I was struggling with what to build first as various nations, and decided to figure out payback periods for various investments. This is useful, since it helps you make a profit faster, and can therefore afford more awesome units.
Some of the figures are difficult to reconcile, since there is some variability. For example, each buildable site can result in a different addition to province wealth (weavers in Luxembourg provide more wealth than those in Spain, eg). Certain farmland is much more productive, etc. I have also used a tax rate of 33% to determine returns. A higher or lower rate will not change the relative results (ie, with a lower tax rate, a port will still be a more attractive investment than a road.
So on to the results.
Basic structures pay back the best, so it is good to get them in
Port 1 -- 5-8 turn payback (not including trade routes)
Port 2 -- 20-26 turns (not including trade bonuses)
Weavers 1 -- 5-8 turns
Weavers 2 -- 14-20 turns
Weavers 3 -- 48 turns
Farms 1 -- 6-7 turns
Farms 2 -- 20-29 turns
Farms 3 -- 11 years
Farms 4 (negative return)
Farms 5 -- a very long time
Vineyards 1 -- 4-5 turns
Gem mine 1 -- 5 turns
Gem mine 2 -- 16 turns
Silver mine 1 -- 4 turns
Silver mine 2 -- 33 turns
Iron mine 1 -- 5 turns
Iron mine 2 -- 45 turns
Gold mine 1 -- <3 turns
Gold mine 2 -- 27 turns
Logging camp 1 -- <3 turns
Logging camp 2 -- 23 turns
Road 1 -- 39 turns
Road 2 -- a freaking long time
Plantation 1 -- 2-4 turns*
Plantation 2 -- 5-10 turns*
Plantation 2 -- 6-12 turns*
Indiaman -- 2-4 turns
Plantations and trade ships are special cases, since their benefits can differ each turn.
*Plantations are odd because they give you a return on the taxes on wealth generated, as well as 100% of the trade income. Assuming that the commodity is worth 15, and a basic plantation produces 15 sacks or loaves or whatever, you get 225 income from trade, and a further 75 income from the tax on wealth. Plus, plantations often give a bonus, of 20%, 50% or 100% of production, so you can get up to double of the trade AND tax income. Plantations can also be subject to unsold production, which lowers the returns, and they can also be affected by blockades, which affects both their tax and trade income generating capability. Also, commodity prices tend to decline, so if you build lots, it can depress prices. I cannot figure out why there is a plantation bonus, but there is. It is one of the only higher level buildings worth building.
Indiamen are unique in that they cost about 600 plus 50/turn for upkeep. They carry trade goods, and can easily pay for themselves in a few turns. Each trade area has 5 slots. Assuming an active, alert single player, you can get 4 in Brazil, 4 in Ivory Coast, 2-4 in Madagascar and 1-3 in the East Indies, and more everywhere if you are the Dutch or Brits. Lets say you can get 12 of the 20 trade slots with 5 Indiamen apiece. That is 60 Indiamen costing 36,000 to construct. The more you invest, the smaller your return will be. But that is OK, because the returns are still better than roads or other higher level structures.
Farms are also a special case, in that the higher level buildings are mainly built to manipulate the happiness levels. The Farms 3 gives a good return, but comes along with -1 happiness for the lower classes. This malus is eliminated in Farms 4 and changed to a bonus for the upper classes in Farms 5.
Given these results, a player trying to build the strongest economy would build basic structures everywhere, and as many Indiamen as possible. Then building up the weavers and ironworkers structures give decent payoffs. Higher level plantations are good provided that you have the trade agreements to properly benefit, and a large enough navy to protect your trade income.
Questions still to answer -- How does the plantation bonus occur? How do trade slots affect trade income?
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