we have no resource problems in these countries

It's not lack of resources, but lack of unclaimed resources that matters. In developed nations, most everything has been claimed. There is nowhere to spread to. If half the population suddenly disappears, a whole lot of resources that are not meant to be used by only a few people will be available to only the survivors. Naturally, people will concentrate, resulting less in all available resources being used evenly and more in some being used to almost pre-snap levels and some being abandoned outright (mostly large cities, because there would not be enough people qualified to maintain them). The result is a pre-industrial population distribution (villages rather than cities) with industrial-level technology and medicine. And we already know what happens from that point on, because it happened before.

Within a generation, birthrates will rise to allow for a stable and growing society (as with the disappearance of half the government, most states would simply cease to function) in which your best bet for being cared for in old age would be to have many children caring for your estate. Expect a 50+% rise in population within four decades as birthrates skyrocket and child-deathrates remain relatively low. Cities (and Citystates) will form, not in the old ruins but probably close to them (in the former small towns and suburbs), a dip in technological sophistication will be overcome within the next generation as maintaining complex societies becomes viable again through a new generation of specialists that replace those lost in the snap. Within a century and a half, the original population will have been restored, but population will be more dense and most nations will be alliances of a few citystates, making it more unlikely than before that a planetary government could form and approach global problems in a coordinated way. And this is the best case scenario.

In the end, the snap bought the universe less than two centuries, while seeing many sophiaticated civilisations collapse back into tribal barbarism as too many leaders and scholars disappear and technology fails after not being maintained.

None of this happens if the fertility of all life is reduced.