Cost-benefit analysis (CBA) is a recognised as the economic evaluation technique that accords most with the underlying principles of standard welfare economic theory. However, due to problems associated with the technique, economists evaluating resources allocation decisions in health care have most often used cost-effective analysis (CEA), in which health benefits are expressed in non-monetary units. As a result, attempts have been made to build a welfare economic bridge between cost-benefit analysis (CBA) and cost-effectiveness analysis (CEA). In this paper, we develops these attempts and finds that, while assumptions can be made to facilitate a constant willingness-to-pay per unit of health outcome, these restrictions are highly unrealistic. We develop an impossibility theorem that shows it is not possible to link CBA and CEA if: (i) the axioms of expected utility theory hold; (ii) the quality-adjusted life-year (QALY) model is valid in a welfare economic sense; and (iii) illness affects the ability to enjoy consumption. We conclude that, within a welfare economic framework, it would be unwise to rely on a link between CBA and CEA in economic evaluations
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