The history of the border between the DDR and FRG is quite nuanced and interesting. The Iron Curtain was more of a cooperative effort, especially early on, and especially outside of Berlin.

Worthwhile reading on the subject: https://www.amazon.com/Burned-Bridge-East-Germans-Curtain/dp....

In some ways, the existence of a physical border begat the political and economic division, as much as the other way around!