Mathematical open problems that (when answered) might unlock MAJOR mathematical (micro)economics/finance/econometrics discoveries
People have argued that if $P \neq NP$ then efficient markets are impossible and certain equalibria may not exist. However, they may hold approximately, so I'm not sure if this qualifies. Additionally, if it turns out that $P=NP$ then certain economic optimization problems (e.g. in logistics) become easily solvable. On the other hand, if $P \neq NP$ then it might imply that encryption is very safe and therefore certain forms of economic arrangements will still be possible in the face of technological advance.