Can the problem of scarcity be resolved?
The problem of scarcity can never be resolved. It is the fundamental problem that makes the study of economics possible. All people, in all places and times, are faced with scarcity.
Scarcity is the condition that arises because people have unlimited wants but only have limited resources with which to fulfill those wants. If we think about this, we will see that this is true for all people, no matter how rich. Let us say that we have as much money as Bill Gates. We will still not be able to have everything we want at each moment. Imagine that Bill Gates wants to buy an island for himself. There are many islands that he cannot have, because they are not for sale. He can also probably not buy every island that would be for sale. Even if he can buy every island that is for sale, he still has to make choices due to scarcity. If he uses $1 billion to buy an island, he cannot use that same $1 billion to invest or to put towards his charitable foundation. Regardless of how much money he has, he has had to make a choice about what to do with that specific amount of money.
Now consider the fact that Bill Gates also does not have unlimited time and he cannot do unlimited things at the same time. Let us say that he wants to go on vacation. While on vacation, he will not be able to work full time (of course, he can bring work, but at any one moment, he will either be relaxing or doing work, not both). For his vacation, he can only go to one place at a time. He cannot be in Hawaii and Jamaica at the same time. He can probably afford to go anywhere he wants, but he cannot go to two places at once. Therefore, he must make choices about what to do and where to go at any given time.
In these ways, scarcity exists for everyone at all times. There is no way to resolve the problem of scarcity in this world.