While Tolkien doesn't say much about '
the Agriculture needed to support the populations involved', he does say enough, in my opinion, to hint at the existence of agricuture and communications sufficient to support those populations. In terms of the Shire, he described what it was like before taken over by the hobbits in the Prologue of
LotR, and in terms of Gondor, he gave a short description of Minas Tirith's fertile surroundings, particularly the Pelennor Fields, in Book 5, Chapter I.
He went into things in more detail in Letter 154 of 25th September 1954 to Naomi Mitchison:
I am not incapable of or unaware of economic thought; and I think as far as the 'mortals' go, Men, Hobbits, and Dwarfs, that the situations are so devised that economic likelihood is there and could be worked out: Gondor has sufficient 'townlands' and fiefs with a good water and road approach to provide for its population; and clearly has many industries though these are hardly alluded to. The Shire is placed in a water and mountain situation and a distance from the sea and a latitude that would give it a natural fertility, quite apart from the stated fact that it was a well-tended region when they [the hobbits] took it over (no doubt with a good deal of older arts and crafts). The Shire-hobbits have no great need of metals, but the Dwarfs are agents; and in the east of the Mountains of Lune are some of their mines (as shown in the earlier legends): no doubt, the reason, or one of them, for their often crossing the Shire.
I'm always amused when I read this letter; because Tolkien here uses 'Dwarfs' instead of his usual 'Dwarves'.
