Quality management experience from other many industries teaches us that defect prevention is cheaper in the long run than defect detection (also known as QA) and subsequent fixing.
They also learned that the long run ranges in most cases from 1 to 2 years, which means that your investment pays off after that. Considering that investments on that scale are usually expected to reach a break even after 4 years, this is pretty good!
The problem is that it took the other industries several decades to accumulate enough data for being able to prove that this is the case for them. You can easily find data to support their conclusion and draw a conclusion for software in analogy to that, but as of today, there is no proof for the software business.
That being said, I believe that the analogous conclusion is valid: A pair of developers and one tester are more productive than one developer and two testers.
If you have problems justifying two expensive developers sitting in front of one computer to the managament, there are many other things that help with defect prevention, but are not as visible (and therefore irritating) to the management.