If $Y=f(AL,K)$ is CRS, $a_k+a_L=1$ by the Euler Theorem.

However, I wanted to know the return to scale of $y=f(1,k)$ (i.e. $Y$ divided by $AL$). I tried $z=p/AL$ , then $py=f(p,pk)$, differentiate w.r.t $p$:

$$y=f(p)+f(pk)\cdot k$$

substitute $p=1$:

$$y=f(p)|_{p=1}+f(k)\cdot k|_{p=1}$$

I stopped here, because I don't know the sign of $f(p)|_{p=1}$.

  • 1
    $\begingroup$ You might want to consider taking some time to format your question and make it more readable :) $\endgroup$ – Art Sep 20 '19 at 2:47

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