This paper examines the effects of expanding public health insurance benefits on individuals' welfare in a highly old-age dependent economy. On the one hand, such a policy would benefit the older generations in the population by improving their health status. On the other hand, an economy that has a high share of the elderly may sharply increase the tax rate that finances the public health insurance program, which is mainly financed by working-age generations. Due to the trade-off, the impact of the policy on average welfare is ambiguous. To quantify this effect, I examine the South Korean plan to expand its public health insurance despite the country's rapidly aging population. I build an overlapping-generations model and track the effect of the proposed public health insurance expansion on welfare over a transition path. The results suggest that the proposed expansion not only increases average welfare, but also the welfare of the working-age generations who would be more likely to resort to preventative medicine. However, such welfare gains can be lost if implementation of the policy were to be postponed to a later highly old-age dependent economy.