Talk:AK model

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i have chosen this topic to edit for my internal assessment

There is a lack of precision: what is the function: f(k)? Yes, I know ... but it should not be necessary to know. — Preceding unsigned comment added by 2.110.183.20 (talk) 09:40, 24 December 2014 (UTC)

Hi, almost a decade later...

I also had difficulties understanding this. It looks wrong to me. It describes $k(t)=s\cdot f(k)-nk$ as a differential equation, but this equation does not contain any (standard?) notation for a differential.

Let's reverse engineer what the writer might have meant: Instead of $k(t)$, read $dk$.

Additional definition:

$f(k)={\frac {AK}{L}}$ (output per unit of labor that is produced as a function of the capital/labor ratio)

Clarification:

${\frac {dL}{L}}=n$ (growth rate of labor)

$dK=sY=sAK$ (change in capital is the part of output that is saved)

Now work out the differential $dk$ from the definition of the capital/labor ratio:

$dk=d\left({\frac {K}{L}}\right)={\frac {1}{L}}dK-{\frac {K}{L^{2}}}dL={\frac {1}{L}}sAK-{\frac {K}{L^{2}}}nL=sk-nk$

Now the rest of the argument reads:

Hence, ${\frac {dk}{k}}=s{\frac {f(k)}{k}}-n$

But in the model ${\frac {f(k)}{k}}=A$

Thus, ${\frac {dk}{k}}=sA-n$ 2003:CD:EF08:2B00:70C2:46B1:748E:5119 (talk) 10:37, 28 September 2022 (UTC)

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The above message was substituted from {{IEP assignment}} by PrimeBOT (talk) on 20:12, 1 February 2023 (UTC)