They can't both be right. I just demonstrated they can't both be right. It's very easy. P = LKT. K and T are constant. You divide both sides by L to get P/L = KT. P/L is your personal productivity. KT is a constant. If L increases, by your own mathematical definition it has no effect on personal productivity, because by your own mathematical definition you've defined personal productivity to be A CONSTANT. You can't define something to be a constant, and they say your definition causes it to vary...
Conversely, if you take your example and plug them into the equation: 100 workers make 100 widgets; taking 'widgets' as an arbitrary unit of measure for P, that's 100 = 100KT, where KT is a constant - specifically, it's a constant equal to 1 widget per laborer. Now if you increase L to 200, you're saying that P only increases to 150...so 150 = 200KT, and KT is now 0.75 widgets/laborer. But you already said that KT is a constant, so how can it change???
Your example and your math do not match. One of them is wrong. But that's not my point. My real point is: you have got to be the dumbest !@#$ing spud on face of the planet if you can't see that the example and the math do not match.