Of course it will affect the price. Miners will have less bitcoin to sell, so by the economic law of supply and demand, it will in theory, increase the price. As the supply is now lower
that depends weather the world will still care as much about bitcoin as before, you are doing an assumption of constant significance.
Well to be fair, the topic at hand is really all about assumptions. We only really know of one variable, which is supply, and we have to provide the rest. We know that the demand won't remain completely constant, but it's easier to assume that it will especially if it's just for some random thought exercise.