Aggregate health expenditures as a share of GDP have risen in the United States from about 5 percent in 1960 to nearly 14 percent in recent years. Why? This paper explores a simple explanation based on technological progress. Technological advances allow diseases to be cured today, at a cost, that could not be cured at any price in the past. When this technological progress is combined with a Medicare-like transfer program to pay the health expenses of the elderly, the model is able to reproduce the basic facts of recent U.S. experience, including the large increase in the health expenditure share, a rise in life expectancy, and an increase in the size of health-related transfer payments as a share of GDP.