Society X leaves the cost of caring for the elderly up to their families. But since the number of the elderly is growing so fast, it is necessary for the government to take a role in providing for the elderly. The final cost to society will be larger IF the government does NOT play a role. How? Well, adult children will have to take time from their jobs to help their elderly parents. This will not be good for society, for those adult children are needed at work. Well, adult children will have to spend their own money to pay for their parents' care. This will not be good for society, for then those adult children will not have money to spend to buy TVs, cars, etc. for their own families. When you buy things, you help the economy. If the government plays a role in caring for the elderly, then the cost to society will be SMALLER. That is to say, those adult children will be able to help the economy by working at their jobs (without taking off time to care for their parents) and by having the money to buy things. Also, if the government takes a role, It will have to build facilities for the elderly to live in. This will help the economy by creating jobs (workers have to build those facilities; workers have to cook the food; workers have to offer medical services, etc.).

여기서 society as a whole은 나라에서 사는 사람들 전부 (사회 전부)고 the final cost은 노인들이 많으면 생기는 부담을 말해요. 그래서 The sooner we realize the importance of the role of government in this matter, the smaller the final cost to society as a whole will be.는 '이 문제에 대한 국가의 중요성을 빨리 알면 알수록 사회의 마지막 (결과가 된) 부담도 작아질 것이다.'란 뜻이에요. :)