But you don't store trade value, how can you buy anything with a currency you always have zero of?
I'm on the fence about this...
On the one hand, you could just add a storage value for trade. Then an empire could build up wealth and buy things all at once.
Here, as you say, trade would be a standard resource who's only purpose is to buy other resources. Food maintains pops. Energy maintains ships. Trade buys things. Etc. That's fine to me because fungibility, existing just to be exchanged for other stuff, is literally the definition of a currency.
On the other hand, you might keep no storage and say that the empire's purchasing power is limited to their monthly income. If I have +200 trade per month, then I can set up standing transactions worth up to 200 TV per month.
In that case, trade less represents a currency than overall market activity. You can harness up to 200 trade value's worth of market activity (in whatever currency) each month and direct it toward the resources your empire needs. In any given month you use it or lose it. I kind of like this version just because it has a pleasing asymmetry. A trade-based empire would have to constantly plan for the moment, which is a little different from how a production-based empire works.
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In all cases, though, I think the key issue here is that trade needs to be produced through some other mechanism than jobs. Sorry, I know I'm a broken record, but when you point out the kind of absurdity in "So we'd have an extra resource who's only job is to be exchanged for resources in the market," I think that's what really going on. It is a little absurd to put pops into a job to produce a resource which only exists to get me the resource that I really want.
Why not just assign those pops to making the alloys in the first place?
To me, we'd need one or both of two answers. One answer is if trade gives you access to other resources, and you produce trade through some asymmetric mechanism. Why not just directly make alloys? Because you lack the population and planets to do so. So instead you produce trade through (insert good idea here) and buy those alloys.
Another answer is if there were resources that I couldn't produce but could only buy. The obvious answer there seems to be to make strategic resources much harder to manufacture and seed the map with higher-value natural deposits. Then, again, we have a reason to generate trade because you
can't just directly produce the resources you really want. If I need 10 motes per month, the only way to get them is through trade (or conquest, of course).
Personally, I'd just do both.