Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery

•General equilibrium financial model.•Variational inequality formulation.•Propositions for the recovery of the economy.

Without using a technical language, but using the universal language of mathematics, we provide simple but significant laws, as Deficit Formula, Balance Law and Liability Formula, for the management of the world economy. Decisions, under these laws, for the recovery of the economy and for the good governance clearly appear. Further a simple but useful economical indicator E(t)E(t) is provided and the results are illustrated with a significant example.