Health, Survival and Consumption over the Life Cycle: An Optimal Control Approach

Michael Kuhn, Max Planck Institute for Demographic Research
Alexia Fuernkranz-Prskawetz, Vienna Institute of Demography
Stefan Wrzaczek, Vienna University of Technology
Gustav Feichtinger, Vienna University of Technology

In recent years most industrialized countries have allocated increasing shares of their GDP to health, while at the same time, life expectancy has continued to increase. The ongoing debate in health economics is on whether too much is spend on health care. In this paper we offer a framework that allows us to determine how a social planner as opposed to an individual allocates resources to consumption versus health investment over the life cycle, assuming that health investment positively affects longevity. By introducing age as a second dynamic variable in addition to time, we are able to study the age patterns of the optimal health investment and consumption paths as endogenously determined by the population structure and age-specific productivity. Applying the concept of the willingness to pay for mortality reductions, we derive the social versus private value of life.