Gaian is a large city situated along a natural cove, defended to the north and south by towering mountains and to the east by the city walls. To the west is the largest ocean in the known world. Gaian is located in the middle of that ocean on Jeweler's Isle, a small, mountainous island rich with ore and crystals.
In the past, the island was just one province in a vast empire, its main export being wool and livestock. Once the riches hidden within its rocks were discovered, the island soon became prosperous. Eventually, this wealth, along with the Gaian's placement as a hub for trade, allowed Jeweler's Isle to win independence during an opportune moment of imperial turmoil. For nearly a century, Jeweler's Isle has remained an independent nation by building strategic alliances and exerting economic influence. In this time, the population and wealth of Gaian exploded, making it dependent on trade with other countries to supply its populace with food.
I need advice on how this economy should look. The following is what I have so far, but I feel that it needs to be reworked.
The majority of the people living outside of Gaian are still farmers, producing grain, fruits and vegetables, livestock, and the like. They often export their surplus through Port Gaian, but being a small island (think the size of the Faroe Islands or smaller) these farmers do not produce enough to make anyone wealthy. The exports which account for most of the wealth of the city are ore and refined metals, jewels and handcrafted jewelry, and textiles. This means that a large portion of the population of Gaian and the outlying villages must be miners, and a smaller part must be jewelers, smiths, or profess other crafts.
The wealth generated by these exports is then used to fuel other parts of the economy. Taxation provides the aristocratic government the ability to hire shipwrights and construct a massive navy. Because Gaian is a high volume port, the hospitality industry flourishes with a myriad of taverns, inns, brothels, and shops. Dockhands, harbormasters, and bureaucrats are required to keep the port running efficiently. Stonemasons and carpenters are hired en masse to construct housing for hundreds of newcomers to the city. Centrally located, Gaian is a frequent stop for merchant sailors traversing the sea to their final destination. Merchants in Gaian import goods from all over and sell them at a premium to sailors from other nations.
This is well and good, but I feel that I am missing a lot of professions that would need to exist to keep this city functioning. I also find it hard to estimate how much wealth Gaian can realistically expect to have. Would merchants buying and reselling actually make that much money? Will jewelry and craftsmen actually be able to support the economy? How many people can Gaian expect to contain given that most of its food will need to be imported? Will the exports of Gaian realistically be able to offset the price of all this imported food? Will there be a surplus of jobs on the market which convince farmers to move to the city? As the city grows, will Gaian be utterly reliant on a large miner workforce to export enough goods to sustain itself? These are all questions that I am having trouble finding answers to.
I don't have a background in economics, so I don't know if my assessment of the island's economy is entirely off base or not. I want to find some way to reasonably justify the existence of such a large and wealthy city given these circumstances. Any thoughts would be much appreciated.