From Longman Business Dictionary
convergecon·verge /kənˈvɜːdʒ-ˈvɜːrdʒ/ verb [intransitiveI]1if two or more rates of interest, unemployment etc converge, they move to the same levelconverge withIrish productivity per worker has converged with the EU norms.
2ECONOMICS if two or more economies converge, they start to have the same characteristics such as the same levels of inflation, interest rates etc. The economies of countries wanting to join the EU have to converge with those of existing members before they can joinconverge withBritain’s economy has not yet converged sufficiently with those of the present participants in the euromarket.
→ compare diverge —convergent adjectiveadjThe Asian crisis showed the convergent, rather than divergent, nature of emerging economies.
—convergence noun [uncountableU]employment policies that work against regional convergence