From f5f71615b8f60b7c562100d6313147cfed9c26e5 Mon Sep 17 00:00:00 2001 From: JingkunZhao <155940781+SylviaZhaooo@users.noreply.github.com> Date: Fri, 26 Jul 2024 16:29:59 +1000 Subject: [PATCH] [solow] Update unfinished suggestions (#511) * [solow] Update unfinished suggestions * Update lectures/solow.md * Revise context --------- Co-authored-by: Matt McKay --- lectures/solow.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/lectures/solow.md b/lectures/solow.md index 484f7664..0a5160b0 100644 --- a/lectures/solow.md +++ b/lectures/solow.md @@ -55,9 +55,11 @@ $$ Production functions with this property include * the **Cobb-Douglas** function $F(K, L) = A K^{\alpha} - L^{1-\alpha}$ with $0 \leq \alpha \leq 1$ and + L^{1-\alpha}$ with $0 \leq \alpha \leq 1$. * the **CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\}^{1/\rho}$ - with $a, b, \rho > 0$. + with $a, b, \rho > 0$. + +Here, $\alpha$ is the output elasticity of capital and $\rho$ is a parameter that determines the elasticity of substitution between capital and labor. We assume a closed economy, so aggregate domestic investment equals aggregate domestic saving. @@ -81,6 +83,7 @@ Setting $k_t := K_t / L$ and using homogeneity of degree one now yields $$ 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 $$