The impact on society of the increasing elderly on societye in the population of elderly people

alternative: The Societal Impact of an Aging Population

One problem related to population aging is that (the) medical costs will increase dramatically and impose a burden on taxpayers.

Therefore, the government should (will be forced to?) increase spending on elderly care and cut the budget(s) for other essential services, such as education.

“Should” sounds like you feel this is the right thing for the government to do. Is this what you mean?

The iImpact of the iIncreasing eElderly on sSociety

Captailize most words in a title. I followed the MLA styling for this title, which is what I use in college.

One problem related to population aging is that the medical cost will increase dramatically andDue to the increasing average population, one clear issue is the dramatic increase of medical costs, impose aing burdens on taxpayers.

The original is fine, but I am improving the phrasing here.

The need for medical care as well as the spending on it tends to increase with ageWith an increase in age, the need for medical care and its costs will rise too.

Again, I improved the phrasing here to connect to the previous sentence more.

Therefore, the government sh[would have]/[are forced] to increase spending on elderly care and cut the budget for other essential services, such as education.