What the Districts do

District 1: Luxury goods
District 2: Medicine
District 3: Manufacturing/technology
District 4: Fishing
District 5: Livestock
District 6: Scientists
District 7: Construction
District 8: Cotton
District 9: Hunting
District 10: Trade and Negotiation
District 11: Agriculture
District 12: Coal Mining
District 13 (destroyed by capitol): Graphite mining/possible nuclear weapons development

This can be corroborated at http://thehungergamesrpg.proboards.com/index.cgi?