My question is this: The nations in my world base their economies on a
rare but renewable commodity. What are some of the effects that it has
on their cultures and policies?
This is not in fact so very different from what we have today. In the end all economies are based on commodities. Note that is plural. An economy cannot function (for long anyway) if it is based solely on a single commodity. Diversification is very important to domestic long term stability.
It all comes down to wealth and good 'ol supply and demand. An economy based on a single export...oil for example, which makes a good modern example. Nations that rely on a single commodity are in significant trouble should that commodity fall. Oil and the 1980's
If this is the single most valuable thing on the planet and it is always in demand (consider that someone will try to come up with an alternative) then you have to ask some questions:
- How much is there?
- How fast does it grow?
- Can it be harvested to extinction?
- How evenly distributed are the crystals globally? (and locally within nations for example)
- Can anyone effectively use it or does it require specialists?
Depending on your answers to these questions it can impact many things. Mainly you need to think about how it impacts the following:
- Wealth distribution, concentration will determine who has how much. Notions of land ownership could be interestingly affected with something this valuable.
- Quantity. If this is a very limited resource then wealth will be consolidated. That happens to be true in our world as well but if this item is more rare it will be an even smaller group of wealthy folks.
- Power. Arguably whoever has this stuff can manipulate world politics. This happens today with fuels and some other natural resources. Wealth = Power in many situations, if what gives you wealth also grants you personal magical power you are rich and powerful...and probably evil...probably.
A system like this can lead to a whole host of differences in the world. Perhaps it has led to the development of an all powerful magocracy (I made that word up) that rules the world with an iron fist. Perhaps the crystals are strictly controlled and used only for public works...I think the sky is the limit for how something like this alters culture and social policies but the impacts to the global marketplace are probably not a big change from how the world developed in reality. People will still need other stuff...you can't eat these crystals...or can you?!
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So. Currency. I think I may have skimmed over the currency aspect as the question in your OP and the title differ slightly in context (economy versus currency).
I am going to use sugar as an example of a renewable commodity. This is a chart from 1950 to 2015 prices from Trading Economics
You notice that there are many rapid swings in the value of sugar. This would wreak utter havoc on an economy mainly because it makes gauging the value of things very difficult. I will not claim that the value of gold does not change, it certainly does (see for yourself on the site). But gold is not impacted by weather. Sure it's value changes BUT it is not as susceptible to rapid changes in value.
The impacts would mainly be a greater potential for rapid shifts in the value of your currency. This makes the currency unreliable, meaning many may not even be willing to use it rather going with bartering or unofficial currencies...gold coins maybe ;)