No operating regime achieves all three objectives

The corridor faces three ideal objectives that cannot be reconciled: high ridership (at the level of ALTO’s public targets), low subsidy (operating surplus), and P3 break-even (revenue covering operating cost plus private capital service). Every point inside the realistic operating frontier is achievable under some combination of fare, subsidy and modal-shift parameters; every point outside it is structurally infeasible.

From three regimes to a continuous spectrum

Note 3 developed three discrete regimes — A (heavy subsidy), B (moderate, at parity with air), C (minimal, P3 yield management) — producing aggregate corridor modal shares of ~40, 30 and 22% and requiring annual operating subsidies of ~$3.5B, $2.0B and $1.0B. This note extends that to a continuous subsidy spectrum to identify the optimisation properties of the corridor’s operating posture.

The framework relates four quantities along the spectrum: annual subsidy (the federal operating contribution for the chosen fare posture), ridership (the resulting modal shift across air, road and existing rail), fare revenue (riders × average fare), and net public cost (subsidy minus revenue, negative meaning self-financing). Each is anchored on Note 3’s central demographic 2055 scenario (corridor population 20.1 million, addressable trips 34.2 million). The mapping from subsidy to fare ratio is a smooth logistic reproducing the three regime anchors — ~1.3 at $1.0B (deep premium), ~1.0 at $2.0B (parity), ~0.6 at $3.5B (deep discount) — and the mapping from fare ratio to per-mode capture comes directly from the Note 1 and Note 2 S-curves.

Ridership, revenue, and net public cost vs subsidy

Disaggregating the relationships folded together in Note 3’s regime summary reveals the corridor’s subsidy frontier across the continuous spectrum, with the three regime anchors (C, B, A) marked.

Revenue and subsidy versus ridership

Plotting the same data with ridership on the horizontal axis shows how subsidy and revenue diverge as the corridor moves up the ridership scale — and overlays the federal capital service ($2.49B/yr at the $75B base case), so each regime shows three quantities: operating subsidy, fare revenue, and full federal cost.

The scissors structure has direct policy implications. Below ~6.5 million annual passengers the corridor runs a net public revenue surplus — fare revenue exceeds the subsidy needed. Above that it crosses into net-public-cost territory, rising convexly with the target. By 11 million (near Regime A) the corridor needs ~$2.4 billion annually in net public outlay above its fare revenue. Beyond 11.5 million the curve steepens sharply — pushing toward the 24-million public target would require an entirely different operating regime than any of the three considered here.

Five objectives, five different optima

The frontier supports several distinct optimisation objectives that each select a different operating posture. There is no single “optimal” point without first specifying the criterion.

Four observations follow. Revenue-maximisation and per-rider welfare-efficiency converge on Regime B — not coincidentally, since the same marginal-revenue-equals-marginal-cost condition defines both the Laffer peak and the marginal-cost-per-rider minimum. Minimum-total-net-public-cost points to Regime C or below, where the corridor runs a small surplus but carries only 5–6 million riders — approximately the posture implied by the Cadence consortium’s announced commercial structure. Ridership-maximisation under a fiscal cap points to Regime A or beyond — but reaching the 24-million target would require pushing past Regime A into subsidy well above $5B/yr and modal share above the 40% ceiling, not feasible under the modal-shift framework. And total-welfare-maximisation is strongly sensitive to the assumed social value per rider: at the illustrative ~$85/rider federal value the optimum is at or below Regime C; only at a high $400/rider — crediting network effects, large emissions externalities, and agglomeration benefits — does it move between B and A.

Capital service dominates the operating choice

The subsidy frontier above considers operating subsidy only — but capital cost service dominates the corridor’s total fiscal commitment, and the capital cost itself is deeply uncertain. ALTO’s materials cite ~$60–90 billion, prepared without reference-class adjustment. The CRI’s reference-class analysis (Flyvbjerg methodology on the international HSR cost database, with corridor-specific complexity premia) produces three scenario points: $75B as the proponent-stated P50, $143B as the reference-class-adjusted P50 (after the 44.7% average rail-project overrun), and $264B as the P95 worst case — with the proponent’s $75B sitting at roughly the 25th percentile of the distribution.

ALTO’s composite engineering complexity score is 73–81 (upper part of the High band, approaching Extreme) — the Frontenac Arch crossing, the Napanee Limestone Plain karst, the Leda clay segment, the St-Lawrence crossing, and a Canadian P3 delivery record that includes Eglinton Crosstown (+280%), the Confederation Line (+57%), and the Ontario Line (+250% scope-adjusted). Under Flyvbjerg reference-class forecasting, a corridor at this complexity cannot be reliably costed from the lower-complexity international comparators the proponent’s estimate appears to draw on. The realistic expected capital cost is between $143B and $264B, producing a benefit-cost ratio materially below 1.0 across the full plausible range.

What this means for the corridor decision

Third, and most important: the public ridership targets cannot be reached from any operating point on the frontier developed here. The 24-million-by-2055 figure would require modal share above the 40% ceiling under heavy subsidy, plus upper-case demographic growth, plus full-corridor mature operation in 2055 — three conditions the modal-shift literature does not support simultaneously. The frontier brackets the realistic operating space; ALTO’s published targets sit outside it. An independent review should ask which point on the frontier the corridor is actually targeting, and what fiscal commitment and modal-shift assumptions that point implies.

Framework and parameters

The framework anchors on Note 3’s central demographic 2055 scenario (corridor population 20.1 million, addressable trips 34.2 million at 1.7 trips per capita) with the regime-coupled phase-maturity factor (Regime C ≈ 0.80, B ≈ 0.88, A ≈ 0.94, following a smooth logistic asymptoting to ≈ 0.96). The market structure is air 15%, existing rail 10%, road 75% of the addressable pool. The mapping from operating subsidy S ($B) to fare ratio r is a logistic, r(S) = 0.4 + 1.3 / (1 + exp(S − 1.8)), calibrated to the three regime anchors; the mapping from fare ratio to per-mode capture comes from the Note 1 air–rail S-curve at 3.0 h and the Note 2 road–rail S-curve at τ = 0.5. Average air fare $160 one-way; rail revenue = riders × (air fare × r). Net public cost = subsidy − revenue.

Capital cost scenarios ($75B / $143B / $264B) are derived from Flyvbjerg reference-class forecasting on the international HSR cost database with corridor-specific complexity adjustments (composite engineering complexity score 73–81). Capital service is computed at 6% blended cost of capital (combining federal debt service and private equity return), 40-year amortisation, 50% federal share. The CRI’s full capital cost analysis is documented separately at citizenresearch.ca.

Principal sources