The Two Prices of Duty

Duty is the cheapest instrument this programme has found: a small internalization weight dissolves the trap that penalties cannot, and the weight is bounded at every stake. This paper asks what duty costs rather than what it requires, and finds the question has two answers because there are two ledgers to ask it in. The material ledger — the one professional selection reads — prices the volunteer’s service at the subsidy he pays relative to the trapped colleague he outworks. The felt ledger — the one he lives — prices it higher, and the distance between the ledgers is an identity rather than an opinion: exactly the internalized share of his blame exposure, first order in the duty weight, and invariant to how the comparison is drawn. Around that one wedge the paper builds the welfare accounting of conscience. The subsidy itself decomposes exactly into the utility-equivalent price of the same clearance through the value channel — what a compensating transfer, rather than a per-outcome bonus, would cost — less a metastability rent, plus the overshoot cost of conscience — a decomposition that also locates where sacrifice begins: at the Maxwell point for a vanishing conscience, and earlier the deeper the conscience runs. Whether the volunteer is a bargain turns out to have no convention-free answer: commensurating the two prices returns conflicting verdicts across located boundaries, and the disagreements equal, term for term, the paper’s own objects. The stock price, finally, is only a price if someone pays it. Under par material accounting the retention wage is a pure transfer, so an institution that declines it is not economizing but converting a transfer into a real loss; the pay-or-erode decision collapses to three dimensionless numbers; and the wage that stops the erosion undershoots the wage that would make the volunteer whole by exactly the wedge — keeping conscience is not making it whole. The margin for keeping it thins toward the highest stakes, where every road in the paper converges: the blind spot this programme has repeatedly located at the top of the book can be assembled from correct arithmetic alone. The failures the programme studies require no one to collude. Here they require no one even to miscalculate — only to keep one ledger where there are two.