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[solow] Update unfinished suggestions #511

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Jul 26, 2024
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[solow] Update unfinished suggestions #511

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[solow] Update unfinished suggestions
SylviaZhaooo Jul 8, 2024
00d8b7b
Update lectures/solow.md
mmcky Jul 23, 2024
d783d83
Revise context
SylviaZhaooo Jul 24, 2024
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7 changes: 5 additions & 2 deletions lectures/solow.md
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Original file line number Diff line number Diff line change
Expand Up @@ -55,9 +55,11 @@ $$
Production functions with this property include

* the **Cobb-Douglas** function $F(K, L) = A K^{\alpha}
L^{1-\alpha}$ with $0 \leq \alpha \leq 1$ and
L^{1-\alpha}$ with $0 \leq \alpha \leq 1$.
* the **CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\}^{1/\rho}$
with $a, b, \rho > 0$.
with $a, b, \rho > 0$.

Here, $\alpha$ is the output elasticity of capital and $\rho$ is a parameter that determines the elasticity of substitution between capital and labor.

We assume a closed economy, so aggregate domestic investment equals aggregate domestic
saving.
Expand All @@ -81,6 +83,7 @@ Setting $k_t := K_t / L$ and using homogeneity of degree one now yields

$$
k_{t+1}
= s \frac{F(K_t, L)}{L} + (1 - \delta) \frac{K_t}{L}
= s \frac{F(K_t, L)}{L} + (1 - \delta) k_t
= s F(k_t, 1) + (1 - \delta) k_t
$$
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