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    "# Spacial Equilibrium Model\n",
    "\n",
    "**Randall Romero Aguilar, PhD**\n",
    "\n",
    "This demo is based on the original Matlab demo accompanying the  <a href=\"https://mitpress.mit.edu/books/applied-computational-economics-and-finance\">Computational Economics and Finance</a> 2001 textbook by Mario Miranda and Paul Fackler.\n",
    "\n",
    "Original (Matlab) CompEcon file: **demslv14.m**\n",
    "\n",
    "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n",
    "\n",
    "    !pip install compecon --upgrade\n",
    "\n",
    "<i>Last updated: 2022-Sept-05</i>\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## About\n",
    "\n",
    "* See textbook page 56 for description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Demand and supply equations\n",
    "\n",
    "| Country  |   Demand      |  Supply       |\n",
    "| :------: | ------------- | ------------- |\n",
    "|       1  |   p = 42 - 2q |  p =  9 + 1q  |\n",
    "|       2  |   p = 54 - 3q |  p =  3 + 2q  |\n",
    "|       3  |   p = 51 - 1q |  p = 18 + 1q  |\n",
    "\n",
    "* Transportation costs:\n",
    "\n",
    "| From      | To country 1 | To country 2 | To country 3 |\n",
    "| :-------- | :----------: | :----------: | :----------: | \n",
    "| Country 1 |       0      |       3      |      9       |\n",
    "| Country 2 |       3      |       0      |      3       | \n",
    "| Country 3 |       6      |       3      |      0       |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from compecon import MCP\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array\n",
    "as_ = A([9, 3, 18])\n",
    "bs = A([1, 2, 1])\n",
    "ad = A([42, 54, 51])\n",
    "bd = A([2, 3, 1])\n",
    "c = A([[0, 3, 9], [3, 0, 3],[6, 3, 0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def market(x):\n",
    "    quantities = x.reshape((3,3))\n",
    "    ps = as_ + bs * quantities.sum(0)\n",
    "    pd = ad - bd * quantities.sum(1)\n",
    "    ps, pd = np.meshgrid(ps, pd)\n",
    "    fval = (pd - ps - c).flatten()\n",
    "    return fval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.zeros(9)\n",
    "b = np.full(9, np.inf)\n",
    "Market = MCP(market, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0 = np.zeros(9)\n",
    "x = Market.zero(x0, transform='minmax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantities = \n",
      " [[ 9.     -0.      0.    ]\n",
      " [ 1.6347  7.3653  0.    ]\n",
      " [ 4.3653  4.6347 12.    ]]\n",
      "Prices = \n",
      " [24. 27. 30.]\n",
      "Net exports =\n",
      " [ 6.  3. -9.]\n"
     ]
    }
   ],
   "source": [
    "quantities = x.reshape(3,3)\n",
    "prices = as_ + bs * quantities.sum(0)\n",
    "exports = quantities.sum(0) - quantities.sum(1)\n",
    "print('Quantities = \\n', quantities)\n",
    "print('Prices = \\n', prices)\n",
    "print('Net exports =\\n', exports)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In autarky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "quantities = (ad - as_) / (bs + bd)\n",
    "prices = as_ + bs * quantities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantities = \n",
      " [11.  10.2 16.5]\n",
      "Prices = \n",
      " [20.  23.4 34.5]\n"
     ]
    }
   ],
   "source": [
    "print('Quantities = \\n', quantities)\n",
    "print('Prices = \\n', prices)"
   ]
  }
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