{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculations and Exercises for: Long-Run Growth Theory: Sources"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
       "    return false;}"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "\n",
    "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
    "    return false;}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# keep output cells from shifting to autoscroll: little scrolling\n",
    "# subwindows within the notebook are an annoyance..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/delong/anaconda3/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "# set up the environment by reading in every library we might need: \n",
    "# os... graphics... data manipulation... time... math... statistics...\n",
    "\n",
    "import sys\n",
    "import os\n",
    "from urllib.request import urlretrieve\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "\n",
    "import pandas as pd\n",
    "from pandas import DataFrame, Series\n",
    "from datetime import datetime\n",
    "\n",
    "import scipy as sp\n",
    "import numpy as np\n",
    "import math\n",
    "import random\n",
    "\n",
    "import seaborn as sns\n",
    "import statsmodels\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# report library versions..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "\n",
    "# put graphs into the notebook itself..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# graphics setup: seaborn-whitegrid and figure size...\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "figure_size = plt.rcParams[\"figure.figsize\"]\n",
    "figure_size[0] = 12\n",
    "figure_size[1] = 10\n",
    "plt.rcParams[\"figure.figsize\"] = figure_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sweden's growth multiple over 1890-2015: 16.4138939671\n",
      "Argentinas growth multiple over 1890-2015: 3.31752104055\n"
     ]
    },
    {
     "data": {
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qqqpSx7y/ePECGRkZACBzHLbww7HqfBHhc0kbQ6ujo8MWcIWvUX0yNjaWWNAD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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a380d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculations for: Long-Run Measured Economic Growth: \n",
    "# Sweden and Argentina, 1890-2017\n",
    "# data previously downloaded\n",
    "# time series for measured real national product per capita for \n",
    "# Sweden and Argentina since 1890, plus source notes, accessible \n",
    "# in the argentina_sweden_dict object for later use, if needed...\n",
    "\n",
    "sourceURL = \"http://delong.typepad.com/2017-08-11-argentina-and-sweden-gdp-per-capita-1890-2015-from-gapminder.org.csv\"\n",
    "argentina_sweden_df = pd.read_csv(sourceURL, index_col = 0)\n",
    "\n",
    "argentina_sweden_dict = {}\n",
    "argentina_sweden_dict[\"df\"] = argentina_sweden_df\n",
    "argentina_sweden_dict[\"sourceURL\"] = sourceURL\n",
    "argentina_sweden_dict[\"sourceDescription\"] = \"Hans Rosling's Gapminder: http://gapminder.org\"   \n",
    "argentina_sweden_dict[\"sourceNotes\"] = \"From Gapminder World data page: http://www.gapminder.org/data/\"\n",
    "\n",
    "argentina_sweden_dict[\"df\"].plot()\n",
    "\n",
    "plt.ylim(0, )\n",
    "plt.xlabel(\"Year\", size = 15)\n",
    "plt.ylabel(\"Real GDP per Capita\", size = 15)\n",
    "plt.title(\"Swedish and Argentinian Economic Growth since 1890\", size = 30)\n",
    "\n",
    "## Calculate the difference in growth multiples between Sweden and\n",
    "## Argentina since 1890\n",
    "\n",
    "# Sweden's measured growth multiple over 1890-2015:\n",
    "\n",
    "Sweden_multiple18902015 = argentina_sweden_df.Sweden[2015]/argentina_sweden_df.Sweden[1890]\n",
    "\n",
    "# Argentina's measured growth multiple over 1890-2015:\n",
    "\n",
    "Argentina_multiple18902015 = argentina_sweden_df.Argentina[2015]/argentina_sweden_df.Argentina[1890]\n",
    "\n",
    "print(\"Sweden's growth multiple over 1890-2015:\", Sweden_multiple18902015)\n",
    "print(\"Argentinas growth multiple over 1890-2015:\", Argentina_multiple18902015)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Box 4.1.2: Gapminder: An Information Source: \n",
    "\n",
    "On the World Wide Web at: <http://gapminder.org> is _Gapminder_. It is, its mission statement says:\n",
    "\n",
    ">an independent Swedish foundation... a fact tank, not a think tank.... fight[ing] devastating misconceptions about global development. Gapminder produces free teaching resources making the world understandable based on reliable statistics. Gapminder promotes a fact-based worldview everyone can understand...\n",
    "\n",
    "and Gapminder exists because:\n",
    "\n",
    ">We humans are born with a craving for... drama. We pay attention to dramatic stories and we get bored if nothing happens. Journalists and lobbyists tell dramatic stories... about extraordinary events and unusual people. The piles of dramatic stories pile up in people’s minds into an overdramatic worldview and strong negative stress feelings: “The world is getting worse!”, “It’s we vs. them!” , “Other people are strange!”, “The population just keeps growing!” and “Nobody cares!” For the first time in human history reliable statistics exist. There’s data for almost every aspect of global development. The data shows a very different picture: a world where most things improve.... [where] decisions [are] based on universal human needs... easy to understand....\n",
    "\n",
    ">Fast population growth will soon be over. The total number of children in the world has stopped growing.... We live in a globalized world, not only in terms of trade and migration. More people than ever care about global development! The world has never been less bad. Which doesn’t mean it’s perfect. The world is far from perfect.\n",
    "\n",
    ">The dramatic worldview has to be dismantled, because it is stressful... wrong.... leads to bad focus and bad decisions. We know this because we have measured the global ignorance... [of] top decision makers... journalists, activists, teachers and the general public. This has nothing to do with intelligence. It’s a problem of factual knowledge. Facts don’t come naturally. Drama and opinions do. Factual knowledge has to be learned. We need to teach global facts in schools and in corporate training. This is an exciting problem to work on and we invite all our users to join the Gapminder movement for global factfulness. The problem can be solved, because the data exists...\n",
    "\n",
    "Do not be globally ignorant! Explore—and use—Gapminder! And watch Ola and Hans Rosling's \"How Not to Be Ignorant about the World\" talk at: <https://www.youtube.com/watch?v=Sm5xF-UYgdg>\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1.6 EXERCISES: Sources of Long-Run Growth\n",
    "\n",
    "**Task 1: Using information sources**:\n",
    "\n",
    "1. Websurf your way over to https://gapminder.org/tools\n",
    "2. Choose a non-U.S. country of interest to you. Select it and the U.S. by clicking on the checkboxes in the country list that should be visible.\n",
    "3. Pull the slider to the right of the \"play\" button all the way back to the left.\n",
    "4. Press the \"play\" button and watch the two countries—the one you selected, and the U.S.—make tracks over the past.\n",
    "5. Take a screenshot of the resulting figure when the animation has finished.\n",
    "6. Upload that screenshot to a URL somewhere on the net.\n",
    "7. Display that screenshot in the markdown cell below using an &lt;img src=\"\" /&gt; tag\n",
    "8. Write a paragraph: What do you learn about economic growth roughly since the Industrial Revolution from the figure you have screenshotted?\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color=\"blue\">PASTE IMG TAG HERE: ___  </font>\n",
    "\n",
    "<font color=\"blue\">WHAT DID YOU LEARN? ANSWER: ___ </font>\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task 2: Reversals of Fortune**:\n",
    "\n",
    "This problem requires you to edit the second Python code cell below. The first cell downloads data and plots Argentinean and Swedish levels of GDP per capita since 1890. Run this first cell. There is no need to change it. Then..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# time series for measured real national product per capita for \n",
    "# Sweden and Argentina since 1890, plus source notes, accessible \n",
    "# in the argentina_sweden_dict object for later use, if needed...\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "sourceURL = \"http://delong.typepad.com/2017-08-11-argentina-and-sweden-gdp-per-capita-1890-2015-from-gapminder.org.csv\"\n",
    "argentina_sweden_df = pd.read_csv(sourceURL, index_col = 0)\n",
    "\n",
    "argentina_sweden_dict = {}\n",
    "argentina_sweden_dict[\"df\"] = argentina_sweden_df\n",
    "argentina_sweden_dict[\"sourceURL\"] = sourceURL\n",
    "argentina_sweden_dict[\"sourceDescription\"] = \"Hans Rosling's Gapminder: http://gapminder.org\"   \n",
    "argentina_sweden_dict[\"sourceNotes\"] = \"From Gapminder World data page: http://www.gapminder.org/data/\"\n",
    "\n",
    "argentina_sweden_dict[\"df\"].plot()\n",
    "\n",
    "plt.ylim(0, )\n",
    "plt.xlabel(\"Year\", size = 15)\n",
    "plt.ylabel(\"Real GDP per Capita\", size = 15)\n",
    "plt.title(\"Swedish and Argentinian Economic Growth since 1890\", size = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.1: Calculate the year that Sweden surpasses Argentina in GDP per capita. Write code to set the variable Sweden_surpasses equal to that year in the code cell below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Sweden_surpasses = 1931"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.2: Calculate the growth rates of Swedish and Argentinean GDP per capita, and their difference, over the periods 1890-1914, 1914-1946, 1946-1980, and 1980-2002. Write code to set the appropriate variables equal to the values in the code cell below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Swedish_Growth18901914 = ___\n",
    "Swedish_Growth19141946 = ___\n",
    "Swedish_Growth19461980 = ___\n",
    "Swedish_Growth19802002 = ___\n",
    "\n",
    "Argentinean_Growth18901914 = ___\n",
    "Argentinean_Growth19141946 = ___\n",
    "Argentinean_Growth19461980 = ___\n",
    "Argentinean_Growth19802002 = ___\n",
    "\n",
    "Difference_Growth18901914 = ___\n",
    "Difference_Growth19141946 = ___\n",
    "Difference_Growth19461980 = ___\n",
    "Difference_Growth19802002 = ___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.3: Calculate the multiple that Swedish GDP per capita in 2015 is of its level in 1890, the multiple that Argentinean GDP per capita in 2015 is of its level in 1890, and the multiple that the quotient is. Write code to set the appropriate variables equal to the values in the code cell below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Sweden_multiple18902015 = ___\n",
    "\n",
    "Argentina_multiple18902015 = ___\n",
    "\n",
    "Quotient_multiple18902015 = ___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catch Our Breath\n",
    "\n",
    "<img src=\"https://tinyurl.com/20181029a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "* Ask me two questions…\n",
    "* Make two comments…\n",
    "* Further reading…\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "Calculations and Exercises for: Long-Run Economic Groswth Theory—Sources: <https://www.icloud.com/keynote/00biHFkmiRWGjrKVCfFCroVNA>   \n",
    "Lecture Support: <>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.1 Sources of Long-Run Economic Growth\n",
    "\n",
    "### Solow Growth Model: Preliminaries\n",
    "\n",
    "* The Eagle's Eye View\n",
    "* Divergences\n",
    "    * Differences in the efficiency of labor\n",
    "    * Differences in capital intensity\n",
    "* Aim to understand why some countries…\n",
    "    * …are growing rapidly and others are not\n",
    "    * …are rich and others are not\n",
    "    * …under conditions of industrial civilization\n",
    "    \n",
    "&nbsp;\n",
    "\n",
    "### Some Facts: Looking Across Countries\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94a0e7b970b-pi\" \n",
    "  alt=\"Gapminder U S Mexican Nigerian and Afghan GDP per Capita and Life Expectancy since 1870\" title=\"4_1_Gapminder__U_S___Mexican__Nigerian__and_Afghan_GDP_per_Capita_and_Life_Expectancy_since_1870__https___tinyurl_com_dl20180122b.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "* U.S. today:\n",
    "    * 3x richer than Mexico\n",
    "    * 9x richer than Nigeria\n",
    "    * 20x richer than Afghanistan\n",
    "        * PPP or RER?\n",
    "* Afghans back at where U.S. was 200 years ago\n",
    "    * Differences between Afghanistan and U.S. then much smaller than now\n",
    "    * In spite of improved communications, transport, etc…\n",
    "    \n",
    "&nbsp;\n",
    "\n",
    "### Some Facts: Looking Over Time\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2d45f78970c-pi\" alt=\"4 2 Gapminder U S GDP per Capita and Life Expectancy since 1870 https tinyurl com dl20180122a\" title=\"4_2_Gapminder__U_S__GDP_per_Capita_and_Life_Expectancy_since_1870__https___tinyurl_com_dl20180122a.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "* 15x in productivity since 1870\n",
    "    * And this might be an underestimate\n",
    "* Doubling of life expectancy since 1870\n",
    "    * Where do you think the 1919 “Spanish Influenza” epidemic is?\n",
    "* Divide $4000 by 13 and you are at a dollar a day\n",
    "    * Anything less, and you are starving to death\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### What Is the Pace of Growth?\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2d45f78970c-pi\" alt=\"4 2 Gapminder U S GDP per Capita and Life Expectancy since 1870 https tinyurl com dl20180122a\" title=\"4_2_Gapminder__U_S__GDP_per_Capita_and_Life_Expectancy_since_1870__https___tinyurl_com_dl20180122a.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "* 60000 today\n",
    "* 4000 150 years ago\n",
    "* What’s the growth rate?\n",
    "\n",
    "1. 2.8%/year\n",
    "2. 1.8%/year\n",
    "3. 0.8%/year\n",
    "4. 5.6%/year\n",
    "5. None of the above\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### Reversals of Fortune\n",
    "\n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2a9cc1f970c-pi\" alt=\"2017 08 11 DeLong and Olney Macroeconomics 3rd Edition\" title=\"2017-08-11_DeLong_and_Olney_Macroeconomics_3rd_Edition.png\" border=\"0\" width=\"400\" height=\"400\" />\n",
    "\n",
    "* Sweden was about like Norway back in 1870\n",
    "    * A “s—-hole country”\n",
    "    * Swedes (and Norwegians) left in droves for the New World\n",
    "* By contrast, Argentina back in 1870 looked like it had it made\n",
    "* Reversals of fortune\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### The Structure of an Economic Model\n",
    "\n",
    "* **Variables**: economic quantities of interest that we can calculate and  measure.\n",
    "* **Behavioral relationships**: relationships that (1) describe how humans, making economic decisions given their opportunities and opportunity costs, decide what to do, and (2) that thus determine the values of the economic variables.\n",
    "* **Equilibrium conditions**: conditions that tell us when the economy is in a position of balance, when some subset of the variables are \"stable\"—that is, are either constant are changing in simple and predictable ways.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### The Structure of the Solow Growth Model\n",
    "\n",
    "* Production function:\n",
    "    * A 1% increase in the efficiency of labor E increases production Y by 1-α%\n",
    "    * A 1% increase in the capital-labor ratio K/L increases production per worker Y/L by α%\n",
    "    * Why these rules of thumb?\n",
    "    * They force us to: $ \\frac{Y}{L} = \\left(\\frac{K}{L}\\right)^α(E)^{(1-α)} $\n",
    "* Capital accumulation equation: dK/dt = sY - δK\n",
    "* Labor force growth: dL/dt = nL\n",
    "* Efficiency of labor (technology and organization) growth: dE/dt = gE\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Production Function II\n",
    "\n",
    "Alternative functional forms:\n",
    "\n",
    "> $ \\frac{Y}{L} = \\left(\\frac{K}{L}\\right)^α(E)^{(1-α)} $\n",
    "\n",
    "> $ \\ln\\left(\\frac{Y}{L}\\right) = α\\ln\\left(\\frac{K}{L}\\right) + (1-α)\\ln(E) $\n",
    "\n",
    "> $ \\frac{Y}{L} = \\left(\\frac{K}{Y}\\right)^\\left(\\frac{α}{1-α}\\right)(E) $\n",
    "\n",
    "> $ \\ln\\left(\\frac{Y}{L}\\right) = \\left(\\frac{α}{1-α}\\right)\\ln\\left(\\frac{K}{L}\\right) + \\ln(E) $\n",
    "\n",
    "> $ \\frac{d\\left(\\ln\\left(\\frac{Y}{L}\\right)\\right)}{dt} = α \\frac{d\\left(\\ln\\left(\\frac{K}{L}\\right)\\right)}{dt} + (1-α)\\frac{d\\left(\\ln\\left(E\\right)\\right)}{dt} $\n",
    "\n",
    "> $ \\frac{d\\left(\\ln\\left(\\frac{Y}{L}\\right)\\right)}{dt} = α \\frac{d\\left(\\ln\\left(K\\right)\\right)}{dt} - α \\frac{d\\left(\\ln\\left(L\\right)\\right)}{dt} + (1-α)\\frac{d\\left(\\ln\\left(E\\right)\\right)}{dt} $\n",
    "\n",
    "> $ \\frac{d\\left(\\ln\\left(\\frac{Y}{L}\\right)\\right)}{dt} = \\left(\\frac{α}{1-α}\\right) \\frac{d\\left(\\ln\\left(\\frac{K}{Y}\\right)\\right)}{dt} + \\frac{d\\left(\\ln\\left(E\\right)\\right)}{dt} $\n",
    "\n",
    "We will use whatever is most convenient for the task at hand at the moment...\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### Simplest Possible Accumulation Equations\n",
    "\n",
    "> $ \\frac{dK}{dt} = sY - {\\delta}K $ :: capital accumulation\n",
    "\n",
    "> $ \\frac{dL}{dt} = nL $ :: labor force growth\n",
    "\n",
    "> $ \\frac{dE}{dt} = gE $ :: efficiency-of-labor growth\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "> $ \\frac{d}{dt}{\\ln}(K) = s\\left(\\frac{Y}{K}\\right) - {\\delta} $ :: capital accumulation\n",
    "\n",
    "> $ \\frac{d}{dt}{\\ln}(L) = n $ :: labor force growth\n",
    "\n",
    "> $ \\frac{d}{dt}{\\ln}(E) = g $ :: efficiency-of-labor growth\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### How Does a System Like This Behave Over Time?\n",
    "\n",
    "* Let’s start it up and see…\n",
    "* <http://datahub.berkeley.edu/user-redirect/interact?account=braddelong&repo=LSF18E101B&branch=master&path=Solow_Growth_Model-Initial_Computations.ipynb>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catch Our Breath\n",
    "\n",
    "<img src=\"https://tinyurl.com/20181029a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "* Ask me two questions…\n",
    "* Make two comments…\n",
    "* Further reading…\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "Sources of Long-Term Growth: <https://www.icloud.com/keynote/00biHFkmiRWGjrKVCfFCroVNA>   \n",
    "Lecture Support: <https://github.com/braddelong/LSF18E101B/blob/master/Calculations_and_Exercises_for_Long-Run_Economic_Growth_Theory-Sources.ipynb>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  }
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