From 410bc4c5e54afcf25530c3ded8498fb079020f33 Mon Sep 17 00:00:00 2001 From: Matt McKay Date: Sat, 18 Jul 2026 17:23:49 +1000 Subject: [PATCH 1/2] =?UTF-8?q?=F0=9F=94=84=20resync=20cass=5Fkoopmans=5F1?= =?UTF-8?q?.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .translate/state/cass_koopmans_1.md.yml | 6 +++++ lectures/cass_koopmans_1.md | 31 +++++++++++++++++++------ 2 files changed, 30 insertions(+), 7 deletions(-) create mode 100644 .translate/state/cass_koopmans_1.md.yml diff --git a/.translate/state/cass_koopmans_1.md.yml b/.translate/state/cass_koopmans_1.md.yml new file mode 100644 index 00000000..ed7e5327 --- /dev/null +++ b/.translate/state/cass_koopmans_1.md.yml @@ -0,0 +1,6 @@ +source-sha: bce028b3121056e0bbb7b57e48b356aa8da050d2 +synced-at: "2026-07-18" +model: claude-sonnet-5 +mode: RESYNC +section-count: 9 +tool-version: 0.17.0 diff --git a/lectures/cass_koopmans_1.md b/lectures/cass_koopmans_1.md index 6e4faf29..4c991dc4 100644 --- a/lectures/cass_koopmans_1.md +++ b/lectures/cass_koopmans_1.md @@ -9,6 +9,23 @@ kernelspec: display_name: Python 3 (ipykernel) language: python name: python3 +translation: + title: Cass-Koopmans模型 + headings: + Overview: 概述 + The Model: 模型 + 'The Model::Digression: Aggregation Theory': 插话：聚合理论 + 'The Model::Digression: Aggregation Theory::An Economy': 一个经济体 + Planning Problem: 规划问题 + Planning Problem::Useful Properties of Linearly Homogeneous Production Function: 线性齐次生产函数的有用性质 + Planning Problem::First-order necessary conditions: 一阶必要条件 + Shooting Algorithm: 打靶算法 + Setting Initial Capital to Steady State Capital: 将初始资本设定为稳态资本 + A Turnpike Property: 收费公路性质（Turnpike property） + A Limiting Infinite Horizon Economy: 极限无限期经济 + Stable Manifold and Phase Diagram: 稳定流形和相图 + Concluding Remarks: 结论 + Concluding Remarks::Exercise: 练习 --- (cass_koopmans_1)= @@ -570,8 +587,8 @@ plt.show() @jit def bisection(pp, c0, k0, T=10, tol=1e-4, max_iter=500, k_ter=0, verbose=True): - # 设置初始边界 - c0_upper = pp.f(k0) + # 猜测c0的初始边界 + c0_upper = pp.f(k0) + (1 - pp.δ) * k0 c0_lower = 0 i = 0 @@ -659,7 +676,7 @@ $$ 1=\beta \frac{u'(\bar{C})}{u'(\bar{C})}[f'(\bar{K})+(1-\delta)] $$ -定义 $\beta = \frac{1}{1+\rho}$，得到 +定义 $\beta = \frac{1}{1+\rho}$，并化简得到 $$ 1+\rho = 1[f'(\bar{K}) + (1-\delta)] @@ -842,7 +859,7 @@ plot_saving_rate(pp, 0.3, k_ss/3, [250, 150, 75, 50], k_ss=k_ss) 合适的做法是将终端条件{eq}`constraint4`替换为 $$ -\lim_{T \rightarrow +\infty} \beta^T u'(C_T) K_{T+1} = 0 +\lim_{T \rightarrow +\infty} \beta^T u'(C_T) K_{T+1} = 0 , $$ 收敛到最优稳态的路径将满足以上条件。 @@ -971,11 +988,11 @@ c_vec2, k_vec2 = bisection(pp, 1e-3, 1e-3, T=200, k_ter=Ks) * 蓝线表示方程 {eq}`eq:tildeC` 所描述的不动点 $C = \tilde C (K)$ 的图像。 * 红线表示方程 {eq}`eq:tildeK` 所描述的不动点 $K = \tilde K(C)$ 的图像。 - * 绿线表示从时间0时任意 $K_0$ 开始收敛到稳态的稳定流形。 + * 绿线表示从时间0时任意 $K_0$ 开始收敛到稳态所描绘出的稳定路径。 * 对于给定的 $K_0$，射击算法将 $C_0$ 设置为绿线上的坐标，以启动一条收敛到最优稳态的路径。 * 绿线上的箭头显示了动态方程{eq}`eq:systemdynamics`推动连续对 $(K_{t+1}, C_t)$ 的方向。 -除了显示三条曲线外，图{numref}`stable_manifold`还绘制了箭头来指示当给定 $K_0$ 时，$C_0$不在绿线所示稳定流形上时，动态方程{eq}`eq:systemdynamics`驱动系统的方向。 +除了这三条曲线外，图{numref}`stable_manifold`还绘制了箭头，指示当给定 $K_0$ 时，若 $C_0$ 不在绿线所示的稳定流形上，动态方程{eq}`eq:systemdynamics`将把系统驱动向何处。 * 如果对给定的$K_0$，$C_0$设置在绿线以下，则积累了过多的资本 @@ -1066,4 +1083,4 @@ plot_saving_rate(pp, 0.3, k_ss*1.5, [130], k_ter=k_ss, k_ss=k_ss, s_ss=s_ss) ``` ```{solution-end} -``` +``` \ No newline at end of file From 02e14934b6f38c14b21af87c795f9c74ceaeab5f Mon Sep 17 00:00:00 2001 From: Matt McKay Date: Sun, 19 Jul 2026 14:04:03 +1000 Subject: [PATCH 2/2] Restore trailing newline (engine issue tracked in QuantEcon/action-translation#116) Co-Authored-By: Claude Fable 5 --- lectures/cass_koopmans_1.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/lectures/cass_koopmans_1.md b/lectures/cass_koopmans_1.md index 4c991dc4..1ab9cd2e 100644 --- a/lectures/cass_koopmans_1.md +++ b/lectures/cass_koopmans_1.md @@ -1083,4 +1083,4 @@ plot_saving_rate(pp, 0.3, k_ss*1.5, [130], k_ter=k_ss, k_ss=k_ss, s_ss=s_ss) ``` ```{solution-end} -``` \ No newline at end of file +```