Abstract
<title>Abstract</title> <p>I develop a continuous-time optimal-control model in which a social planner chooses a country’s health-investment share of GDP to manage a chronic, non-eradicable disease burden. The burden stock follows a constant-incidence law of motion with an isoelastic, investment-driven reduction technology; output is linear in burden, and the planner maximizes discounted log consumption net of a linear burden disutility. I solve the model with Pontryagin’s Maximum Principle, cross-check it against its Hamilton Jacobi-Bellman dynamic-programming counterpart, and derive a closed-form sufficient condition for saddle-path stability. I calibrate the model separately for each World Bank income group, combining WHO health-expenditure data, a WHO/World Bank chronic disease mortality proxy, and World Bank output data to invert the steady-state system in closed form. The exercise recovers a health-system-productivity parameter that rises monotonically with income: cross-country differences in optimal health spending and disease burden are structural, not evidence of coordination failure or policy error. A welfare counterfactual confirms this: raising a low-income country’s spending share to a high-income level without also raising its health-system productivity buys almost no reduction in burden and lowers welfare once the consumption cost is counted. JEL Classification: I15 , I18 , H51 , C61 , O11</p>