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I need help with the following question, I would really appreciate any help. For the general case of any production function, the differential equation for k(superscript dot) looked as follows: k(superscript dot) = sf(k)− (n + g +  )k. Derive – for this case with a specific Cobb-Douglas production function – the capital accumulation equation of the Solow model expressing k(superscript dot) as a function of k.

Many thanks

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  • $\begingroup$ Hint: Is k=K/L i.e. capital per person? If so then take a Cobb-Douglas function $GDP = A(t) \cdot L^\alpha K^{(1-\alpha )} $ and divide both sides by L to get $ GDP/L = A(t) \cdot k^{(1-\alpha )} $. Then (I think) take the time derivative of both sides. $\endgroup$
    – Daniel
    Oct 30, 2023 at 14:39

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