What if half of the planet population was erased from existence, as Avengers Infinity War proposes?

Let's imagine our world, not the fictional one created by Marvel. There are no superheroes to fight the fights we cannot. It is just the normal word we are used to. But, all of a sudden, half of the existence in planet earth disappears. It just vanishes, for no reason. All vanished living creatures have been chosen randomly, with no criteria. So, to put an example there would be half of the doctors in the world gone, half of Americans gone, half of woman in the world gone, half of the dogs from Australia gone. In an approximate proportion, half of everything that moves is gone (not plants, plants are still the same). But maybe you have lost your whole family, it has been chosen randomly. So, what if this happened to our planet?

The purpose for this action in the film is to balance the universe, so that people left have more than enough to live, and so that they don't live in poverty. But we are not sure it would bring positive effects.

First of all there would be a massive confusion with immediate collateral deaths. Many people would die because of being in a vehicle driven by a person that has died. People in vehicles such as aircrafts, would surely die if the pilot dies. Many others would parish in the biggest worldwide simultaneous car accident, implying cars, buses, trucks, bikes... People would also die because of being in situations where your life depends on a person that has vanished, such as surgical operations, babies of pregnant women... Maybe some nuclear accidents may happen, either because of nuclear plants that fail or because of the explosion of nuclear bombs carried in vehicles. And let's don't forget about people who would suicide, having seen his family, his friends, or his whole live falling apart. Lastly remind that we are talking about vanishing people, so the dead body doesn't remain on earth. If so, diseases and putrefaction would spread through all cities causing them to get uninhabited and killing millions of more people. But that's not the case. 

Once this initial massive homicide, people would start to understand what had happened. The pain for the loss of family and friends would persist for days. Gotten to this point two scenarios may occur. 

The first one is the most probable, and the worst of all them. The catastrophic event would lead to anarchy, to the collapse of the society structure and to the regression of social civilisation. Many world leaders would die, and many government members, so probably every country would loose its political structure, leading to an abandonment of public administration, causing no more hospitals nor social infrastructures. The energetic resources would probably disappear, energy plants would stop working and electricity would no longer arrive to people. The same would happen with food distribution and all the other businesses. Probably no business would survive.

People would panic and start do think just about their own survival. Vandalism and chaos would now be the new world order. A world based on gangs, groups of people trying to survive, fighting with other gangs for goods. Robberies would be the less of the matters. Days after the realisations of what had happen, people would search for the latest technology to keep it and use it, such as weapons, vehicles, communicators... New trading businesses would emerge in a black market, founding a new economy based society. Leaders of biggest gangs would probably start owning territory, and building an small empire, making allies and, of course, enemies. Richest people at the time before the incident would probably be between this leaders, they would give food and roof to their subjects in exchange of protection. 

And the thing that would surely happen is the rise of a new zealot order blaming someone the incident. People would join because of fear, empowering it and making it the biggest group of the world. 

All this would happen in continents and probably the rest of the world, but maybe some regions such as islands (let's take the example of Iceland or New Zealand) would learn to live as before, in a civilised way. They would restore their previous system and protect it from external menaces. So maybe civilisation survives in some places, that will keep progressing. 

(By the way, this is film material. It is a great post apocalyptic situation for a film. I don't think I'm posting this.)

The second scenario is the one in which we learn to live without the lost, we restore the society with what's left, and we live happily ever after. If people adopted a positive mentality, governments managed to keep it floating, we would soon recover. If everyone carried social actions like helping hurt people, replacing vital job positions that have been empty, cleaning the streets, rebuilding structures... community collaboration would be the key for the survival of humanity as we know it. 

In few years, maybe some decade, we would reach the wellbeing level we had before. Even better. People wouldn't have to work that much (well, yes the first years, but from then on not that much), because there wouldn't be the same amount of people. But this wouldn't last a lot. In approximately 100 years we would soon get to the number of population we had, given the precedent of 1930 to now, time in which we doubled the word's population. This would happen unless we settled a maximum birth rate to control population and maintain the level of wellbeing caused by the disappearance of half the planet. 

This are two possible scenarios that would probably happen if half of the planet was erased from existence.