In the region, not so much. There isn't an organized kingdom as there is in Cormyr.
Waterdeep has its own system of fees, but no taxes:
1 cp/day for a market stall
1 sp + fines for anybody convicted in the Magesterial or Lord's Court
1 gp per wagon leaving the city (empty or full)
1 gp per sword sold
5 gp per ship that docks for up to 14 days
Periodic taxes when needed include things like a fire tax (1 gp/household) if there is a fire that destroys a large part of the city, a wall or harbor tax (also 1 gp/household) when repairs or expansions are needed, and a lance tax (1 sp/week/household for as long as needed) when mercenaries are required for defense.
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For a small village such as Phandalin, you could tax the goods sold (which would often be too high of a tax), wagons of goods coming in or going out, or a simple fee for owning a business. Depending on the business this won't be much either. The bigger expenses will be upkeep and employees. However, a small village might be more inclined to require a certain percentage of goods, and/or service to the village (guard duty, whatever) instead.
Keep in mind that most business, even today, don't make a huge margin on their sales. A typical business might make 20%, and overhead expenses come from that 20%, not from the cost of manufacture (raw materials, etc.) or purchasing goods. A good month for a business might net the owner 5 gp/month for example.
In the end, unless you want it to be a big part of your campaign, I'd keep it simple and incorporate sales, expenses, and taxes into a simple check:
1) A new business provides income equal to a poor standard of living (or less if you prefer).
2) At the start of each quarter, make a DC 11 check. On a success, the business does 10% better than expected. On a failure, 10% worse. You can alter the DC as you see fit.
3) If you have three successes before three failures, then the business moves one step up the quality of living chart. Three failures, it moves down the chart.
If you are not there to run the business (out adventuring) then your income is one step lower than the business itself. That is, you are paying additional expenses to have others run the business, but it's not affecting the business itself.
A mine is just another business. It moves more coin, but has more expenses.
Note that the PC is still responsible for covering their cost of living, and if they're lucky (smart) they'll have some coin left over.
