What is the value of increasing testing productivity by 50%?
Productivity increase of 50% means that a testing expert can carry out (1+50%) times as much work as before, i.e. one person can do the job of one and half persons.
A quite common way of thinking about this question is the following: instead of 30 experts, you only need 20, because now those 20 can do all the work previously carried out by the 30. This is cost reduction of 5/15 = 1/3 = 33%, so the value is 33% * [personnel cost of 30 testing experts]. If one testing expert costs $100.000 / a (say), that is $1.000.000 value per annum.
However, there should be a second thought. Let's say you have those 30 experts working for you. Because you have hired them and continue to pay wages to them, the value generated by them must exceed the value of their wages (otherwise having them in does not make business sense), so every expert generates some amount of economic value higher than $100.000 / a. Because of the law of diminishing results, it might be that value is not the same for everyone, so we put the testing experts into an (arbitrary) order, and mark the economic value generated by the experts by V, V, ..., V; it is a decreasing sequence (V > V > ... > V). We can then extend this decreasing sequence hypothetically to V, ..., marking the economic value of testing experts that could be recruited. Let's denote the cost of one test engineer per annum by C (C = $100.000 in this example).
Now if you are a superhuman manager you have your team set up so that V > C but V < C. That is, you have sized your team perfectly: everyone in the team is adding economic value, but increasing the team size by one would lead to a net loss. (This is a very hard thing to achieve in practice!) If you are a manager in a typical organization, your team is under-resourced and actually it would make business sense to have more testing resources but for one reason or another you can't pull that off (politics, lack of good management, etc.).
Now if you improve your teams productivity by 50%, you actually have the equivalent of 45 testers available, as everyone is doing the work of 1 1/2 experts. This means that the additional economic value generated is V + V+ . ..+ V. In the scenario where you reduce your workforce to 20 the value generated is 10 * C. If your team is under-resourced (as it is usual), it is likely so that even V > C, so the additional value generated by keeping all the experts is greater than 15 * C (above $1.500.000, compare this to $1.000.000 that you net out if you let 10 people go). Even if your team is optimally resourced it can be still so that it is a much better business decision to capitalize the productivity improvement by keeping everyone in the team, as it is enough that (V+ ... +V) / 15 > (2/3 C), i.e. that on the average the value added by the 15 next testing experts is at least 2/3 of their wages!
If you can improve your testing productivity, the chances are that the best way to capitalize that on enterprise level is to keep everyone in the team and pocket the business benefits of better testing. This is in line with most software process experts tend to think. However, if you are a test manager and subject to rigid budgeting where you are rewarded more for cost reduction than quality increase, your mileage may wary.