A hypothetical economy produces two goods, X and Y. The performance (yield) for every worker is steady, and every worker for Y can produce 10 units of product. If $L_x+L_Y=200 $ (meaning that the total workforce is 200):
(My problem is in (d), everything else is just assisting so you get a better view of the problem)
-a) How many units can every X worker produce?
-b) Find the equation of the first production possibilities frontier (PPF)
-c) Find the equation of the second production possibilities frontier (PPF)
-d) If the technology of the production and the performance of workers for X and Y did not change, what was the change of the workforce between the first and second PPF?
My tries:
-a) If $L_Y=0 \to Y=0$ then $L_X=200$ and for $Y = 0 \to X=400$, so every worker for X can produce $\frac{400}{200}=2$ units
-b) For $y = λx+β \Rightarrow ... \Rightarrow y = -5x+2000$
-c) As the two equations are parallel, $y' = -5x + β' \Rightarrow ... \Rightarrow y' = -5x+2500$
-d) Now for d, where my problem is situated, my try is that the percentage change must equal = $\frac{2500-2000}{2000}100= 25$% but even if that's the correct answer I can't fully understand why this would be the case. What does the $β$ and $β'$ have to do with the workforce? I can't seem to be able to wrap my head around it. Can anyone help me?