Why did the soviets not allow people to leave occupied east germany

Its been a while since I did this topic, but I believe it was mostly because under communism there was little work for intellectuals, so they were often the ones who left the country. This resulted in a 'brain drain', a lack of knowledgable people. I seem to remember reading about the entire maths department of a university just up and leaving at one point. You could also argue that it was damaging for the image of communism if so many people were trying to leave.