Because man has done pretty well, food-wise, since turning from hunter-gathering to agriculture 10,000 years ago, we have so far postponed the catastrophe that is to follow — as it has affected every other species that has gone along the same route — vast world over-population. A steep decline in population in all countries is the least of it.
Most of the 180 non-advanced countries haven’t a chance of avoiding catastrophe because they’ll be unable to reduce their populations fast enough to match their declining incomes — from trade, from advanced country hand-outs, remittances from emigrants — or the brutal exclusion their brightest and the most enterprising of their young people will receive when trying to enter the advanced countries for jobs or state welfare.
The only populations that will do well in the next 500 years are the social elite of the advanced countries — those in government, business and scientific discovery and development — roughly about 20% of their populations. Not only do these elites mostly own and take economic decisions on existing manufacturing but they are also at the forefront in applying new automated techniques to almost every other job that still requires human muscular effort. The social elites will be able to trade for products that no-one else can.
Back of an envelope calculations suggests that the total social elite population of the world will then — AD 2500? — be between half and a billion and a billion. This is pretty well the same as the total world population was when we were hunter-gatherers before being inveigled up the agricultural path.
This time it won’t be a matter of starting all over again. We will also have had the benefit of 700 years of evolutionary selection for intelligence — something that started in earnest at the beginning of the industrial revolution at around 1800.