From ba320a7045c058da2aafa7464ba794252b05ac00 Mon Sep 17 00:00:00 2001 From: JingkunZhao Date: Mon, 8 Jul 2024 13:44:21 +1000 Subject: [PATCH 1/3] [solow] Update unfinished suggestions --- lectures/solow.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/lectures/solow.md b/lectures/solow.md index 484f7664d..9d76d62e4 100644 --- a/lectures/solow.md +++ b/lectures/solow.md @@ -55,9 +55,9 @@ $$ Production functions with this property include * the **Cobb-Douglas** function $F(K, L) = A K^{\alpha} - L^{1-\alpha}$ with $0 \leq \alpha \leq 1$ and + L^{1-\alpha}$ with $0 \leq \alpha \leq 1$. Here, $\alpha$ is the output elasticity of capital. * the **CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\}^{1/\rho}$ - with $a, b, \rho > 0$. + with $a, b, \rho > 0$. Here, $\rho$ is a parameter that determines the elasticity of substitution between capital and labor. We assume a closed economy, so aggregate domestic investment equals aggregate domestic saving. @@ -81,6 +81,7 @@ Setting $k_t := K_t / L$ and using homogeneity of degree one now yields $$ 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 $$ From 00d8b7be25ec16be631f9cd390c875546a90b9f8 Mon Sep 17 00:00:00 2001 From: Matt McKay Date: Tue, 23 Jul 2024 16:59:21 +1000 Subject: [PATCH 2/3] Update lectures/solow.md --- lectures/solow.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/lectures/solow.md b/lectures/solow.md index 9d76d62e4..c967ac340 100644 --- a/lectures/solow.md +++ b/lectures/solow.md @@ -57,7 +57,9 @@ Production functions with this property include * the **Cobb-Douglas** function $F(K, L) = A K^{\alpha} L^{1-\alpha}$ with $0 \leq \alpha \leq 1$. Here, $\alpha$ is the output elasticity of capital. * the **CES** function $F(K, L) = \left\{ a K^\rho + b L^\rho \right\}^{1/\rho}$ - with $a, b, \rho > 0$. Here, $\rho$ is a parameter that determines the elasticity of substitution between capital and labor. + with $a, b, \rho > 0$. + +Here, $\rho$ is a parameter that determines the elasticity of substitution between capital and labor. We assume a closed economy, so aggregate domestic investment equals aggregate domestic saving. From d783d83f891234d313d9005b429f75f8b8ce4bec Mon Sep 17 00:00:00 2001 From: JingkunZhao Date: Wed, 24 Jul 2024 17:02:56 +1000 Subject: [PATCH 3/3] Revise context --- lectures/solow.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/lectures/solow.md b/lectures/solow.md index c967ac340..0a5160b0c 100644 --- a/lectures/solow.md +++ b/lectures/solow.md @@ -55,11 +55,11 @@ $$ Production functions with this property include * the **Cobb-Douglas** function $F(K, L) = A K^{\alpha} - L^{1-\alpha}$ with $0 \leq \alpha \leq 1$. Here, $\alpha$ is the output elasticity of capital. + 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 $a, b, \rho > 0$. -Here, $\rho$ is a parameter that determines the elasticity of substitution between capital and labor. +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.