Good luck with that. There are a lot of reasons why it may not happen that way. Suggest checking out the book <em>Countdown</em> by Alan Weisman who addresses these and many other issues.
Take for example Africa. One might think increased standard of living would reduce population just as it did in Japan etc.. but in reality that has not happened. Why? One reason is because in Africa there are so many endemic diseases there is a high morbidity rate (morbidity means people are sickly but not dead). This means mothers still need large families because she can't count on 2 healthy children. Malaria might be solved in a long time but it's just one of very many diseases in Africa. Corruption, crime and wars also take a toll needing bigger families.
Or take Pakistan. It is projected to have more people than the USA in a region smaller than Texas, with a similar lack of water as Texas. Have you ever seen a conservative Islam man (eg. Taliban) embrace condoms and family planning?
Or Iran which has started a national policy to increase population to counter the threat from neighboring countries who have increasing populations (eg. Pakistan). When the Ayatollah wants something, people listen.
Certain places in the world can get away with reducing population, other places are much more difficult. It's not so simple as increased wealth = less population. That's a first world, liberal democracy late stage capitalism phenomenon.
So this video was uploaded in 2012, so I guess the actual movie never got made. If anyone is interested in this type of subject matter there's a movie called Surviving Progress that you may want to check out. I'd also recommend the book Countdown it is a very well written book about population and how different countries and cultures around the world are dealing with it.