Mathematical Foundations of Health Economics: Arrow, Garber, and the Economics of Medical Uncertainty

This article examines the intellectual connections between the works of Kenneth Arrow, Alan Garber, and Peter Zweifel in the context of the economics of medicine, with particular emphasis on uncertainty, decision-making, and risk. It argues that health economics should be understood not merely as an applied field, but as a domain in which economic theory, mathematical economics, and actuarial science intersect. Arrow's analysis establishes uncertainty and information asymmetry as structural features of medical care markets, challenging standard welfare-theoretic assumptions. Garber extends this insight by formalizing medical decision-making through cost-effectiveness analysis and decision theory, translating clinical uncertainty into economically tractable choice problems. Zweifel's contributions to actuarial risk theory provide the mathematical foundations for health insurance systems, enabling the aggregation, pricing, and long-term management of medical risk. Taken together, these approaches demonstrate that modern health economics relies on mathematical formalization not only to model behavior, but to sustain the institutional viability of health care systems through insurance, risk pooling, and intertemporal solvency. The economics of medicine thus emerges as a field in which mathematical economics and actuarial methods are indispensable for understanding how societies manage health-related uncertainty.