Egypt was mainly used as a grain province after the seizure and transformation of the province into a province directly under the control of the emperor. Augustus initially created a praefectus annonae position whose sole role was to handle the grain supply of the city.
In terms of buying grain, the lands were rented out and farmed with part of the payment being a share of the farmed grain. This was then usually transported to Alexandria from which it was then shipped to Rome. This was done by a few state merchant ships but by regular merchants mainly. Grain was not the best good to trade so incentitives were offered by the state to merchants; some of those listed below.
If you could transport over 10,000 modii of grain then you would not have to pay a harbour and a smaller goods tax. This resulted in huge ships being built to transport grain. If you also lost your ship in a storm and had paid for the grain via credit then the debt was placed on the loaner not the loanee (Suetonius, Claudius 18-19; Digest, 50.6.6 .5-6).
Essentially, the state had regular merchants transport the grain through the offer of incentitives.
Once the grain was shipped from Alexandria, it arrived mainly at Ostia which was a town just outside of Rome. A harbour was built there by Julius Caesar. Claudius then built a harbour known as portus which was still close to Ostia; the aim was to create a protection against the storm damage(unloading grain was a long process). This port was then further developed by Trajan. The large ships, after anchoring, would unload the grain into smaller ships which would then go up the River Tiber to Rome. Once in Rome, the grain would be unloaded into both State Owned and Private Owned warehouses who would then store the grain and distribute it as they please, either through the grain dole or through selling it.
Some sources and further reading:
Garnsey, P. (1983), ‘Grain for Rome’, in P. Garnsey, K. Hopkins and C. R. Whittaker (eds.), Trade in the Ancient Economy, London: 118-30.
Garnsey, P. (1988), Famine and Food Supply in the Graeco-Roman World, Cambridge.
Hopkins, K. (1980) ‘Taxes and Trade in the Roman Empire (200 B.C. – A.D. 400)’, The Journal of Roman Studies Vol. 70: 101-125
Mattingly, D. and Aldrete, G. (2000), ‘The feeding of imperial Rome: the mechanics of the food supply system’, in J. Coulston and H. Dodge (eds.), Ancient Rome: The Archaeology of the Eternal City, Oxford: 142-59.
Heya,
I don't know how much, if any, grain was shipped from Egypt in Republican times, though I do know that the later Roman administration preserved many of the earlier Greek systems of government. A while back, though, I did write a post here on how the supply chain went between the Egyptian farm and Rome in Imperial times, when Egypt was incorporated into the Empire. I've copied it out below, touched up a bit to better answer your question directly.
The short: The Egyptians in paid their taxes in grain, which was then shipped to Rome.
Of course, it was more complicated than that in practice.
In Egypt there existed over a hundred different taxes people had to pay. (Not all regularly, mind. This includes all kinds of special sales taxes on specific products and such.) Some taxes were in money, others in grain. In an average year, 135000 tons of grain was shipped to Rome, which amounted to roughly a third of Rome's total grain consumption. In addition, the Egyptians had to cough up the grain needed to feed the Roman army occupying the country.
The grain tax was mostly levied on land, but not all land was taxed equally. There were private farmers, who paid an amount roughly equivalent to the medieval tithe, but in some places it was twice that. Then there were farmers who leased Imperial owned estates had to pay much more: in the most extreme case, 14 times as much grain! That's in absolute quantities, not percentages. And the Imperial lands would be far more productive than the lowly taxed private lands.
(Large landholdings were widespread in late Republican and Imperial times, but the popular image of giant plantation-style slave worked estates isn't really found much. Instead, the big land-owners let the land to small tenant-farmers)
Taxes could get pretty extortionate, particularly whilst the good old publicani tax-farming system was still in place. (Emperor sells tax-collecting contract to private company, anything the company extracts over that amount is profit. Guess how corrupt this got.)
The farmer not only had to pay his tax in grain, he also had to tresh the grain and then deliver it to the appropriate state-owned granary at his own cost, and was responsible for the whole until it arrived and he got a receipt. (Lots of those receipts were preserved, so we can study them quite easily.)
The grain then went from the granaries to the Nile (by donkey or by small boats over the irrigation canals) and then on to Neapolis near Alexandria, where a giant grain depot was situated. From there it was then shipped to Rome in giant grain-fleets. All this work, until the grain reached Alexandria, was also imposed on the locals as so-called "liturgies" which were a kind of corvée basically like medieval feudal duties. I.e. unpaid labour as a form of extra tax. (There were lots of these. Did I mention there was a lot of tax?)
And that's not even starting on the corruption faced by the locals. We have some hilariously depressing accounts of papyrus which list all kinds of bribes and "protection moneys" paid to Roman soldiers and the like. For example:
>For extortion ---- 2,200 dr. To Hermias, Police Agent ---- 100 dr. To the soldier, at his demand ---- 500 dr.
As a result of all this, destitute Egyptian farmers often fled their lands and took to the desert to live as bandits, rather than face the punishment for tax-arrears.
All data and information taken from N. Lewis' "Life in Egypt under Roman Rule," which is an amazingly interesting book.