One of the first things to remember about role-playing pre-modern "economics" is that the concept itself is mostly likely alien to the people of that particular world.
In real-world history, Adam Smith didn't publish The Wealth of Nations until 1776. It wasn't until well into the 19th century that European powers began to think in terms of total national production (even then, it was often very rudimentary; the typical concerns would be which country is out-producing the rest in terms of steel or battleships, for example). And, as recently as the Second World War in the 1940s, more than half the world lived in rural communities based on mostly agrarian production. Most towns and villages were largely self-sufficient, and mostly traded to get things they couldn't produce on their own.
Which is to say, the concept of an "economy" is very modern. In an Eorzean context, it's probably only the Garleans — or perhaps the Allagans, the only civilisation we know of that came close to world domination — who would think in terms of "gross national production".
So how did pre-modern countries think about GNP or GDP? Well, they thought about it mostly in terms of the sovereign treasury. Are the country's coffers empty or full? If it's empty, where will the funds come from? Through taxes or, more usually, through expensive loans, or the sale of the sovereign's personal assets.
As others in this thread have pointed out, Eorzea currently appears to be in a pre-modern era. There is some trade, and some form of proto-industrialisation ("proto" in the sense that the mass-production lines invented by Earth's Henry T. Ford probably do not yet exist). Manufacturing, where it does occur, is carried out mostly on the scale of cottage industry (ie, lots of craftsmen — such as those in Eorzea's trade guilds — working together to meet large orders).
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None of this is meant to suggest, however, that pre-modern merchants don't dream about making lucrative investments. Trade as a means to wealth is as old as human history. Arab merchants sailed the sea routes to India and China to trade. Other merchants braved the dangers of the long and arduous Silk Road to ferry exotic (and highly profitable) goods to and from Europe and China.
A trader like Kraft Lawrence (I loved the anime back in the day, although I'm not as fond of Horo as many people are) would probably think in same way as merchant-adventurers like Marco Polo: Which are the most exotic and lucrative goods, and where are they the most sought after? He'd go to where those goods come from, and depending on how much he can carry, he'd buy as much as he can, then take the goods to another place where they're rare, and sell them for as much as he could.
So, what do the city-states of Eorzea most likely need, and what do they have in exchange?
Limsa Lominsa
• It's rebuilding its navy, and it's in desperate need of more timber; the Lominsans are increasingly turning to Gridania to supply the wood of high-enough quality for shipbuilding. The Gridanians, in exchange, seek the high-quality weapons that Lominsan craftsmen are known to produce.
• Limsa Lominsa has plenty of pirates and fishermen; but as of now, I'm yet to come across any mention of it having a merchant fleet; most of its maritime "trade" are carried out, in effect, by privateers raiding Garlean ships.
• But merchant ships do pass through Limsa, which translates to custom duties and taxes for the Lominsan treasury (in terms of geography, I'm not sure why maritime merchants who intend to trade in mainland Eorzea don't go directly to Vesper Bay in Thanalan; the implication seems to be that there are other trading destinations across the Indigo Deep and Rhotano Sea, making Limsa the last major transit stop for them).
• Domestically, Limsa Lominsa is self-sufficient in food; the people produce their own vegetables, mutton (sheep, lots of them, which makes me wonder why Limsa Lominsa isn't exporting its wool) and fish.
Ul'dah
• As mentioned, it's the centre of trade and commerce in Eorzea. There's Lolorito's East Aldernard Trading Company, which holds a monopoly over the city-state's textiles and jewellery guilds (Ul'dah's key exports). My best guess — given the company's name — would be that Lolorito exports most of his products to the Near East. What he gets in return from Radz-at-Han is anyone's guess, as we don't really know much about that city, apart from it being home to highly advanced forms of alchemy.
• Ul'dah used to be the centre of a thriving trade in crystals, but that collapsed some 15 to 20 years ago with the start of beast-tribe hostilities. But the Ashcrown Consortium still exists, and its owners are trying to repair relations with the beast tribes, possibly in hopes of reviving trade with them.
• What's often forgotten by many players, is that Ul'dah is also the entertainment capital of Eorzea. The city-state has a thriving colosseum within its walls, and another up-and-coming one rising from the ashes of Halatali. What do these entertainment centres need? Powerful men and women eager to earn a fortune through blood sport, and ravenous monsters for them to fight. A shrewd merchant who knows where and how to safely procure these commodities would make a handsome fortune, I reckon.
• For all its material wealth, Ul'dah is sorely lacking in one key commodity: food. Curiously, the city-state doesn't appear short on water, and it's the only urban centre in Eorzea with an extensive sewer system. But it still needs food, and a lot of it, especially given its growing immigrant population. Ul'dah does have agriculture of its own, but given its desert climate, it's obviously not doing well.
• And, yes, there's the drug trade. It's implied to exist, and it's apparently quite lucrative. There's the somnus weed that desperate refugees are cultivating outside Ul'dah's walls. And then, there's pluto. I don't know if they are the same, but both drugs are clearly contraband. That's another way for an enterprising merchant of questionable ethics to make his money.
Gridania
• Situated as it is within a bountiful forest, Gridania's most likely exports are food and timber (produced most likely by the botanist and carpentry guilds, respectively).
• Unlike the other two city-states, however, Gridania functions more like a very large agrarian commune, and it's largely self-sufficient. Gridanians are, for example, known to have a strong dislike of foreigners, and I imagine this extends to their attitudes towards foreign trade. Cracking this Gridanian nut would therefore be tougher than for the other cities.
• As I mentioned above, though, about the only thing that Gridanians sorely lack are high-grade weapons, and there are merchants already trying to capitalise on this by establishing a weapons trade with Limsa Lominsa. As for why Gridanians would need more weapons, it's useful to remember that they remain very much at the frontlines of the on-again-off-again war with Garlemald. So, no matter how pacifist they may be, the Gridanians know they have to prepare for war.