[expat2]

whereas food production could only increase at an arithmetical rate

Where did this assertion come from?
Until very recently, food production was always a labor-intensive activity, so it should rise proportionately with population, which was rising exponentially, according to you. Ergo......

[Sherman Logan]

food production was always a labor-intensive activity, so it should rise proportionately with population

To a minor extent.

However, the best land is put into production first. Production, especially back then, before modern fertilizers, etc. dropped off really rapidly as marginal land was put into use.

And, of course, there's only so much land. Doubling the number of workers on a 40 acre wheat field will not double production. Might increase it somewhat, but not proportionately to the number of workers.