the central 22.5 percent, $0.0901/W. Full marks require the last clause: the deployment figure of 7,460 GW is the input you are less sure of, and it moves the answer more than the whole learning interval does.

10. A 100 MW solar farm produces 220 GWh a year at an LCOE of $0.044/kWh. The buyer wants 40 percent of the output delivered in the evening. Using the chapter's firming cost of $0.1076 per shifted kilowatt-hour, what is the blended price, and by what factor does it exceed the headline?

Energy shifted: 220 × 0.40 = 88.0 GWh. Extra cost: 88.0 GWh × $0.1076/kWh = $9.47 m. Base cost: 220 GWh × $0.044 = $9.68 m. Blended: ($9.68 m + $9.47 m) / 220 GWh = $0.0871/kWh — an uplift of 1.98× on the headline LCOE. The stronger answer states the conclusion in the right register: the headline was never wrong, it was answering a different question, and the shaped product is a different product with a different price.

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 one thing you have become measurably better at through repetition rather than instruction? How would you know the rate, if you had kept the records — and why did you not keep them?

Where in your own work do you pay a price that you have always negotiated and never tried to move by committing volume instead? What has stopped you?

Think of a forecast you made that was wrong in the same direction more than once. What model were you using without knowing you had chosen it?

Which of the things you rely on is on a falling curve, and which is on a rising one? Write the two lists before you read the next question.

Now look at the second list. What would it take to move one item from it to the first list — not to reduce its price, but to change the sign of its exponent?

When did you last say a number out loud with its interval attached, in a room where a point estimate would have been more persuasive? What did it cost you, and what did it buy?

What are you currently calling a subsidy, a sunk cost or an indulgence that might be capital expenditure that nobody has classified correctly — in your organisation, or in your own life?

What is a piece of your work that could be made small, repeated and standardised, and what would you lose by doing that? Answer the second half honestly before deciding.

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. Was it a subsidy or a purchase? The chapter argues that deployment support which produces a durable, non-excludable price reduction is capital expenditure misfiled as consumption, and shows that the annual global saving exceeds the whole German programme cost several times over. Argue either that this is the correct accounting treatment and should change how such programmes are authorised and audited, or that the counterfactual is too weak to sustain the claim — that the price fall would have arrived by another route, and that the payment purchased timing rather than level. Use Arrow (1962) and Nemet (2019), and one source on public investment accounting or additionality that the chapter does not cite.

2. The forecasting failure — incompetence or model class? Institutional outlooks under-projected solar deployment in the same direction for roughly fifteen consecutive editions while annual additions grew at 26.1 percent a year. Argue whether this is best understood as a correctable model-class error, as the predictable consequence of an institution's incentive to be conservative, or as a reasonable response to genuine uncertainty that only looks foolish with hindsight. Engage Way et al. (2022), and at least one source on forecasting institutions, expert judgement or scenario practice that the chapter does not cite.

3. Is LCOE still fit for purpose? Joskow argued in 2011 that comparing intermittent and dispatchable technologies on levelised cost is economically meaningless. Fourteen years on, LCOE remains the dominant public metric. Take a position: should it be replaced by a value-adjusted measure, supplemented with a published integration adder, or retained as a generator-level metric with a clearer statement of its boundary? Use Joskow (2011) and Ueckerdt et al. (2013), and one source on system planning or capacity expansion modelling that the chapter does not cite.

4. Nuclear, and what negative learning proves. Grubler (2010) reports a factor of about 3.5 real cost increase across the French programme; Lovering, Yip and Nordhaus (2016) find greater heterogeneity across countries. Write the case that the French experience demonstrates a structural property of large bespoke construction — and then the strongest rebuttal, that it demonstrates a property of one regulatory and industrial era. Conclude with which you find more persuasive and what evidence would change your mind. Use both cited sources and at least one account of a modular or serial nuclear programme the chapter does not cite.

5. The fragmenting curve. The chapter's learning rate is a global rate on global cumulative volume, and warns that tariffs and local-content rules split one world curve into several national ones that each double less often. Argue either that the resilience, employment and sovereignty gains justify the slower exponent, or that the cost is systematically understated because it falls on everybody including the country imposing it. Use Malhotra and Schmidt (2020) or Arthur (1989) from the chapter, and one source on industrial policy, trade measures or supply-chain concentration that the chapter does not cite.