why was economic prosperity a necessary precondition for the Renaissance?

Answer 1

Not only do you need fabulously wealthy people to be able to afford to patronize artists, you also need a middle class that can stimulate trade and the exchange of ideas that comes from international trade. Without new ideas percolating through Italy, France, England, Germany and Spain, there would have been a much narrower Renaissance.

Answer 2

because it always is.
You need "patrons" to pay for artists to devote themselves to painting and sculpturing. A large number of "master pieces" where painting done for or of those patrons.
These patrons in turn had to be rich to afford such luxuries...hence the need for economic prosperity.