From 07649d0647e164ce99c51d7b8c54d1d100ba9683 Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Sun, 7 Oct 2018 20:03:01 -0400 Subject: [PATCH] misc --- README.md | 1 + firm_problems/inventory_dp.ipynb | 273 +++++++++++++++++++++++++++++++ lectures/lecture10.pdf | Bin 0 -> 324961 bytes lectures/lecture9.pdf | Bin 224567 -> 224569 bytes 4 files changed, 274 insertions(+) create mode 100644 firm_problems/inventory_dp.ipynb create mode 100644 lectures/lecture10.pdf diff --git a/README.md b/README.md index d00f031..2f8fa00 100644 --- a/README.md +++ b/README.md @@ -43,3 +43,4 @@ See NYU Classes * [Lecture 7](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture7.pdf) * [Lecture 8](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture8.pdf) * [Lecture 9](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture9.pdf) +* [Lecture 10](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture10.pdf) diff --git a/firm_problems/inventory_dp.ipynb b/firm_problems/inventory_dp.ipynb new file mode 100644 index 0000000..362a83a --- /dev/null +++ b/firm_problems/inventory_dp.ipynb @@ -0,0 +1,273 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Inventories and Dynamic Programming\n", + "\n", + "#### John Stachurski\n", + "\n", + "Fall semester 2018\n", + "\n", + "Attempts to generate $(s, S)$ dynamics in an optimizing model." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from numba import njit" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "p = 0.4 # Higher p means lower demand\n", + "\n", + "@njit\n", + "def ϕ(d):\n", + " return (1 - p)**d * p\n", + "\n", + "@njit\n", + "def mx(a):\n", + " return max(a, 0)\n", + "\n", + "d_max = 100" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "@njit\n", + "def bellman_op(v, v_out, σ, β, S, c, k):\n", + "\n", + " n = len(v) \n", + " \n", + " for x in range(n):\n", + " # compute the value of not ordering\n", + " vno = 0.0\n", + " for d in range(d_max):\n", + " vno += (min(x, d) + β * v[mx(x-d)]) * ϕ(d)\n", + " # compute the value of ordering\n", + " if x <= (k - 1) * S:\n", + " vo = -c\n", + " for d in range(d_max):\n", + " vo += (min(x, d) + β * v[mx(x-d) + S]) * ϕ(d)\n", + " else:\n", + " vo = -np.inf\n", + " \n", + " # take the max\n", + " v_out[x] = max(vo, vno)\n", + " if vo > vno:\n", + " σ[x] = 1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "β = 0.98\n", + "S = 100\n", + "c = 2\n", + "k = 2\n", + "n = k * S + 1" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "v_in = np.ones(n, dtype=int)\n", + "v_out = np.ones(n, dtype=int)\n", + "σ = np.zeros(n, dtype=int)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "i = 0\n", + "iter_max = 500\n", + "tol = 1e-6\n", + "ϵ = tol + 1\n", + "\n", + "while i < iter_max and ϵ > tol:\n", + " bellman_op(v_in, v_out, σ, β, S, c, k)\n", + " ϵ = np.max(np.abs(v_in - v_out))\n", + " v_in[:] = v_out\n", + " i += 1" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "28" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "i" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(np.arange(n), v_out, label=\"$v^*$\")\n", + "ax.set_xlabel(\"inventory\", fontsize=12)\n", + "ax.set_ylabel(\"value\", fontsize=12)\n", + "ax.legend(fontsize=12)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(np.arange(len(v_out)), σ, label=\"$\\\\sigma^*$\")\n", + "ax.set_xlabel(\"inventory\")\n", + "\n", + "ax.set_yticks((0, 1))\n", + "\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def simulate(ts_length, x_init=S):\n", + " x = np.empty(ts_length, dtype=int)\n", + " x[0] = x_init\n", + " for t in range(ts_length-1):\n", + " d = np.random.geometric(p)\n", + " x[t+1] = mx(x[t] - d) + S * σ[x[t]]\n", + " return x\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "x = simulate(100)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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