Is there an overview of the dwarf fortress economy?

I don't think there is a complete table that covers what you want.

There is a flowchart on the wiki, although it's utility may be questionable if you don't know what you're doing. It shows what materials go into and out of workshops, though it doesn't specify specific item formulas.

Alternately, the article on Crafts has a great table of links that cover the trade goods. You can use the links to figure out what workshops, professions and raw materials go into different items.

It may be worth it to delve into the reactions files. They're in the folder raw\objects in your DF install. Just search the contents of the files (with F3 on Windows/grep on Linux) for the thing you want to make, and (hopefully!) you'll get an idea what you need. For example, searching for soap found this in reactions_other.txt:

[REACTION:MAKE_SOAP]
    [NAME:make soap]
    [BUILDING:SOAP_MAKER:CUSTOM_S]
    [REAGENT:A:1:BARREL:NONE:NONE:NONE][CONTAINS_LYE]
    [REAGENT:B:1:GLOB:NONE:NONE:NONE][REACTION_CLASS:TALLOW][UNROTTEN]
            [HAS_MATERIAL_REACTION_PRODUCT:SOAP_MAT]
    [PRODUCT:100:1:GLOB:NONE:GET_MATERIAL_FROM_REAGENT:B:SOAP_MAT]
    [SKILL:SOAP_MAKING]

Which to me seems to indicate that you need a barrel of lye and a glob of tallow. How to get those in turn is another story, but don't forget the wiki!