{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Economic Models: trade-offs and trade\n",
    "## Prof. Rabanal [Econ 133]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Why models ---simplified representations of reality--- play a crucial role in economics?\n",
    "- Models are used to better understand real-life situations. \n",
    "- The goal of a model is to make a prediction about the most likely outcome of an economic situation. \n",
    "- The prediction made will be based on the \"other things equal\" assumption, meaning that all other relevant factors are being held unchanged.\n",
    "- The model of comparative advantage was developed by David Ricardo (1772 - 1823) in his book \"Principles of Political Economy and Taxation,\" published in 1817.\n",
    "- The model argues that individuals or other collective entities\n",
    "  have a lot to gain by specializing in the production of goods in\n",
    "  which they have the so called **comparative advantage** and trading\n",
    "  the rest of the goods with other individuals or entities.\n",
    "- To understand the concept of comparative advantage, first we\n",
    "  have remember the concept of opportunity cost, which we have already\n",
    "  learned.\n",
    "- **Opportunity cost** is the value of the next best available\n",
    "  alternative. \n",
    "- Imagine that Castle Black (**CB**) can produce only canons (C) and\n",
    "  books (B) according with the following graph.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10cba5250>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yAFcDlYHkH1vinPtv2CILoUQj4XLihOOjWWt5fswSTjj4V4da3NyiMtFRFnRo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\nREQkrJRoREQkrJRoREQkrJRoREQkrP4fBuNsSgukItsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c92c050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x = np.arange(0.,101, 5)\n",
    "y = 50 - x/2\n",
    "plt.plot(x,y)\n",
    "plt.ylabel('canons')\n",
    "plt.xlabel('books')\n",
    "plt.title('Figure 1: The Production Possibility Frontier (PPF) in Castle Black')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- What’s the opportunity cost of one book? one cannon?\n",
    "\n",
    "- Winterfell (**W**) is not as good as Castle Back in producing cannons and books. Now, the opportunity cost of producing one book is 3 cannons, and Winterfell can produce at most 10 books.\n",
    "\n",
    "- In autarky (no trade), CB prefers to consume 90 books. How many units of cannons are they able to consume?\n",
    "\n",
    "- W consumes 18 cannons in autarky. How many units of books are they able to consume?\n",
    "\n",
    "- Oh! But what if we allow them to trade? Who is better in producing books?\n",
    "- Assume that both regions decide to exchange one-to-one books for\n",
    "  canons, and CB still prefers to consume 90 books. How many units of\n",
    "  canons CB consume? What about W?\n",
    "- What determines the terms of trade between CB and W? We can\n",
    "  think that they enter in a negotiation. \n",
    "- Negotiations between two parties is a different trading\n",
    "  mechanism compared to the double auction game we play. Usually, the\n",
    "  terms of trade depend on the outside options each party has, and the\n",
    "  bargaining power. This concept is due to John Nash. \n",
    "- The key idea of the Ricardian model is that two countries\n",
    "  specialize in what they are better at, i.e. the good in which they have lower opportunity cost compared to the other country, they can gain from trading the other good with each other.\n",
    "- In sum, an entity (individual, country, etc.) has comparative\n",
    "  advantage in producing a good or service, if it faces a lower\n",
    "  opportunity cost in the production of that good or service compared\n",
    "  to other entities. \n",
    "- Notice that our results hold in spite of the fact that Castle\n",
    "  Back  is, in absolute terms, better at producing both books and\n",
    "  canons. With the same amount of resources, CB can produce more books\n",
    "  and more canons than Winterfell. Thus, CB has absolute advantage in\n",
    "  producing both books and canons. \n",
    "- Technically, an entity has absolute advantage in producing a\n",
    "  good or a service, if it is better at producing that good or service\n",
    "  compared to another entity (e.g. a country can produce more output\n",
    "  per worker than another country).\n",
    "- In our example, we have assume a constant opportunity cost\n",
    "  between books and canons. Probably, it makes more sense to assume\n",
    "  that it is easier that opportunity cost is increasing in terms of\n",
    "  production. In this case, the relationship between cannons and books\n",
    "  look like "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Annotation at 0x10cd12410>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TXy3mP+MXkRwfS++2DfcGQ6cmabXuXEzvvPMOgwYNomPHjjRq1IgZM2bQs2fPoMuSajR7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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c92c210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a= 100**2\n",
    "b =.8\n",
    "z = (a- b*x**2)**(.5)-(a-b*100**2)**(.5)\n",
    "plt.plot(x,z)\n",
    "plt.ylabel('canons')\n",
    "plt.xlabel('books')\n",
    "plt.title('Figure 2: Increasing opportunity cost PPF')\n",
    "plt.plot([20,40,80], [20,(a- b*40**2)**(.5)-(a-b*100**2)**(.5),50], 'ro')\n",
    "plt.annotate(\"A\", xy=(40,50), xytext=(41,51))\n",
    "plt.annotate(\"B\", xy=(20,20), xytext=(21,21))\n",
    "plt.annotate(\"C\", xy=(80,50), xytext=(81,51))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- In Figure 2, point B is feasible but inefficient, because one can produce more cannons or books without giving up an additional unit. Point C is unfeasible, because there is no technogology available that can produce C and point A is one of the efficient points along the PPF. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Arvo:400,700,400italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=PT+Mono' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Shadows+Into+Light' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Nixie+One' rel='stylesheet' type='text/css'>\n",
       "<link href='https://fonts.googleapis.com/css?family=Source+Code+Pro' rel='stylesheet' type='text/css'>\n",
       "<style>\n",
       "\n",
       "@font-face {\n",
       "    font-family: \"Computer Modern\";\n",
       "    src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "}\n",
       "\n",
       "#notebook_panel { /* main background */\n",
       "    background: rgb(245,245,245);\n",
       "}\n",
       "\n",
       "div.cell { /* set cell width */\n",
       "    width: 750px;\n",
       "}\n",
       "\n",
       "div #notebook { /* centre the content */\n",
       "    background: #fff; /* white background for content */\n",
       "    width: 1000px;\n",
       "    margin: auto;\n",
       "    padding-left: 0em;\n",
       "}\n",
       "\n",
       "#notebook li { /* More space between bullet points */\n",
       "    margin-top:0.8em;\n",
       "}\n",
       "\n",
       "/* draw border around running cells */\n",
       "div.cell.border-box-sizing.code_cell.running { \n",
       "    border: 1px solid #111;\n",
       "}\n",
       "\n",
       "/* Put a solid color box around each cell and its output, visually linking them*/\n",
       "div.cell.code_cell {\n",
       "    background-color: rgb(256,256,256); \n",
       "    border-radius: 0px; \n",
       "    padding: 0.5em;\n",
       "    margin-left:1em;\n",
       "    margin-top: 1em;\n",
       "}\n",
       "\n",
       "div.text_cell_render{\n",
       "    font-family: 'Alegreya Sans' sans-serif;\n",
       "    line-height: 140%;\n",
       "    font-size: 125%;\n",
       "    font-weight: 400;\n",
       "    width:600px;\n",
       "    margin-left:auto;\n",
       "    margin-right:auto;\n",
       "}\n",
       "\n",
       "\n",
       "/* Formatting for header cells */\n",
       ".text_cell_render h1 {\n",
       "    font-family: 'Nixie One', serif;\n",
       "    font-style:regular;\n",
       "    font-weight: 400;    \n",
       "    font-size: 45pt;\n",
       "    line-height: 100%;\n",
       "    color: rgb(0,51,102);\n",
       "    margin-bottom: 0.5em;\n",
       "    margin-top: 0.5em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h2 {\n",
       "    font-family: 'Nixie One', serif;\n",
       "    font-weight: 400;\n",
       "    font-size: 30pt;\n",
       "    line-height: 100%;\n",
       "    color: rgb(0,51,102);\n",
       "    margin-bottom: 0.1em;\n",
       "    margin-top: 0.3em;\n",
       "    display: block;\n",
       "}\t\n",
       "\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Nixie One', serif;\n",
       "    margin-top:16px;\n",
       "    font-size: 22pt;\n",
       "    font-weight: 600;\n",
       "    margin-bottom: 3px;\n",
       "    font-style: regular;\n",
       "    color: rgb(102,102,0);\n",
       "}\n",
       "\n",
       ".text_cell_render h4 {    /*Use this for captions*/\n",
       "    font-family: 'Nixie One', serif;\n",
       "    font-size: 14pt;\n",
       "    text-align: center;\n",
       "    margin-top: 0em;\n",
       "    margin-bottom: 2em;\n",
       "    font-style: regular;\n",
       "}\n",
       "\n",
       ".text_cell_render h5 {  /*Use this for small titles*/\n",
       "    font-family: 'Nixie One', sans-serif;\n",
       "    font-weight: 400;\n",
       "    font-size: 16pt;\n",
       "    color: rgb(163,0,0);\n",
       "    font-style: italic;\n",
       "    margin-bottom: .1em;\n",
       "    margin-top: 0.8em;\n",
       "    display: block;\n",
       "}\n",
       "\n",
       ".text_cell_render h6 { /*use this for copyright note*/\n",
       "    font-family: 'PT Mono', sans-serif;\n",
       "    font-weight: 300;\n",
       "    font-size: 9pt;\n",
       "    line-height: 100%;\n",
       "    color: grey;\n",
       "    margin-bottom: 1px;\n",
       "    margin-top: 1px;\n",
       "}\n",
       "\n",
       ".CodeMirror{\n",
       "    font-family: \"Source Code Pro\";\n",
       "    font-size: 90%;\n",
       "}\n",
       "\n",
       ".alert-box {\n",
       "    padding:10px 10px 10px 36px;\n",
       "    margin:5px;\n",
       "}\n",
       "\n",
       ".success {\n",
       "    color:#666600;\n",
       "    background:rgb(240,242,229);\n",
       "}\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"],\n",
       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  }
 ],
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