The conventional wisdom says that because the cost of health care for the aged is more than that of the young at any time, there is a positive relationship between the aging or higher life expectancy of the population and aggregate health care spending. It is difficult, however, to find evidence to support this argument. We present a simple framework that shows how aging of the population may not necessarily increase the total cost of medical care over time or be observed across nations. This follows because numerous other factors that change with aging affect cost of care in ways that are not age-neutral. Such factors include age-specific shifts in morbidity and mortality, growth in income and insurance coverage, rising levels of education and changing technology. Consequently, the relative medical costs of the aged may indeed increase, at least for demographic reasons. Simultaneously, however, the costs of the young may decrease for the same reasons. The Israeli experience, used as a basis for a cursory empirical discussion of the issues, supports the line of reasoning presented in the paper.