In the future, if everyone doesn't die.  Wouldn't the world blow up?  Good question.  But do notice that scientists once have done an experiment by caging two mice allowing them to multiply until the cage is full.  After the mice community has reached 70, the female mice started to experience automatic abortions.  Humans will react the same if the population grows too high.

The main reason why humans give birth to children is:
When YOU become old, your son or daughter can take care of you.

But in the future, you don't age.  What do you want children for?  You no longer need people to take care of you.  The Immortality Device and futuristic medicine will keep you extremely healthy for eternity.  Imagine if your children also decide to have their own children.  Then this planet will really blow up.  In the future, people will change their ways of thinking.  Children are no longer needed.  Today's people love children.  Tomorrow, children become hindrances.  The more children we produce, the more mouth to feed.  Soon everyone would be living on the street.  Then your children and your grand children will blame you for producing them.  They believe that you are responsible for their misery.  Take a look at this cartoon:

Kids in the future will become colder to parents.  Think about it.  If you become physically immortal, you will never die.  And you think your kids are supposed to take care of you and respect you forever?  Say if you reached 60, and you want to retire.  So you ask your kid to send you 15% of his income every month to support you.  Since you will never die, your kid must give you 15% of his income for eternity?  Right now, since people age and die, it's okay to ask your own children to support you until you die.  But in the future, you will live forever.  I don't think that kids in the future are going to be as generous as today's kids.  Honestly speaking, YOU WILL NOT BE GENEROUS TO YOUR KIDS EITHER.  Your kids learn from you and produce their own children.  The next thing you know, you have 400 grand-children.  All poor like hell due to population-overgrowth.  They all come chasing behind you asking you for help.   Since they are your offsprings, you should help them.  Right?  Well, good luck.