Hypothetically, how would the world economy change if the problem of scarcity of resources is solved?

If the problem of the scarcity and resources is solved, then the economy will not face the problem of choice. The problem of choice prevents the producer to invest in scarce resources if there are government regulations. But, if there is no scarcity, the producer has a free choice to produce that particular good which gives higher returns on the investment.

Actually, it is a utopian society where scarcity is completely removed. If scarcity is completely removed, prices will come down to zero. It is because of the limitless supply in the economy. Though there would be negative externalities. For example, a firm is supplying an infinite quantity of cigarettes, then the negative externality tends to increase for people who do not smoke.