The case is genuinely hard. ΔK_knowledge > 0 (results enter the public domain with positive spillovers); ΔK_human > 0 (trained researchers); but ΔK_produced < 0 for taxpayers — who are external parties (they fund the grant through coerced transfers without being participants in the research transaction). The verdict turns on whether the knowledge gains that eventually accrue back to the same taxpayers (cheaper medicine, better materials, public-domain methods) exceed the per-capita tax cost. For basic research with broad, non-rivalrous spillovers, this is likely yes — so the criterion declines to brake it. Narrowly captured grants that spill over only to the recipient (industry-specific subsidies, company-town infrastructure) fail Q1.