Talk:AK model

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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:
 * $$\frac{d L}{L} = n$$ (growth rate of labor)
 * $$ dK = s Y = s A K $$ (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:
 * $$ dk = d \left( \frac{K}{L} \right) = \frac{1}{L} dK - \frac{K}{L^2} dL = \frac{1}{L} sAK - \frac{K}{L^2} n L = s k - n k$$
 * 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, $$ \frac{dk}{k} = s A - n $$ 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 by PrimeBOT (talk) on 20:12, 1 February 2023 (UTC)