Cost-Effectiveness, Insurance Solvency, and Health Capital: A Joint Incompatibility Theorem and Dynamic Research Programme

Jakub Ryłow

No 2026-6, Working Papers from Faculty of Economic Sciences, University of Warsaw

Abstract: This paper examines the mathematical architecture of health economics through four analytical traditions—Arrow’s welfare economics of medical care, Grossman’s health capital model, Garber’s cost-effectiveness analysis, and Zweifel’s actuarial insurance theory—and derives three original results. C1 (Joint Incompatibility Theorem): under empirically standard regularity conditions, no health system simultaneously satisfies the Garber–Phelps WTP-based cost-effectiveness criterion, Zweifel’s actuarial solvency condition under community rating, and the Pauly–Zweifel optimal coinsurance rule; the proof proceeds via three lemmas, each isolating a separate incompatibility. C2 (Dynamic Cost-Effectiveness Threshold): the cost-effectiveness threshold λ*(t) is derived as an endogenous co-state variable of a unified dynamic optimisation, and shown to equal the present value of future marginal health benefits discounted at the user cost of health capital ρ + δ(t). C3 (Demographic Suboptimality of Uniform Thresholds): as a corollary, uniform thresholds are dynamically inconsistent with any population whose age-specific depreciation rate is increasing, with the direction of the depreciation channel being theoretically determinate. Together, C1 converts a collection of separately noted tensions into a single structural result, while C2 and C3 convert that result into a constructive research programme for dynamic health economic evaluation.

Keywords: health economics; cost-effectiveness threshold; health capital; actuarial solvency; moral hazard; dynamic cost-effectiveness; QALY; Grossman model; incompatibility theorem; endogenous threshold (search for similar items in EconPapers)
JEL-codes: C61 D81 D82 G22 I11 I13 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2026
New Economics Papers: this item is included in nep-hea, nep-hpe and nep-rmg
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https://www.wne.uw.edu.pl/download_file/7112/4282 First version, 2026 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:war:wpaper:2026-6

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