You're correct, Engimas. Generally, longer-lived species do not breed as fast as shorter-lived species. 

Unrelated, but so-called 'Tolkien' elves also unknowingly come with an ungodly amount of shortcomings that most people that are into fantasy don't realize, most important of which are the detrimental effects associated with immortality. 

However, just because it's an elf doesn't necessarily mean that it must abide by the general tropes associated with elves.