Haute Lumière
Commerce · V.01 · MMXXVI · daylight
TEN CONCEPT BRIEFS · Chapter V.01 — What a Person Is Worth
One page each. A reader who reads only these ten pages has the chapter.
BRIEF 1 — Marginal Revenue Product
The idea. The marginal revenue product of labour is the extra revenue a firm receives from one more hour of a given kind of work. It answers exactly one question: should this firm hire one more, and what is the most it could pay without losing money on the hire?
That is a real and useful question. It is not the question what should this person be paid, and it is not the question what is this person worth. It is a statement about a firm's revenue function, and the person appears in it only as an input.
Worked example. A workshop's output rises by 62.00 USD of gross margin for each additional fitted hour. That is the marginal revenue product. It is the ceiling on the wage, not the wage — everything between the ceiling and the actual pay is decided by something other than productivity.
The figure to carry. MRP is a ceiling, and in a competitive labour market the wage is pushed up against it. The evidence that labour markets are not competitive in this sense is the subject of Brief 2.
You already know this because you have worked somewhere that made obvious money on your hours and paid you a number that had nothing to do with it, and somewhere else that paid better for less valuable work. Both were normal. Neither was a mistake in the accounts.
BRIEF 2 — The Monopsony Markdown
The idea. If a firm must raise everyone's pay in order to attract one more worker, it faces an upward-sloping labour supply curve, and it will stop hiring before the wage reaches marginal revenue product. The shortfall is called the markdown and it has a closed form:
w = MRP · e / (1 + e)
e = elasticity of labour supply to the individual firmWorked example. At an elasticity of 2.50 the wage is 71.4 per cent of marginal revenue product. Applied to the workshop in Brief 1: 62.00 USD of product predicts a wage of 44.29 USD, a gap of 17.71 USD an hour, which over a 1,900-hour year is 33,657 USD that the arithmetic says is produced and not paid.
The figure to carry. The markdown across plausible elasticities: 60.0 per cent of product at e = 1.5, 75.0 per cent at e = 3.0, 83.3 per cent at e = 5.0, 90.9 per cent at e = 10.0. Published firm-level elasticities sit in the low single digits, so the low rows are the relevant ones.
Why it matters. The markdown is a property of the market's plumbing — search costs, geography, non-compete clauses, information, the cost of moving a family — not of the worker. It is therefore movable by policy, by unionisation, by portable benefits, by anything that makes leaving cheaper. That is a design problem, and design problems can be solved.
You already know this because you have stayed in a job longer than it was worth staying in, for reasons that had nothing to do with the work, and you knew at the time that your employer knew.
BRIEF 3 — The Productivity–Pay Gap, and Its Contest
The idea. In the United States, net productivity and typical hourly compensation tracked each other closely for a generation after the war and then separated. Between 1979 and 2019, net productivity grew 59.7 per cent and the typical worker's hourly compensation grew 15.8 per cent — a ratio of 3.78 x.
The honest complication, which is part of the concept. The size of that gap depends on choices: whether you compare wages or total compensation, whether you deflate both sides with the same price index, whether you use the median or the average. Make the most generous set of those choices and the gap narrows considerably. Make the least generous and it widens. No defensible set of choices makes it zero, and the direction has never been in dispute — which is why the honest way to cite it is with the method attached.
Worked example. A rent-sharing elasticity of 0.05 to 0.15 means a firm that raises value added per worker by 10 per cent passes between 0.5 and 1.5 per cent into wages. That is the same fact at the level of one firm rather than one economy, measured a completely different way, and it points the same direction.
You already know this because you have watched a business you worked in have its best year and seen what arrived in your pay, and you did not need a series to know the two were only loosely connected.
BRIEF 4 — The Value of a Statistical Life
The idea. A VSL is not the value of anyone's life. It is the price of a unit of risk, obtained by dividing what people will pay by the size of the risk change, and then re-scaled to one whole statistical death.
VSL = willingness to pay / change in riskWorked example, both directions. The United States Department of Transportation's guidance figure is 13,200,000 USD. A risk step of 1 in 10,000 is therefore worth 1,320 USD to each person exposed — ten thousand people paying that sum spend one VSL and one of them, never identified, does not die. Run it backwards: workers accepting about 900 USD a year for an extra annual fatal risk of 1 in 10,000 reveal an implied VSL of 9,000,000 USD.
The figure to carry. One government holds more than one. The Environmental Protection Agency's central value of 7,400,000 USD in 2006 money is 11.5 million in 2024 money, and the transport figure stands 1.15 x above it. Different statutes, different risks, different instruments.
What it is for. Writing rules that apply to populations before anyone knows who will be affected. It is not for, and cannot survive, being applied to a person whose name you know.
You already know this because you have paid more for a car with better crash ratings, or refused a job on a roof, and in doing so quoted your own price for a risk without noticing you had one.
BRIEF 5 — The Statistical Life-Year and the Budget's Shadow Price
The idea. Annuitise a VSL and you get a price per year of life. Set that beside what a health system pays per quality-adjusted life year, and the two numbers are not close.
Worked example. Annuitising 13,200,000 USD over 40 years at a 3 per cent real discount rate gives an annuity factor of 23.115 and a value of 571,063 USD per statistical life-year. NICE's upper threshold of 30,000 GBP is 38,100 USD at a working rate of 1.27 — a multiple of 14.99 x. Against the measured displacement figure of 12,936 GBP, or 16,429 USD, the multiple is 34.76 x.
The concept that resolves it. They answer different questions. A VSL is a willingness to pay: what would a population spend to avoid a risk. A cost-per-QALY threshold is a shadow price of a budget constraint: what does this fixed pot give up when it is spent. The first is a preference; the second is an opportunity cost. Only the second falls when the budget rises.
The related instrument. HM Treasury's wellbeing guidance values a WELLBY — a one-point change in life satisfaction held for a year — at 13,000 GBP, which is 16,510 USD at our working rate. It lets schemes whose entire benefit is that people feel better enter the same appraisal arithmetic as a road.
You already know this because you have felt the difference between what you would pay to avoid something and what you can actually afford this month, and never confused the two about your own money.
BRIEF 6 — Human Capital
The idea. A person's human capital is the present value of what they will earn: the discounted stream of future labour income. It is the oldest of the five numbers and the one that behaves most like an asset.
Worked example. Earnings of 60,000 USD, 40 working years, real earnings growth of 1 per cent, a 3 per cent real discount rate. The growing annuity factor is 27.18, so the present value is 1,630,736 USD. The transport VSL is 8.09 x that figure — the same person, the same morning, two numbers an order of magnitude apart, both correct for their own question.
The figure to carry. The World Bank's wealth accounting puts human capital at about 64.0 per cent of global wealth: the largest asset class on the planet. It is also the one no company may capitalise — IAS 38 forbids recognising an internally generated workforce. A firm may put a purchased customer list on the balance sheet and may not put the crew that took nine years to train.
What it is for. National accounts, education investment appraisal, and the starting point of a wrongful-death computation. It is a payroll forecast, and it carries every inequality already in the payroll.
You already know this because you have chosen a course or a training on the grounds that it would pay for itself, and in doing so discounted your own future earnings without writing the formula down.
BRIEF 7 — Human Life Value, as an Underwriter Uses It
The idea. Life insurance does not insure a life. It insures an income statement. The face amount an underwriter will write is capped at a multiple of earned income, higher for the young and lower for the old, because the thing being replaced is the stream of money a household loses.
Worked example. On earnings of 60,000 USD, the customary range gives 600,000 USD at ten times income, 900,000 USD at fifteen, 1,200,000 USD at twenty. Note what the number is deliberately blind to: the insured's character, their relationships, their usefulness to anybody who is not financially dependent on them.
Why that blindness is correct — and why it is dangerous. As an underwriting rule it is exactly right: it prevents the contract becoming a wager on a life and keeps it a replacement of a loss. As a statement about a person it is meaningless, and the confusion between the two is why the phrase "human life value" does more damage than any other term in this chapter.
You already know this because somebody has asked you how much cover you need and the conversation was entirely about your mortgage and your dependants, and nobody present thought that was a description of you.
BRIEF 8 — Tort Valuation and the Unindexed Cap
The idea. A court's award is not an estimate of worth either. It is a transfer that has to be computed consistently across thousands of cases by people who will never meet the claimant, and administrability is a design constraint with as much force as accuracy.
Worked example. California capped non-economic damages at 250,000 USD in 1975 and did not index it. Deflated, that cap is worth 45,951 USD in the money it was legislated in — 18.4 per cent of its original value. To hold that value in 2024 it would have to read 1,457,714 USD. An unindexed number is a policy being changed every year by arithmetic nobody has to vote for.
The contrasting case. The September 11th Victim Compensation Fund paid an average death award of about 2,080,000 USD across 2,880 death claims, and about 400,000 USD across 2,680 injury claims — roughly 7,062,400,000 USD reconstructed, against 7,049,000,000 USD as reported, a difference of 0.19 per cent explained by rounding in the published averages. Around 97 per cent of eligible families took it rather than litigate. The Special Master has since said he would now pay every family the same, which is the clearest statement anyone has made that the formula answered a different question from the one the families were asking.
You already know this because you have seen two people receive very different settlements for the same injury and understood immediately that the difference was about their salaries, not about their pain.
BRIEF 9 — The Implied Price of a Revealed Decision
The idea. Every budget decision that trades money against risk contains a price for a life, whether or not anybody names it. Divide the money saved by the expected deaths and the price falls out.
implied price = money saved / statistical deaths acceptedWorked example. The cladding substitution at Grenfell Tower produced a recorded saving of 293,368 GBP. Seventy-two people died in the fire whose spread the inquiry attributed principally to that cladding. The division gives 4,075 GBP per life — 5,175 USD — against a transport department figure of 13,200,000 USD, which is 2,551 x higher. Nobody chose 4,075 GBP. It was left behind.
Two calmer cases, same mechanism. American states raising highway speed limits revealed an implied value of about 1,540,000 USD in 1997 money — 3,009,956 USD today, which the same government's own guidance exceeds by 4.39 x. The 1973 Ford memorandum used the road-safety agency's own figure of 200,000 USD, worth 1,500,957 USD today: one ninth of what the same agency uses now.
The lesson, which is the chapter's honest negative. Refusing to name a price does not withhold one. It hands the price to whoever set the budget, unexamined and unappealable, and the implicit figure is reliably lower than the explicit one.
You already know this because you have watched a maintenance item be deferred for a year, and known perfectly well what was being traded, and heard nobody say it out loud.
BRIEF 10 — A Price for a Decision, Not a Measurement of a Person
The idea. This is the brief that makes the other nine safe to use. Every one of the five numbers is the price of a decision. Not one of them is a measurement of a person, and every argument that feels obscene in this field is an argument that has quietly swapped the first for the second.
Follow the arithmetic and watch the person vanish. Divide willingness to pay by a risk change and the individual cancels out of the equation like a common factor; what remains is a price per unit of risk. Human capital contains a payroll forecast. The underwriter's multiple contains a household's income statement. The court's award contains a rule that has to work across ten thousand cases. There is no person in any of them, which is not a failure of the arithmetic — it is the condition under which the arithmetic is allowed to be used at all.
The rule that follows. A population price may be used for decisions taken before anyone knows who is affected. It may never be applied to a named individual. The EPA's 2003 analysis that discounted lives over seventy by 37.0 per cent was internally consistent and indefensible, and was withdrawn. Transferring a value between countries at an income elasticity of 1.00 gives a country with one thirtieth the income a figure of 440,000 USD, which licenses a cheaper guard rail there for a reason having nothing to do with anyone living there.
Worked example of the discipline. A guard-rail programme costs 2,400,000 USD and avoids 6.0 statistical deaths over twenty years: 400,000 USD per statistical life, 33.00 x below the published price. That sentence decides the case in one line, and it decides it for a population of unnamed future drivers, which is precisely the use the number was built for.
You already know this because you have been in a room where somebody said the quantitative thing and everybody flinched, and you could tell that the flinch was about a different sentence from the one that had been said.