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# ## <font color="880000"> Solow Growth Model: What If _s_ is the Net Rather than the Gross Savings Rate? </font>
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# Last edited: 2019-08-17
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# Definition of capital-output ratio:
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# >(1) $ κ_t = \frac{K_t}{Y_t} $
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# Factor accumulation:
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# >(2) $ \frac{dL_t}{dt} = nL_t $
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# >(3) $ \frac{dE_t}{dt} = gE_t $
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# >(4) $ \frac{dK_t}{dt} = s(Y_t - \delta K_t) $
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# >(5) $ \frac{dK_t}{dt} = s(1 - \delta κ_t)Y_t $
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# Production function:
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# >(6) $ Y_t = K_t^α(L_tE_t)^{(1-α)} $
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# >(7) $ Y_t = κ_t^{(α/(1-α))}L_tE_t $
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# >(8) $ κ^* = \frac{s(1 - \delta κ^*)}{n+g} $
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# >(9) $ κ^* + \delta κ^* \frac{s}{n+g} = \frac{s}{n+g} $
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# >(10) $ κ^* \left( \frac{n + g + \delta s}{n+g} \right)  = \frac{s}{n+g} $
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# >(11) $ κ^* = \frac{s}{n+g + \delta s} $
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# >(12) $ Y^*_t = \left( \frac{s}{n+g + \delta s} \right)^{(α/(1-α))}L_tE_t  $
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# > (13) $ \ln(Y^*_t) = (α/(1-α)) \left( \ln(s) - \ln(n+g+\delta s)  \right) + \ln(E_t) + \ln(L_t) $
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# > (13) $ \ln(Y^{*net}_t) = (α/(1-α)) \left( \ln(s) - \ln(n+g+\delta s)  \right) + \ln(E_t) + \ln(L_t) + \ln(n+g) - \ln(n+g+\delta s)) $
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# >(14) $ Y^{*net}_t =  \left( \frac{n + g}{n+g+\delta s} \right) \left( \frac{s}{n+g + \delta s} \right)^{(α/(1-α))}L_tE_t  $
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# ## <font color="880000"> Solow Growth Model: What If $ s $ is the Net Rather than the Gross Savings Rate?</font>
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# <img src="https://tinyurl.com/20190119a-delong" width="300" style="float:right" />
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# ### <font color="000088">Catch Our Breath—Further Notes:</font>
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# <br clear="all" />
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# ----
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# * Weblog Support <https://github.com/braddelong/LS2019/blob/master/SGM-s-net-savings-rate.ipynb>
# * nbViewer <https://nbviewer.jupyter.org/github/braddelong/LS2019/blob/master/SGM-s-net-savings-rate.ipynb>
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