examples.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext autoreload"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "autoreload 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import sympy as sym\n",
      "\n",
      "import inputs\n",
      "import models\n",
      "import solvers"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Example: \n",
      "\n",
      "## Worker skill and firm productivity are $\\sim U[a, b]$..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define some workers skill\n",
      "x, a, b = sym.var('x, a, b')\n",
      "skill_cdf = (x - a) / (b - a)\n",
      "skill_params = {'a': 1.0, 'b': 2.0}\n",
      "skill_bounds = [skill_params['a'], skill_params['b']]\n",
      "\n",
      "workers = inputs.Input(var=x,\n",
      "                       cdf=skill_cdf,\n",
      "                       params=skill_params,\n",
      "                       bounds=skill_bounds,\n",
      "                       )\n",
      "\n",
      "# define some firms\n",
      "y = sym.var('y')\n",
      "productivity_cdf = (y - a) / (b - a)\n",
      "productivity_params = skill_params\n",
      "productivity_bounds = skill_bounds\n",
      "\n",
      "firms = inputs.Input(var=y,\n",
      "                     cdf=productivity_cdf,\n",
      "                     params=productivity_params,\n",
      "                     bounds=productivity_bounds,\n",
      "                     )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## ...and production function is multiplicatively separable.\n",
      "A particularly attractive case arises under multiplicative separability of the form\n",
      "\n",
      "$$F(x, y, l, r) = A(x, y)B(l, r)$$\n",
      "\n",
      "In this case the condition for positive assortative matching can be written as \n",
      "\n",
      "$$\\frac{AA_{xy}}{A_xA_y}\\frac{BB_{lr}}{B_lB_r} \\ge 1$$\n",
      "\n",
      "If $B$ has constant elasticity of substitution form, then we obtain an even simpler condition\n",
      "\n",
      "$$\\frac{AA_{xy}}{A_xA_y} \\frac{1}{\\sigma_{lr}}\\ge 1$$\n",
      "\n",
      "where $\\sigma_{lr}$ is the elasticity of substitution between $l$ and $r$. \n",
      "\n",
      "Finally, if $A$ also has constant elasticity of substitution form, then we obtain an even simpler condition\n",
      "\n",
      "$$\\frac{1}{\\sigma_{xy}\\sigma_{lr}}\\ge 1 \\iff \\sigma_{xy}\\sigma_{lr} \\le 1$$\n",
      "\n",
      "where $\\sigma_{xy}$ is the elasticity of substitution between $x$ and $y$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define symbolic expression for CES between x and y\n",
      "omega_A, sigma_A = sym.var('omega_A, sigma_A')\n",
      "A = ((omega_A * x**((sigma_A - 1) / sigma_A) + \n",
      "     (1 - omega_A) * y**((sigma_A - 1) / sigma_A))**(sigma_A / (sigma_A - 1))) \n",
      "\n",
      "# define symbolic expression for Cobb-Douglas between l and r\n",
      "l, r, omega_B, sigma_B = sym.var('l, r, omega_B, sigma_B')\n",
      "B = l**omega_B * r**(1 - omega_B)\n",
      "\n",
      "F = A * B"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create an instance of the `models.Model` class and an instance of the `solvers.ShootingSolver` class..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Positive assortative matching"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "F_params = {'omega_A':0.5, 'omega_B':0.45, 'sigma_A':0.95, 'sigma_B':1.0}\n",
      "\n",
      "model = models.Model(assortativity='positive',\n",
      "                     workers=workers,\n",
      "                     firms=firms,\n",
      "                     production=F,\n",
      "                     params=F_params)\n",
      "\n",
      "solver = solvers.ShootingSolver(model=model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solve(1e1, tol=1e-6, number_knots=100, atol=1e-15, rtol=1e-12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Success! All workers and firms are matched\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# examine the solution attribute\n",
      "solver.solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>firm productivity</th>\n",
        "      <th>firm size</th>\n",
        "      <th>wage</th>\n",
        "      <th>profit</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>x</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1.000000</th>\n",
        "      <td> 0.999999</td>\n",
        "      <td> 1.089348</td>\n",
        "      <td> 0.429310</td>\n",
        "      <td> 0.571594</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.010101</th>\n",
        "      <td> 1.009285</td>\n",
        "      <td> 1.086340</td>\n",
        "      <td> 0.434131</td>\n",
        "      <td> 0.576417</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.020202</th>\n",
        "      <td> 1.018595</td>\n",
        "      <td> 1.083403</td>\n",
        "      <td> 0.438957</td>\n",
        "      <td> 0.581249</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.030303</th>\n",
        "      <td> 1.027931</td>\n",
        "      <td> 1.080534</td>\n",
        "      <td> 0.443788</td>\n",
        "      <td> 0.586090</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.040404</th>\n",
        "      <td> 1.037292</td>\n",
        "      <td> 1.077730</td>\n",
        "      <td> 0.448625</td>\n",
        "      <td> 0.590940</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.050505</th>\n",
        "      <td> 1.046676</td>\n",
        "      <td> 1.074990</td>\n",
        "      <td> 0.453467</td>\n",
        "      <td> 0.595799</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.060606</th>\n",
        "      <td> 1.056084</td>\n",
        "      <td> 1.072310</td>\n",
        "      <td> 0.458313</td>\n",
        "      <td> 0.600666</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.070707</th>\n",
        "      <td> 1.065516</td>\n",
        "      <td> 1.069689</td>\n",
        "      <td> 0.463165</td>\n",
        "      <td> 0.605541</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.080808</th>\n",
        "      <td> 1.074970</td>\n",
        "      <td> 1.067126</td>\n",
        "      <td> 0.468022</td>\n",
        "      <td> 0.610425</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.090909</th>\n",
        "      <td> 1.084447</td>\n",
        "      <td> 1.064617</td>\n",
        "      <td> 0.472884</td>\n",
        "      <td> 0.615316</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.101010</th>\n",
        "      <td> 1.093946</td>\n",
        "      <td> 1.062161</td>\n",
        "      <td> 0.477751</td>\n",
        "      <td> 0.620214</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.111111</th>\n",
        "      <td> 1.103466</td>\n",
        "      <td> 1.059756</td>\n",
        "      <td> 0.482622</td>\n",
        "      <td> 0.625120</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.121212</th>\n",
        "      <td> 1.113009</td>\n",
        "      <td> 1.057401</td>\n",
        "      <td> 0.487499</td>\n",
        "      <td> 0.630033</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.131313</th>\n",
        "      <td> 1.122572</td>\n",
        "      <td> 1.055094</td>\n",
        "      <td> 0.492380</td>\n",
        "      <td> 0.634954</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.141414</th>\n",
        "      <td> 1.132156</td>\n",
        "      <td> 1.052834</td>\n",
        "      <td> 0.497266</td>\n",
        "      <td> 0.639881</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.151515</th>\n",
        "      <td> 1.141760</td>\n",
        "      <td> 1.050619</td>\n",
        "      <td> 0.502157</td>\n",
        "      <td> 0.644815</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.161616</th>\n",
        "      <td> 1.151384</td>\n",
        "      <td> 1.048447</td>\n",
        "      <td> 0.507053</td>\n",
        "      <td> 0.649755</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.171717</th>\n",
        "      <td> 1.161028</td>\n",
        "      <td> 1.046318</td>\n",
        "      <td> 0.511953</td>\n",
        "      <td> 0.654702</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.181818</th>\n",
        "      <td> 1.170692</td>\n",
        "      <td> 1.044229</td>\n",
        "      <td> 0.516858</td>\n",
        "      <td> 0.659656</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.191919</th>\n",
        "      <td> 1.180374</td>\n",
        "      <td> 1.042180</td>\n",
        "      <td> 0.521767</td>\n",
        "      <td> 0.664615</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.202020</th>\n",
        "      <td> 1.190076</td>\n",
        "      <td> 1.040170</td>\n",
        "      <td> 0.526681</td>\n",
        "      <td> 0.669580</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.212121</th>\n",
        "      <td> 1.199796</td>\n",
        "      <td> 1.038197</td>\n",
        "      <td> 0.531600</td>\n",
        "      <td> 0.674551</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.222222</th>\n",
        "      <td> 1.209535</td>\n",
        "      <td> 1.036260</td>\n",
        "      <td> 0.536523</td>\n",
        "      <td> 0.679528</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.232323</th>\n",
        "      <td> 1.219291</td>\n",
        "      <td> 1.034359</td>\n",
        "      <td> 0.541451</td>\n",
        "      <td> 0.684511</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.242424</th>\n",
        "      <td> 1.229066</td>\n",
        "      <td> 1.032491</td>\n",
        "      <td> 0.546383</td>\n",
        "      <td> 0.689499</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.252525</th>\n",
        "      <td> 1.238857</td>\n",
        "      <td> 1.030657</td>\n",
        "      <td> 0.551320</td>\n",
        "      <td> 0.694493</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.262626</th>\n",
        "      <td> 1.248667</td>\n",
        "      <td> 1.028854</td>\n",
        "      <td> 0.556260</td>\n",
        "      <td> 0.699491</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.272727</th>\n",
        "      <td> 1.258493</td>\n",
        "      <td> 1.027083</td>\n",
        "      <td> 0.561206</td>\n",
        "      <td> 0.704495</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.282828</th>\n",
        "      <td> 1.268336</td>\n",
        "      <td> 1.025343</td>\n",
        "      <td> 0.566155</td>\n",
        "      <td> 0.709504</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.292929</th>\n",
        "      <td> 1.278195</td>\n",
        "      <td> 1.023632</td>\n",
        "      <td> 0.571109</td>\n",
        "      <td> 0.714518</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.707071</th>\n",
        "      <td> 1.694467</td>\n",
        "      <td> 0.971475</td>\n",
        "      <td> 0.777619</td>\n",
        "      <td> 0.923313</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.717172</th>\n",
        "      <td> 1.704869</td>\n",
        "      <td> 0.970515</td>\n",
        "      <td> 0.782733</td>\n",
        "      <td> 0.928466</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.727273</th>\n",
        "      <td> 1.715282</td>\n",
        "      <td> 0.969566</td>\n",
        "      <td> 0.787849</td>\n",
        "      <td> 0.933621</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.737374</th>\n",
        "      <td> 1.725706</td>\n",
        "      <td> 0.968626</td>\n",
        "      <td> 0.792969</td>\n",
        "      <td> 0.938778</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.747475</th>\n",
        "      <td> 1.736139</td>\n",
        "      <td> 0.967697</td>\n",
        "      <td> 0.798093</td>\n",
        "      <td> 0.943937</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.757576</th>\n",
        "      <td> 1.746582</td>\n",
        "      <td> 0.966778</td>\n",
        "      <td> 0.803219</td>\n",
        "      <td> 0.949098</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.767677</th>\n",
        "      <td> 1.757035</td>\n",
        "      <td> 0.965869</td>\n",
        "      <td> 0.808349</td>\n",
        "      <td> 0.954262</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.777778</th>\n",
        "      <td> 1.767498</td>\n",
        "      <td> 0.964970</td>\n",
        "      <td> 0.813482</td>\n",
        "      <td> 0.959427</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.787879</th>\n",
        "      <td> 1.777970</td>\n",
        "      <td> 0.964079</td>\n",
        "      <td> 0.818619</td>\n",
        "      <td> 0.964594</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.797980</th>\n",
        "      <td> 1.788453</td>\n",
        "      <td> 0.963198</td>\n",
        "      <td> 0.823759</td>\n",
        "      <td> 0.969763</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.808081</th>\n",
        "      <td> 1.798944</td>\n",
        "      <td> 0.962326</td>\n",
        "      <td> 0.828901</td>\n",
        "      <td> 0.974934</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.818182</th>\n",
        "      <td> 1.809445</td>\n",
        "      <td> 0.961463</td>\n",
        "      <td> 0.834048</td>\n",
        "      <td> 0.980108</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.828283</th>\n",
        "      <td> 1.819956</td>\n",
        "      <td> 0.960609</td>\n",
        "      <td> 0.839197</td>\n",
        "      <td> 0.985282</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.838384</th>\n",
        "      <td> 1.830476</td>\n",
        "      <td> 0.959763</td>\n",
        "      <td> 0.844350</td>\n",
        "      <td> 0.990459</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.848485</th>\n",
        "      <td> 1.841005</td>\n",
        "      <td> 0.958926</td>\n",
        "      <td> 0.849505</td>\n",
        "      <td> 0.995638</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.858586</th>\n",
        "      <td> 1.851543</td>\n",
        "      <td> 0.958097</td>\n",
        "      <td> 0.854664</td>\n",
        "      <td> 1.000818</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.868687</th>\n",
        "      <td> 1.862090</td>\n",
        "      <td> 0.957276</td>\n",
        "      <td> 0.859826</td>\n",
        "      <td> 1.006000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.878788</th>\n",
        "      <td> 1.872647</td>\n",
        "      <td> 0.956463</td>\n",
        "      <td> 0.864992</td>\n",
        "      <td> 1.011184</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.888889</th>\n",
        "      <td> 1.883212</td>\n",
        "      <td> 0.955657</td>\n",
        "      <td> 0.870160</td>\n",
        "      <td> 1.016369</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.898990</th>\n",
        "      <td> 1.893786</td>\n",
        "      <td> 0.954860</td>\n",
        "      <td> 0.875331</td>\n",
        "      <td> 1.021556</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.909091</th>\n",
        "      <td> 1.904369</td>\n",
        "      <td> 0.954070</td>\n",
        "      <td> 0.880506</td>\n",
        "      <td> 1.026745</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.919192</th>\n",
        "      <td> 1.914961</td>\n",
        "      <td> 0.953287</td>\n",
        "      <td> 0.885683</td>\n",
        "      <td> 1.031935</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.929293</th>\n",
        "      <td> 1.925561</td>\n",
        "      <td> 0.952512</td>\n",
        "      <td> 0.890864</td>\n",
        "      <td> 1.037127</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.939394</th>\n",
        "      <td> 1.936170</td>\n",
        "      <td> 0.951744</td>\n",
        "      <td> 0.896048</td>\n",
        "      <td> 1.042321</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.949495</th>\n",
        "      <td> 1.946787</td>\n",
        "      <td> 0.950983</td>\n",
        "      <td> 0.901235</td>\n",
        "      <td> 1.047516</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.959596</th>\n",
        "      <td> 1.957413</td>\n",
        "      <td> 0.950229</td>\n",
        "      <td> 0.906424</td>\n",
        "      <td> 1.052713</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.969697</th>\n",
        "      <td> 1.968047</td>\n",
        "      <td> 0.949481</td>\n",
        "      <td> 0.911617</td>\n",
        "      <td> 1.057911</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.979798</th>\n",
        "      <td> 1.978690</td>\n",
        "      <td> 0.948740</td>\n",
        "      <td> 0.916813</td>\n",
        "      <td> 1.063110</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.989899</th>\n",
        "      <td> 1.989341</td>\n",
        "      <td> 0.948006</td>\n",
        "      <td> 0.922012</td>\n",
        "      <td> 1.068311</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2.000000</th>\n",
        "      <td> 2.000000</td>\n",
        "      <td> 0.947279</td>\n",
        "      <td> 0.927213</td>\n",
        "      <td> 1.073514</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>100 rows \u00d7 4 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "          firm productivity  firm size      wage    profit\n",
        "x                                                         \n",
        "1.000000           0.999999   1.089348  0.429310  0.571594\n",
        "1.010101           1.009285   1.086340  0.434131  0.576417\n",
        "1.020202           1.018595   1.083403  0.438957  0.581249\n",
        "1.030303           1.027931   1.080534  0.443788  0.586090\n",
        "1.040404           1.037292   1.077730  0.448625  0.590940\n",
        "1.050505           1.046676   1.074990  0.453467  0.595799\n",
        "1.060606           1.056084   1.072310  0.458313  0.600666\n",
        "1.070707           1.065516   1.069689  0.463165  0.605541\n",
        "1.080808           1.074970   1.067126  0.468022  0.610425\n",
        "1.090909           1.084447   1.064617  0.472884  0.615316\n",
        "1.101010           1.093946   1.062161  0.477751  0.620214\n",
        "1.111111           1.103466   1.059756  0.482622  0.625120\n",
        "1.121212           1.113009   1.057401  0.487499  0.630033\n",
        "1.131313           1.122572   1.055094  0.492380  0.634954\n",
        "1.141414           1.132156   1.052834  0.497266  0.639881\n",
        "1.151515           1.141760   1.050619  0.502157  0.644815\n",
        "1.161616           1.151384   1.048447  0.507053  0.649755\n",
        "1.171717           1.161028   1.046318  0.511953  0.654702\n",
        "1.181818           1.170692   1.044229  0.516858  0.659656\n",
        "1.191919           1.180374   1.042180  0.521767  0.664615\n",
        "1.202020           1.190076   1.040170  0.526681  0.669580\n",
        "1.212121           1.199796   1.038197  0.531600  0.674551\n",
        "1.222222           1.209535   1.036260  0.536523  0.679528\n",
        "1.232323           1.219291   1.034359  0.541451  0.684511\n",
        "1.242424           1.229066   1.032491  0.546383  0.689499\n",
        "1.252525           1.238857   1.030657  0.551320  0.694493\n",
        "1.262626           1.248667   1.028854  0.556260  0.699491\n",
        "1.272727           1.258493   1.027083  0.561206  0.704495\n",
        "1.282828           1.268336   1.025343  0.566155  0.709504\n",
        "1.292929           1.278195   1.023632  0.571109  0.714518\n",
        "...                     ...        ...       ...       ...\n",
        "1.707071           1.694467   0.971475  0.777619  0.923313\n",
        "1.717172           1.704869   0.970515  0.782733  0.928466\n",
        "1.727273           1.715282   0.969566  0.787849  0.933621\n",
        "1.737374           1.725706   0.968626  0.792969  0.938778\n",
        "1.747475           1.736139   0.967697  0.798093  0.943937\n",
        "1.757576           1.746582   0.966778  0.803219  0.949098\n",
        "1.767677           1.757035   0.965869  0.808349  0.954262\n",
        "1.777778           1.767498   0.964970  0.813482  0.959427\n",
        "1.787879           1.777970   0.964079  0.818619  0.964594\n",
        "1.797980           1.788453   0.963198  0.823759  0.969763\n",
        "1.808081           1.798944   0.962326  0.828901  0.974934\n",
        "1.818182           1.809445   0.961463  0.834048  0.980108\n",
        "1.828283           1.819956   0.960609  0.839197  0.985282\n",
        "1.838384           1.830476   0.959763  0.844350  0.990459\n",
        "1.848485           1.841005   0.958926  0.849505  0.995638\n",
        "1.858586           1.851543   0.958097  0.854664  1.000818\n",
        "1.868687           1.862090   0.957276  0.859826  1.006000\n",
        "1.878788           1.872647   0.956463  0.864992  1.011184\n",
        "1.888889           1.883212   0.955657  0.870160  1.016369\n",
        "1.898990           1.893786   0.954860  0.875331  1.021556\n",
        "1.909091           1.904369   0.954070  0.880506  1.026745\n",
        "1.919192           1.914961   0.953287  0.885683  1.031935\n",
        "1.929293           1.925561   0.952512  0.890864  1.037127\n",
        "1.939394           1.936170   0.951744  0.896048  1.042321\n",
        "1.949495           1.946787   0.950983  0.901235  1.047516\n",
        "1.959596           1.957413   0.950229  0.906424  1.052713\n",
        "1.969697           1.968047   0.949481  0.911617  1.057911\n",
        "1.979798           1.978690   0.948740  0.916813  1.063110\n",
        "1.989899           1.989341   0.948006  0.922012  1.068311\n",
        "2.000000           2.000000   0.947279  0.927213  1.073514\n",
        "\n",
        "[100 rows x 4 columns]"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_residual_mu(ax, x, deg, normed=False):\n",
      "    residual = solver.evaluate_residual(x, k=deg)\n",
      "    residual_mu = np.abs(residual[:,0])\n",
      "    residual_mu_line, = ax.plot(x, residual_mu)\n",
      "    ax.set_xlim(solver.model.workers.lower, solver.model.workers.upper)\n",
      "    ax.set_yscale('log')\n",
      "    ax.grid('on')\n",
      "    \n",
      "    return [residual_mu_line]\n",
      "\n",
      "def plot_residual_theta(ax, x, deg, normed=False):\n",
      "    residual = solver.evaluate_residual(x, k=deg)\n",
      "    residual_theta, = ax.plot(x, np.abs(residual[:,1]))\n",
      "    ax.set_xlim(solver.model.workers.lower, solver.model.workers.upper)\n",
      "    ax.set_yscale('log')\n",
      "    ax.grid('on')\n",
      "    \n",
      "    return [residual_theta]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1,1, figsize=(8,6))\n",
      "plot_residual_mu(ax, np.linspace(1, 2, 1000), deg=5)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mKxzIjol/6EPAf/wHucFZxNkSr62luPBjjwF//Su9xuuXH320S1ZjEe/vp32q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\nJzCyiLMIcx/zKl25pvjxd0mKOA+cADe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j7jnpTpd9FuX54POzSDHynNyWffvCLXG+kfG5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\nEEJqCo04IYQQUlNoxAkhhJCa8v8WPbRKR0FJbgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113d628d0>"
       ]
      }
     ],
     "prompt_number": 100
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1,1, figsize=(8,6))\n",
      "plot_residual_theta(ax, np.linspace(1, 2, 1000), deg=5)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fSI30eIiIp0iimPh47nRbxO3jM0W8xLZElribUZ/IEndXcFMqVsS5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\nnttnLO5LlsQOGFh0E7nTbZd7vEI37vXovlFPmwsKYqdVsYD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VLcb33ec9CKOhqH3i/v5P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\nKGAApeEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11498b890>"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.evaluate_rhs(solver.solution.index.values, solver.solution[['firm productivity', 'firm size']].values.T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "array([ 0.91798057,  0.92052183,  0.92301727,  0.92546817,  0.92787578,\n",
        "        0.93024131,  0.93256592,  0.93485074,  0.93709686,  0.93930532,\n",
        "        0.94147715,  0.94361332,  0.94571478,  0.94778246,  0.94981723,\n",
        "        0.95181997,  0.95379149,  0.9557326 ,  0.95764408,  0.95952669,\n",
        "        0.96138115,  0.96320816,  0.96500842,  0.96678258,  0.96853128,\n",
        "        0.97025515,  0.97195478,  0.97363076,  0.97528365,  0.97691401,\n",
        "        0.97852236,  0.98010922,  0.98167509,  0.98322045,  0.98474577,\n",
        "        0.98625151,  0.98773812,  0.98920602,  0.99065562,  0.99208735,\n",
        "        0.99350158,  0.9948987 ,  0.99627908,  0.99764309,  0.99899107,\n",
        "        1.00032337,  1.00164031,  1.00294222,  1.00422941,  1.00550219,\n",
        "        1.00676084,  1.00800567,  1.00923695,  1.01045496,  1.01165995,\n",
        "        1.01285219,  1.01403193,  1.01519941,  1.01635488,  1.01749856,\n",
        "        1.01863069,  1.01975147,  1.02086114,  1.02195989,  1.02304793,\n",
        "        1.02412547,  1.02519269,  1.02624978,  1.02729693,  1.02833431,\n",
        "        1.02936211,  1.0303805 ,  1.03138964,  1.03238969,  1.03338082,\n",
        "        1.03436317,  1.03533691,  1.03630218,  1.03725912,  1.03820788,\n",
        "        1.03914859,  1.04008138,  1.0410064 ,  1.04192377,  1.0428336 ,\n",
        "        1.04373604,  1.04463119,  1.04551918,  1.04640012,  1.04727412,\n",
        "        1.04814129,  1.04900173,  1.04985557,  1.05070288,  1.05154379,\n",
        "        1.05237838,  1.05320675,  1.054029  ,  1.05484522,  1.05565549,\n",
        "       -0.30129466, -0.2942018 , -0.28736374, -0.28076888, -0.27440625,\n",
        "       -0.26826547, -0.26233671, -0.25661066, -0.2510785 , -0.24573187,\n",
        "       -0.24056282, -0.23556384, -0.23072776, -0.2260478 , -0.2215175 ,\n",
        "       -0.21713074, -0.21288167, -0.20876475, -0.20477469, -0.20090646,\n",
        "       -0.19715528, -0.19351657, -0.18998598, -0.18655937, -0.18323277,\n",
        "       -0.18000241, -0.17686467, -0.17381612, -0.17085346, -0.16797355,\n",
        "       -0.16517338, -0.16245008, -0.15980089, -0.15722319, -0.15471446,\n",
        "       -0.15227228, -0.14989434, -0.14757843, -0.14532243, -0.14312431,\n",
        "       -0.14098211, -0.13889397, -0.13685808, -0.13487273, -0.13293626,\n",
        "       -0.13104708, -0.12920367, -0.12740456, -0.12564834, -0.12393365,\n",
        "       -0.1222592 , -0.12062372, -0.11902602, -0.11746493, -0.11593934,\n",
        "       -0.11444817, -0.11299038, -0.11156498, -0.110171  , -0.10880752,\n",
        "       -0.10747364, -0.1061685 , -0.10489128, -0.10364116, -0.10241738,\n",
        "       -0.10121919, -0.10004587, -0.09889673, -0.09777108, -0.09666829,\n",
        "       -0.09558772, -0.09452877, -0.09349086, -0.09247341, -0.09147589,\n",
        "       -0.09049775, -0.08953849, -0.08859762, -0.08767465, -0.08676911,\n",
        "       -0.08588057, -0.08500858, -0.08415272, -0.08331259, -0.08248779,\n",
        "       -0.08167794, -0.08088266, -0.0801016 , -0.0793344 , -0.07858073,\n",
        "       -0.07784026, -0.07711267, -0.07639766, -0.07569492, -0.07500416,\n",
        "       -0.0743251 , -0.07365747, -0.073001  , -0.07235543, -0.07172051])"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n",
      "solver.plot_equilibrium_firm_size(ax, 'firm_productivity')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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km3oGclAxIMXkuefg6KPhF7+Aq66CLl2SjkhE0kY9A5IIjQHGrybHPXuGNQ5+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\nPeoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1151933d0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Negative assortative matching"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# negative assortativity requires that sigma_A * sigma_B > 1\n",
      "F_params = {'omega_A':0.25, 'omega_B':0.5, 'sigma_A':1.5, 'sigma_B':1.0}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = models.Model(assortativity='negative',\n",
      "                     workers=workers,\n",
      "                     firms=firms,\n",
      "                     production=F,\n",
      "                     params=F_params)\n",
      "\n",
      "solver = solvers.ShootingSolver(model=model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solve(2e0, tol=1e-6, number_knots=100, atol=1e-15, rtol=1e-12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exhausted firms: initial guess of 1.0 for firm size is too low.\n",
        "Exhausted firms: initial guess of 1.5 for firm size is too low.\n",
        "Exhausted firms: initial guess of 1.75 for firm size is too low.\n",
        "Exhausted workers: initial guess of 1.875 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 1.8125 for firm size was too low!\n",
        "Exhausted workers: initial guess of 1.84375 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 1.828125 for firm size was too low!\n",
        "Exhausted workers: initial guess of 1.8359375 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 1.83203125 for firm size is too high!\n",
        "Exhausted workers: initial guess of 1.830078125 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 1.8291015625 for firm size was too low!\n",
        "Exhausted firms: Initial guess of 1.82958984375 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 1.82983398438 for firm size is too high!\n",
        "Exhausted workers: initial guess of 1.82971191406 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 1.82965087891 for firm size is too high!\n",
        "Exhausted firms: Initial guess of 1.82962036133 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 1.82963562012 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 1.82964324951 for firm size is too high!\n",
        "Success! All workers and firms are matched"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>firm productivity</th>\n",
        "      <th>firm size</th>\n",
        "      <th>wage</th>\n",
        "      <th>profit</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>x</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1.000000</th>\n",
        "      <td> 2.000000</td>\n",
        "      <td> 1.829639</td>\n",
        "      <td> 0.630705</td>\n",
        "      <td> 1.153963</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.010101</th>\n",
        "      <td> 1.994455</td>\n",
        "      <td> 1.813970</td>\n",
        "      <td> 0.633368</td>\n",
        "      <td> 1.148910</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.020202</th>\n",
        "      <td> 1.988863</td>\n",
        "      <td> 1.798401</td>\n",
        "      <td> 0.636024</td>\n",
        "      <td> 1.143826</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.030303</th>\n",
        "      <td> 1.983222</td>\n",
        "      <td> 1.782931</td>\n",
        "      <td> 0.638673</td>\n",
        "      <td> 1.138710</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.040404</th>\n",
        "      <td> 1.977532</td>\n",
        "      <td> 1.767557</td>\n",
        "      <td> 0.641317</td>\n",
        "      <td> 1.133564</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.050505</th>\n",
        "      <td> 1.971792</td>\n",
        "      <td> 1.752276</td>\n",
        "      <td> 0.643954</td>\n",
        "      <td> 1.128386</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.060606</th>\n",
        "      <td> 1.966003</td>\n",
        "      <td> 1.737087</td>\n",
        "      <td> 0.646586</td>\n",
        "      <td> 1.123175</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.070707</th>\n",
        "      <td> 1.960162</td>\n",
        "      <td> 1.721986</td>\n",
        "      <td> 0.649212</td>\n",
        "      <td> 1.117933</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.080808</th>\n",
        "      <td> 1.954271</td>\n",
        "      <td> 1.706973</td>\n",
        "      <td> 0.651832</td>\n",
        "      <td> 1.112659</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.090909</th>\n",
        "      <td> 1.948327</td>\n",
        "      <td> 1.692044</td>\n",
        "      <td> 0.654446</td>\n",
        "      <td> 1.107352</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.101010</th>\n",
        "      <td> 1.942331</td>\n",
        "      <td> 1.677197</td>\n",
        "      <td> 0.657056</td>\n",
        "      <td> 1.102012</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.111111</th>\n",
        "      <td> 1.936282</td>\n",
        "      <td> 1.662431</td>\n",
        "      <td> 0.659660</td>\n",
        "      <td> 1.096639</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.121212</th>\n",
        "      <td> 1.930179</td>\n",
        "      <td> 1.647743</td>\n",
        "      <td> 0.662259</td>\n",
        "      <td> 1.091233</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.131313</th>\n",
        "      <td> 1.924021</td>\n",
        "      <td> 1.633132</td>\n",
        "      <td> 0.664853</td>\n",
        "      <td> 1.085793</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.141414</th>\n",
        "      <td> 1.917808</td>\n",
        "      <td> 1.618594</td>\n",
        "      <td> 0.667443</td>\n",
        "      <td> 1.080319</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.151515</th>\n",
        "      <td> 1.911540</td>\n",
        "      <td> 1.604130</td>\n",
        "      <td> 0.670027</td>\n",
        "      <td> 1.074810</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.161616</th>\n",
        "      <td> 1.905214</td>\n",
        "      <td> 1.589736</td>\n",
        "      <td> 0.672607</td>\n",
        "      <td> 1.069268</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.171717</th>\n",
        "      <td> 1.898832</td>\n",
        "      <td> 1.575410</td>\n",
        "      <td> 0.675183</td>\n",
        "      <td> 1.063690</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.181818</th>\n",
        "      <td> 1.892391</td>\n",
        "      <td> 1.561152</td>\n",
        "      <td> 0.677754</td>\n",
        "      <td> 1.058076</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.191919</th>\n",
        "      <td> 1.885891</td>\n",
        "      <td> 1.546958</td>\n",
        "      <td> 0.680321</td>\n",
        "      <td> 1.052428</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.202020</th>\n",
        "      <td> 1.879331</td>\n",
        "      <td> 1.532828</td>\n",
        "      <td> 0.682883</td>\n",
        "      <td> 1.046743</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.212121</th>\n",
        "      <td> 1.872711</td>\n",
        "      <td> 1.518759</td>\n",
        "      <td> 0.685442</td>\n",
        "      <td> 1.041022</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.222222</th>\n",
        "      <td> 1.866029</td>\n",
        "      <td> 1.504751</td>\n",
        "      <td> 0.687997</td>\n",
        "      <td> 1.035264</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.232323</th>\n",
        "      <td> 1.859285</td>\n",
        "      <td> 1.490800</td>\n",
        "      <td> 0.690548</td>\n",
        "      <td> 1.029469</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.242424</th>\n",
        "      <td> 1.852478</td>\n",
        "      <td> 1.476906</td>\n",
        "      <td> 0.693095</td>\n",
        "      <td> 1.023637</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.252525</th>\n",
        "      <td> 1.845606</td>\n",
        "      <td> 1.463067</td>\n",
        "      <td> 0.695639</td>\n",
        "      <td> 1.017767</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.262626</th>\n",
        "      <td> 1.838670</td>\n",
        "      <td> 1.449281</td>\n",
        "      <td> 0.698180</td>\n",
        "      <td> 1.011858</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.272727</th>\n",
        "      <td> 1.831667</td>\n",
        "      <td> 1.435546</td>\n",
        "      <td> 0.700716</td>\n",
        "      <td> 1.005911</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.282828</th>\n",
        "      <td> 1.824597</td>\n",
        "      <td> 1.421862</td>\n",
        "      <td> 0.703250</td>\n",
        "      <td> 0.999924</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.292929</th>\n",
        "      <td> 1.817458</td>\n",
        "      <td> 1.408225</td>\n",
        "      <td> 0.705781</td>\n",
        "      <td> 0.993898</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.707071</th>\n",
        "      <td> 1.446606</td>\n",
        "      <td> 0.871852</td>\n",
        "      <td> 0.808071</td>\n",
        "      <td> 0.704518</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.717172</th>\n",
        "      <td> 1.434933</td>\n",
        "      <td> 0.858825</td>\n",
        "      <td> 0.810563</td>\n",
        "      <td> 0.696132</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.727273</th>\n",
        "      <td> 1.423081</td>\n",
        "      <td> 0.845771</td>\n",
        "      <td> 0.813056</td>\n",
        "      <td> 0.687660</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.737374</th>\n",
        "      <td> 1.411045</td>\n",
        "      <td> 0.832690</td>\n",
        "      <td> 0.815552</td>\n",
        "      <td> 0.679102</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.747475</th>\n",
        "      <td> 1.398818</td>\n",
        "      <td> 0.819576</td>\n",
        "      <td> 0.818049</td>\n",
        "      <td> 0.670454</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.757576</th>\n",
        "      <td> 1.386393</td>\n",
        "      <td> 0.806429</td>\n",
        "      <td> 0.820548</td>\n",
        "      <td> 0.661714</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.767677</th>\n",
        "      <td> 1.373764</td>\n",
        "      <td> 0.793244</td>\n",
        "      <td> 0.823050</td>\n",
        "      <td> 0.652879</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.777778</th>\n",
        "      <td> 1.360923</td>\n",
        "      <td> 0.780018</td>\n",
        "      <td> 0.825554</td>\n",
        "      <td> 0.643947</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.787879</th>\n",
        "      <td> 1.347862</td>\n",
        "      <td> 0.766748</td>\n",
        "      <td> 0.828061</td>\n",
        "      <td> 0.634914</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.797980</th>\n",
        "      <td> 1.334573</td>\n",
        "      <td> 0.753431</td>\n",
        "      <td> 0.830571</td>\n",
        "      <td> 0.625778</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.808081</th>\n",
        "      <td> 1.321046</td>\n",
        "      <td> 0.740063</td>\n",
        "      <td> 0.833083</td>\n",
        "      <td> 0.616534</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.818182</th>\n",
        "      <td> 1.307271</td>\n",
        "      <td> 0.726639</td>\n",
        "      <td> 0.835599</td>\n",
        "      <td> 0.607179</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.828283</th>\n",
        "      <td> 1.293240</td>\n",
        "      <td> 0.713157</td>\n",
        "      <td> 0.838119</td>\n",
        "      <td> 0.597710</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.838384</th>\n",
        "      <td> 1.278940</td>\n",
        "      <td> 0.699610</td>\n",
        "      <td> 0.840642</td>\n",
        "      <td> 0.588122</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.848485</th>\n",
        "      <td> 1.264360</td>\n",
        "      <td> 0.685996</td>\n",
        "      <td> 0.843170</td>\n",
        "      <td> 0.578411</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.858586</th>\n",
        "      <td> 1.249486</td>\n",
        "      <td> 0.672308</td>\n",
        "      <td> 0.845701</td>\n",
        "      <td> 0.568572</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.868687</th>\n",
        "      <td> 1.234306</td>\n",
        "      <td> 0.658542</td>\n",
        "      <td> 0.848237</td>\n",
        "      <td> 0.558600</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.878788</th>\n",
        "      <td> 1.218804</td>\n",
        "      <td> 0.644692</td>\n",
        "      <td> 0.850778</td>\n",
        "      <td> 0.548489</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.888889</th>\n",
        "      <td> 1.202965</td>\n",
        "      <td> 0.630751</td>\n",
        "      <td> 0.853324</td>\n",
        "      <td> 0.538235</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.898990</th>\n",
        "      <td> 1.186770</td>\n",
        "      <td> 0.616714</td>\n",
        "      <td> 0.855875</td>\n",
        "      <td> 0.527830</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.909091</th>\n",
        "      <td> 1.170201</td>\n",
        "      <td> 0.602573</td>\n",
        "      <td> 0.858432</td>\n",
        "      <td> 0.517268</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.919192</th>\n",
        "      <td> 1.153236</td>\n",
        "      <td> 0.588320</td>\n",
        "      <td> 0.860995</td>\n",
        "      <td> 0.506541</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.929293</th>\n",
        "      <td> 1.135854</td>\n",
        "      <td> 0.573948</td>\n",
        "      <td> 0.863565</td>\n",
        "      <td> 0.495641</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.939394</th>\n",
        "      <td> 1.118029</td>\n",
        "      <td> 0.559447</td>\n",
        "      <td> 0.866141</td>\n",
        "      <td> 0.484560</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.949495</th>\n",
        "      <td> 1.099734</td>\n",
        "      <td> 0.544807</td>\n",
        "      <td> 0.868725</td>\n",
        "      <td> 0.473288</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.959596</th>\n",
        "      <td> 1.080937</td>\n",
        "      <td> 0.530019</td>\n",
        "      <td> 0.871317</td>\n",
        "      <td> 0.461814</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.969697</th>\n",
        "      <td> 1.061606</td>\n",
        "      <td> 0.515068</td>\n",
        "      <td> 0.873917</td>\n",
        "      <td> 0.450127</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.979798</th>\n",
        "      <td> 1.041702</td>\n",
        "      <td> 0.499944</td>\n",
        "      <td> 0.876526</td>\n",
        "      <td> 0.438214</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.989899</th>\n",
        "      <td> 1.021183</td>\n",
        "      <td> 0.484630</td>\n",
        "      <td> 0.879145</td>\n",
        "      <td> 0.426060</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2.000000</th>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.469110</td>\n",
        "      <td> 0.881774</td>\n",
        "      <td> 0.413649</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>100 rows \u00d7 4 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "          firm productivity  firm size      wage    profit\n",
        "x                                                         \n",
        "1.000000           2.000000   1.829639  0.630705  1.153963\n",
        "1.010101           1.994455   1.813970  0.633368  1.148910\n",
        "1.020202           1.988863   1.798401  0.636024  1.143826\n",
        "1.030303           1.983222   1.782931  0.638673  1.138710\n",
        "1.040404           1.977532   1.767557  0.641317  1.133564\n",
        "1.050505           1.971792   1.752276  0.643954  1.128386\n",
        "1.060606           1.966003   1.737087  0.646586  1.123175\n",
        "1.070707           1.960162   1.721986  0.649212  1.117933\n",
        "1.080808           1.954271   1.706973  0.651832  1.112659\n",
        "1.090909           1.948327   1.692044  0.654446  1.107352\n",
        "1.101010           1.942331   1.677197  0.657056  1.102012\n",
        "1.111111           1.936282   1.662431  0.659660  1.096639\n",
        "1.121212           1.930179   1.647743  0.662259  1.091233\n",
        "1.131313           1.924021   1.633132  0.664853  1.085793\n",
        "1.141414           1.917808   1.618594  0.667443  1.080319\n",
        "1.151515           1.911540   1.604130  0.670027  1.074810\n",
        "1.161616           1.905214   1.589736  0.672607  1.069268\n",
        "1.171717           1.898832   1.575410  0.675183  1.063690\n",
        "1.181818           1.892391   1.561152  0.677754  1.058076\n",
        "1.191919           1.885891   1.546958  0.680321  1.052428\n",
        "1.202020           1.879331   1.532828  0.682883  1.046743\n",
        "1.212121           1.872711   1.518759  0.685442  1.041022\n",
        "1.222222           1.866029   1.504751  0.687997  1.035264\n",
        "1.232323           1.859285   1.490800  0.690548  1.029469\n",
        "1.242424           1.852478   1.476906  0.693095  1.023637\n",
        "1.252525           1.845606   1.463067  0.695639  1.017767\n",
        "1.262626           1.838670   1.449281  0.698180  1.011858\n",
        "1.272727           1.831667   1.435546  0.700716  1.005911\n",
        "1.282828           1.824597   1.421862  0.703250  0.999924\n",
        "1.292929           1.817458   1.408225  0.705781  0.993898\n",
        "...                     ...        ...       ...       ...\n",
        "1.707071           1.446606   0.871852  0.808071  0.704518\n",
        "1.717172           1.434933   0.858825  0.810563  0.696132\n",
        "1.727273           1.423081   0.845771  0.813056  0.687660\n",
        "1.737374           1.411045   0.832690  0.815552  0.679102\n",
        "1.747475           1.398818   0.819576  0.818049  0.670454\n",
        "1.757576           1.386393   0.806429  0.820548  0.661714\n",
        "1.767677           1.373764   0.793244  0.823050  0.652879\n",
        "1.777778           1.360923   0.780018  0.825554  0.643947\n",
        "1.787879           1.347862   0.766748  0.828061  0.634914\n",
        "1.797980           1.334573   0.753431  0.830571  0.625778\n",
        "1.808081           1.321046   0.740063  0.833083  0.616534\n",
        "1.818182           1.307271   0.726639  0.835599  0.607179\n",
        "1.828283           1.293240   0.713157  0.838119  0.597710\n",
        "1.838384           1.278940   0.699610  0.840642  0.588122\n",
        "1.848485           1.264360   0.685996  0.843170  0.578411\n",
        "1.858586           1.249486   0.672308  0.845701  0.568572\n",
        "1.868687           1.234306   0.658542  0.848237  0.558600\n",
        "1.878788           1.218804   0.644692  0.850778  0.548489\n",
        "1.888889           1.202965   0.630751  0.853324  0.538235\n",
        "1.898990           1.186770   0.616714  0.855875  0.527830\n",
        "1.909091           1.170201   0.602573  0.858432  0.517268\n",
        "1.919192           1.153236   0.588320  0.860995  0.506541\n",
        "1.929293           1.135854   0.573948  0.863565  0.495641\n",
        "1.939394           1.118029   0.559447  0.866141  0.484560\n",
        "1.949495           1.099734   0.544807  0.868725  0.473288\n",
        "1.959596           1.080937   0.530019  0.871317  0.461814\n",
        "1.969697           1.061606   0.515068  0.873917  0.450127\n",
        "1.979798           1.041702   0.499944  0.876526  0.438214\n",
        "1.989899           1.021183   0.484630  0.879145  0.426060\n",
        "2.000000           1.000000   0.469110  0.881774  0.413649\n",
        "\n",
        "[100 rows x 4 columns]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can do all the cool things that one can do with Pandas..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solution['firm size'].plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x111c78a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109f3b190>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Example:\n",
      "\n",
      "Multiplicative separability with log-normal worker skill and firm productivity distributions..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define some workers skill\n",
      "mu1, sigma1 = sym.var('mu1, sigma1')\n",
      "skill_cdf = 0.5 + 0.5 * sym.erf((sym.log(x) - mu1) / sym.sqrt(2 * sigma1**2))\n",
      "skill_params = {'mu1': 0.0, 'sigma1': 1.0}\n",
      "skill_bounds = [1e-3, 5e1]\n",
      "\n",
      "workers = inputs.Input(var=x,\n",
      "                       cdf=skill_cdf,\n",
      "                       params=skill_params,\n",
      "                       bounds=skill_bounds,\n",
      "                       )\n",
      "\n",
      "# define some firms\n",
      "mu2, sigma2 = sym.var('mu2, sigma2')\n",
      "productivity_cdf = 0.5 + 0.5 * sym.erf((sym.log(y) - mu2) / sym.sqrt(2 * sigma2**2))\n",
      "productivity_params = {'mu2': 0.0, 'sigma2': 1.0}\n",
      "productivity_bounds = [1e-3, 5e1]\n",
      "\n",
      "firms = inputs.Input(var=y,\n",
      "                     cdf=productivity_cdf,\n",
      "                     params=productivity_params,\n",
      "                     bounds=productivity_bounds,\n",
      "                     )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Positive assortative matching"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define symbolic expression for CES between x and y\n",
      "omega_A, sigma_A = sym.var('omega_A, sigma_A')\n",
      "A = ((omega_A * x**((sigma_A - 1) / sigma_A) + \n",
      "     (1 - omega_A) * y**((sigma_A - 1) / sigma_A))**(sigma_A / (sigma_A - 1))) \n",
      "\n",
      "# define symbolic expression for Cobb-Douglas between l and r\n",
      "l, r, omega_B, sigma_B = sym.var('l, r, omega_B, sigma_B')\n",
      "B = l**omega_B * r**(1 - omega_B)\n",
      "\n",
      "F = A * B\n",
      "\n",
      "F_params = {'omega_A':0.5, 'omega_B':0.45, 'sigma_A':0.5, 'sigma_B':1.0}\n",
      "\n",
      "model = models.Model('positive',\n",
      "                     workers=workers,\n",
      "                     firms=firms,\n",
      "                     production=F,\n",
      "                     params=F_params)\n",
      "\n",
      "solver = solvers.ShootingSolver(model=model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solve(5e-1, tol=1e-6, number_knots=5000, integrator='lsoda',\n",
      "             with_jacobian=True, atol=1e-12, rtol=1e-9)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exhausted firms: initial guess of 0.25 for firm size is too low.\n",
        "Exhausted firms: initial guess of 0.375 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/drpugh/anaconda/lib/python2.7/site-packages/scipy/integrate/_ode.py:1127: UserWarning: lsoda: Excess work done on this call (perhaps wrong Dfun type).\n",
        "  'Unexpected istate=%s' % istate))\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>firm productivity</th>\n",
        "      <th>firm size</th>\n",
        "      <th>wage</th>\n",
        "      <th>profit</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>x</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0.001000 </th>\n",
        "      <td>  0.001067</td>\n",
        "      <td> 3.549875</td>\n",
        "      <td>  0.000232</td>\n",
        "      <td>  0.001005</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.051049 </th>\n",
        "      <td>  0.043892</td>\n",
        "      <td> 1.585344</td>\n",
        "      <td>  0.016516</td>\n",
        "      <td>  0.032003</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.101098 </th>\n",
        "      <td>  0.086925</td>\n",
        "      <td> 1.429779</td>\n",
        "      <td>  0.034621</td>\n",
        "      <td>  0.060501</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.151147 </th>\n",
        "      <td>  0.129960</td>\n",
        "      <td> 1.345459</td>\n",
        "      <td>  0.053521</td>\n",
        "      <td>  0.088013</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.201196 </th>\n",
        "      <td>  0.172995</td>\n",
        "      <td> 1.288533</td>\n",
        "      <td>  0.072958</td>\n",
        "      <td>  0.114900</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.251245 </th>\n",
        "      <td>  0.216032</td>\n",
        "      <td> 1.245988</td>\n",
        "      <td>  0.092806</td>\n",
        "      <td>  0.141332</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.301294 </th>\n",
        "      <td>  0.259069</td>\n",
        "      <td> 1.212244</td>\n",
        "      <td>  0.112987</td>\n",
        "      <td>  0.167405</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.351343 </th>\n",
        "      <td>  0.302107</td>\n",
        "      <td> 1.184414</td>\n",
        "      <td>  0.133450</td>\n",
        "      <td>  0.193185</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.401392 </th>\n",
        "      <td>  0.345146</td>\n",
        "      <td> 1.160814</td>\n",
        "      <td>  0.154158</td>\n",
        "      <td>  0.218716</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.451441 </th>\n",
        "      <td>  0.388186</td>\n",
        "      <td> 1.140382</td>\n",
        "      <td>  0.175083</td>\n",
        "      <td>  0.244030</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.501490 </th>\n",
        "      <td>  0.431227</td>\n",
        "      <td> 1.122406</td>\n",
        "      <td>  0.196201</td>\n",
        "      <td>  0.269155</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.551540 </th>\n",
        "      <td>  0.474268</td>\n",
        "      <td> 1.106387</td>\n",
        "      <td>  0.217496</td>\n",
        "      <td>  0.294109</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.601589 </th>\n",
        "      <td>  0.517310</td>\n",
        "      <td> 1.091959</td>\n",
        "      <td>  0.238953</td>\n",
        "      <td>  0.318910</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.651638 </th>\n",
        "      <td>  0.560353</td>\n",
        "      <td> 1.078853</td>\n",
        "      <td>  0.260558</td>\n",
        "      <td>  0.343572</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.701687 </th>\n",
        "      <td>  0.603397</td>\n",
        "      <td> 1.066857</td>\n",
        "      <td>  0.282303</td>\n",
        "      <td>  0.368105</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.751736 </th>\n",
        "      <td>  0.646441</td>\n",
        "      <td> 1.055808</td>\n",
        "      <td>  0.304177</td>\n",
        "      <td>  0.392519</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.801785 </th>\n",
        "      <td>  0.689487</td>\n",
        "      <td> 1.045576</td>\n",
        "      <td>  0.326172</td>\n",
        "      <td>  0.416824</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.851834 </th>\n",
        "      <td>  0.732533</td>\n",
        "      <td> 1.036054</td>\n",
        "      <td>  0.348282</td>\n",
        "      <td>  0.441026</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.901883 </th>\n",
        "      <td>  0.775580</td>\n",
        "      <td> 1.027156</td>\n",
        "      <td>  0.370501</td>\n",
        "      <td>  0.465131</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>0.951932 </th>\n",
        "      <td>  0.818627</td>\n",
        "      <td> 1.018809</td>\n",
        "      <td>  0.392822</td>\n",
        "      <td>  0.489146</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.001981 </th>\n",
        "      <td>  0.861676</td>\n",
        "      <td> 1.010952</td>\n",
        "      <td>  0.415241</td>\n",
        "      <td>  0.513076</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.052030 </th>\n",
        "      <td>  0.904725</td>\n",
        "      <td> 1.003536</td>\n",
        "      <td>  0.437754</td>\n",
        "      <td>  0.536924</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.102079 </th>\n",
        "      <td>  0.947775</td>\n",
        "      <td> 0.996515</td>\n",
        "      <td>  0.460356</td>\n",
        "      <td>  0.560696</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.152128 </th>\n",
        "      <td>  0.990826</td>\n",
        "      <td> 0.989852</td>\n",
        "      <td>  0.483043</td>\n",
        "      <td>  0.584395</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.202177 </th>\n",
        "      <td>  1.033878</td>\n",
        "      <td> 0.983515</td>\n",
        "      <td>  0.505813</td>\n",
        "      <td>  0.608025</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.252226 </th>\n",
        "      <td>  1.076930</td>\n",
        "      <td> 0.977474</td>\n",
        "      <td>  0.528662</td>\n",
        "      <td>  0.631588</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.302275 </th>\n",
        "      <td>  1.119983</td>\n",
        "      <td> 0.971705</td>\n",
        "      <td>  0.551587</td>\n",
        "      <td>  0.655087</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.352324 </th>\n",
        "      <td>  1.163038</td>\n",
        "      <td> 0.966186</td>\n",
        "      <td>  0.574586</td>\n",
        "      <td>  0.678525</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.402373 </th>\n",
        "      <td>  1.206093</td>\n",
        "      <td> 0.960898</td>\n",
        "      <td>  0.597655</td>\n",
        "      <td>  0.701905</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1.452422 </th>\n",
        "      <td>  1.249148</td>\n",
        "      <td> 0.955823</td>\n",
        "      <td>  0.620793</td>\n",
        "      <td>  0.725228</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.548578</th>\n",
        "      <td> 47.782881</td>\n",
        "      <td> 0.626701</td>\n",
        "      <td> 28.025228</td>\n",
        "      <td> 21.466424</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.598627</th>\n",
        "      <td> 47.856867</td>\n",
        "      <td> 0.626869</td>\n",
        "      <td> 28.057248</td>\n",
        "      <td> 21.496718</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.648676</th>\n",
        "      <td> 47.931017</td>\n",
        "      <td> 0.627039</td>\n",
        "      <td> 28.089273</td>\n",
        "      <td> 21.527071</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.698725</th>\n",
        "      <td> 48.005333</td>\n",
        "      <td> 0.627209</td>\n",
        "      <td> 28.121305</td>\n",
        "      <td> 21.557486</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.748774</th>\n",
        "      <td> 48.079815</td>\n",
        "      <td> 0.627381</td>\n",
        "      <td> 28.153343</td>\n",
        "      <td> 21.587963</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.798823</th>\n",
        "      <td> 48.154466</td>\n",
        "      <td> 0.627554</td>\n",
        "      <td> 28.185387</td>\n",
        "      <td> 21.618502</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.848872</th>\n",
        "      <td> 48.229287</td>\n",
        "      <td> 0.627729</td>\n",
        "      <td> 28.217437</td>\n",
        "      <td> 21.649103</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.898921</th>\n",
        "      <td> 48.304279</td>\n",
        "      <td> 0.627905</td>\n",
        "      <td> 28.249494</td>\n",
        "      <td> 21.679767</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.948970</th>\n",
        "      <td> 48.379445</td>\n",
        "      <td> 0.628082</td>\n",
        "      <td> 28.281558</td>\n",
        "      <td> 21.710495</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48.999019</th>\n",
        "      <td> 48.454784</td>\n",
        "      <td> 0.628260</td>\n",
        "      <td> 28.313628</td>\n",
        "      <td> 21.741288</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.049068</th>\n",
        "      <td> 48.530300</td>\n",
        "      <td> 0.628440</td>\n",
        "      <td> 28.345705</td>\n",
        "      <td> 21.772145</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.099117</th>\n",
        "      <td> 48.605993</td>\n",
        "      <td> 0.628621</td>\n",
        "      <td> 28.377788</td>\n",
        "      <td> 21.803067</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.149166</th>\n",
        "      <td> 48.681864</td>\n",
        "      <td> 0.628803</td>\n",
        "      <td> 28.409878</td>\n",
        "      <td> 21.834055</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.199215</th>\n",
        "      <td> 48.757917</td>\n",
        "      <td> 0.628987</td>\n",
        "      <td> 28.441975</td>\n",
        "      <td> 21.865110</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.249264</th>\n",
        "      <td> 48.834153</td>\n",
        "      <td> 0.629172</td>\n",
        "      <td> 28.474079</td>\n",
        "      <td> 21.896232</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.299313</th>\n",
        "      <td> 48.910573</td>\n",
        "      <td> 0.629359</td>\n",
        "      <td> 28.506189</td>\n",
        "      <td> 21.927422</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.349362</th>\n",
        "      <td> 48.987179</td>\n",
        "      <td> 0.629547</td>\n",
        "      <td> 28.538307</td>\n",
        "      <td> 21.958680</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.399411</th>\n",
        "      <td> 49.063971</td>\n",
        "      <td> 0.629736</td>\n",
        "      <td> 28.570432</td>\n",
        "      <td> 21.990006</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.449460</th>\n",
        "      <td> 49.140903</td>\n",
        "      <td> 0.629926</td>\n",
        "      <td> 28.602557</td>\n",
        "      <td> 22.021386</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.499510</th>\n",
        "      <td> 49.218053</td>\n",
        "      <td> 0.630118</td>\n",
        "      <td> 28.634693</td>\n",
        "      <td> 22.052845</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.549559</th>\n",
        "      <td> 49.295391</td>\n",
        "      <td> 0.630311</td>\n",
        "      <td> 28.666836</td>\n",
        "      <td> 22.084373</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.599608</th>\n",
        "      <td> 49.372918</td>\n",
        "      <td> 0.630506</td>\n",
        "      <td> 28.698986</td>\n",
        "      <td> 22.115971</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.649657</th>\n",
        "      <td> 49.450632</td>\n",
        "      <td> 0.630702</td>\n",
        "      <td> 28.731141</td>\n",
        "      <td> 22.147637</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.699706</th>\n",
        "      <td> 49.528536</td>\n",
        "      <td> 0.630900</td>\n",
        "      <td> 28.763304</td>\n",
        "      <td> 22.179374</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.749755</th>\n",
        "      <td> 49.606634</td>\n",
        "      <td> 0.631099</td>\n",
        "      <td> 28.795473</td>\n",
        "      <td> 22.211182</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.799804</th>\n",
        "      <td> 49.684927</td>\n",
        "      <td> 0.631299</td>\n",
        "      <td> 28.827648</td>\n",
        "      <td> 22.243062</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.849853</th>\n",
        "      <td> 49.763416</td>\n",
        "      <td> 0.631501</td>\n",
        "      <td> 28.859831</td>\n",
        "      <td> 22.275013</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.899902</th>\n",
        "      <td> 49.842100</td>\n",
        "      <td> 0.631704</td>\n",
        "      <td> 28.892020</td>\n",
        "      <td> 22.307037</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49.949951</th>\n",
        "      <td> 49.920980</td>\n",
        "      <td> 0.631909</td>\n",
        "      <td> 28.924216</td>\n",
        "      <td> 22.339133</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>50.000000</th>\n",
        "      <td> 50.000000</td>\n",
        "      <td> 0.632115</td>\n",
        "      <td> 28.956412</td>\n",
        "      <td> 22.371282</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>1000 rows \u00d7 4 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "           firm productivity  firm size       wage     profit\n",
        "x                                                            \n",
        "0.001000            0.001067   3.549875   0.000232   0.001005\n",
        "0.051049            0.043892   1.585344   0.016516   0.032003\n",
        "0.101098            0.086925   1.429779   0.034621   0.060501\n",
        "0.151147            0.129960   1.345459   0.053521   0.088013\n",
        "0.201196            0.172995   1.288533   0.072958   0.114900\n",
        "0.251245            0.216032   1.245988   0.092806   0.141332\n",
        "0.301294            0.259069   1.212244   0.112987   0.167405\n",
        "0.351343            0.302107   1.184414   0.133450   0.193185\n",
        "0.401392            0.345146   1.160814   0.154158   0.218716\n",
        "0.451441            0.388186   1.140382   0.175083   0.244030\n",
        "0.501490            0.431227   1.122406   0.196201   0.269155\n",
        "0.551540            0.474268   1.106387   0.217496   0.294109\n",
        "0.601589            0.517310   1.091959   0.238953   0.318910\n",
        "0.651638            0.560353   1.078853   0.260558   0.343572\n",
        "0.701687            0.603397   1.066857   0.282303   0.368105\n",
        "0.751736            0.646441   1.055808   0.304177   0.392519\n",
        "0.801785            0.689487   1.045576   0.326172   0.416824\n",
        "0.851834            0.732533   1.036054   0.348282   0.441026\n",
        "0.901883            0.775580   1.027156   0.370501   0.465131\n",
        "0.951932            0.818627   1.018809   0.392822   0.489146\n",
        "1.001981            0.861676   1.010952   0.415241   0.513076\n",
        "1.052030            0.904725   1.003536   0.437754   0.536924\n",
        "1.102079            0.947775   0.996515   0.460356   0.560696\n",
        "1.152128            0.990826   0.989852   0.483043   0.584395\n",
        "1.202177            1.033878   0.983515   0.505813   0.608025\n",
        "1.252226            1.076930   0.977474   0.528662   0.631588\n",
        "1.302275            1.119983   0.971705   0.551587   0.655087\n",
        "1.352324            1.163038   0.966186   0.574586   0.678525\n",
        "1.402373            1.206093   0.960898   0.597655   0.701905\n",
        "1.452422            1.249148   0.955823   0.620793   0.725228\n",
        "...                      ...        ...        ...        ...\n",
        "48.548578          47.782881   0.626701  28.025228  21.466424\n",
        "48.598627          47.856867   0.626869  28.057248  21.496718\n",
        "48.648676          47.931017   0.627039  28.089273  21.527071\n",
        "48.698725          48.005333   0.627209  28.121305  21.557486\n",
        "48.748774          48.079815   0.627381  28.153343  21.587963\n",
        "48.798823          48.154466   0.627554  28.185387  21.618502\n",
        "48.848872          48.229287   0.627729  28.217437  21.649103\n",
        "48.898921          48.304279   0.627905  28.249494  21.679767\n",
        "48.948970          48.379445   0.628082  28.281558  21.710495\n",
        "48.999019          48.454784   0.628260  28.313628  21.741288\n",
        "49.049068          48.530300   0.628440  28.345705  21.772145\n",
        "49.099117          48.605993   0.628621  28.377788  21.803067\n",
        "49.149166          48.681864   0.628803  28.409878  21.834055\n",
        "49.199215          48.757917   0.628987  28.441975  21.865110\n",
        "49.249264          48.834153   0.629172  28.474079  21.896232\n",
        "49.299313          48.910573   0.629359  28.506189  21.927422\n",
        "49.349362          48.987179   0.629547  28.538307  21.958680\n",
        "49.399411          49.063971   0.629736  28.570432  21.990006\n",
        "49.449460          49.140903   0.629926  28.602557  22.021386\n",
        "49.499510          49.218053   0.630118  28.634693  22.052845\n",
        "49.549559          49.295391   0.630311  28.666836  22.084373\n",
        "49.599608          49.372918   0.630506  28.698986  22.115971\n",
        "49.649657          49.450632   0.630702  28.731141  22.147637\n",
        "49.699706          49.528536   0.630900  28.763304  22.179374\n",
        "49.749755          49.606634   0.631099  28.795473  22.211182\n",
        "49.799804          49.684927   0.631299  28.827648  22.243062\n",
        "49.849853          49.763416   0.631501  28.859831  22.275013\n",
        "49.899902          49.842100   0.631704  28.892020  22.307037\n",
        "49.949951          49.920980   0.631909  28.924216  22.339133\n",
        "50.000000          50.000000   0.632115  28.956412  22.371282\n",
        "\n",
        "[1000 rows x 4 columns]"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solution['firm size'].plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x113f3a490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEPCAYAAAC9RFRvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1141375d0>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Negative assortative matching"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "F_params = {'omega_A':0.5, 'omega_B':0.45, 'sigma_A':1.5, 'sigma_B':1.0}\n",
      "\n",
      "model = models.Model('negative',\n",
      "                     workers=workers,\n",
      "                     firms=firms,\n",
      "                     production=F,\n",
      "                     params=F_params)\n",
      "\n",
      "solver = solvers.ShootingSolver(model=model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 197
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solve(1e3, tol=1e-6, number_knots=1000, atol=1e-12, rtol=1e-9)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exhausted firms: initial guess of 500.0 for firm size is too low.\n",
        "Exhausted workers: initial guess of 750.0 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 625.0 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 687.5 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 718.75 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 703.125 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 695.3125 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 699.21875 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.265625 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 698.2421875 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.75390625 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.509765625 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.631835938 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.570800781 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.540283203 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.525024414 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.51739502 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.521209717 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.519302368 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520256042 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.52073288 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520971298 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520852089 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520911694 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520881891 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.52086699 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520874441 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520870715 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520872578 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520873509 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520873044 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520873277 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.52087316 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520873218 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: initial guess of 697.520873247 for firm size is too low."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873262 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873269 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520873273 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873271 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873272 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873272 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted workers: initial guess of 697.520873273 for firm size is too high!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873273 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Exhausted firms: Initial guess of 697.520873273 for firm size was too low!"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Success! All workers and firms are matched"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 198
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 199,
       "text": [
        "array([[  1.00000000e-04,   5.00000000e+01,   6.97520873e+02,\n",
        "          7.96982563e-02,   6.79447968e+01],\n",
        "       [  1.00200000e-01,   4.38421936e+01,   2.76462641e+02,\n",
        "          1.62305818e-01,   5.48429383e+01],\n",
        "       [  2.00300000e-01,   3.01915720e+01,   1.25086665e+02,\n",
        "          1.99932868e-01,   3.05664771e+01],\n",
        "       ..., \n",
        "       [  9.97998000e+01,   2.00562063e-02,   4.40863126e-04,\n",
        "          4.66712075e+02,   2.51479732e-01],\n",
        "       [  9.98999000e+01,   1.70657087e-02,   4.33023425e-04,\n",
        "          4.67696609e+02,   2.47528829e-01],\n",
        "       [  1.00000000e+02,   9.99753364e-04,   3.61574332e-04,\n",
        "          4.68687387e+02,   2.07124291e-01]])"
       ]
      }
     ],
     "prompt_number": 199
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(solver.solution[:, 0], solver.solution[:, 2])\n",
      "plt.xscale('log')\n",
      "plt.yscale('log')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Nz6+sv7lKZviWxN1XFJaGKPZ/6wIBmFnHukDXAncXnnNl4XfnAm94odRp093y\nmdko4EygN7CsVvGWq4Ly/TUwGtjHzA519/9Xs6BLVEHZ+gFXA8PNbKa7z65Z0GUqp4zALcCcQh9b\nJubslFM+M9tERj63DmV+fidRxt9c1Sv/HSj+eglhZvDIrp7o7nfVJKJk7bJ87r4cWF7LoBJUSvlu\nIVQmWVNK2bYAF9UyqIR1WUZ3fxc4P05IidpR+bL+uXXYUfkuAX5Y6kVijfZJZSs+QSpfduW5bB3y\nXkaVrwSxKv+8rwuk8mVXnsvWIe9lVPlKEKvyz/u6QCpfduW5bB3yXkaVrxQ16K1eBLwGfEDIU51X\nOD8OeJnQa31F7F51la/+ypfnstVLGVW+7pcv1ZO8RESkOlK9vIOIiFSHKn8RkTqkyl9EpA6p8hcR\nqUOq/EVE6pAqfxGROqTKX0SkDqnyFxGpQ/8LhoHNhiZrGToAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10de21b10>"
       ]
      }
     ],
     "prompt_number": 200
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Example:\n",
      "\n",
      "More sophisticated production function that is not multiplicatively separable..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define some workers skill\n",
      "x, mu1, sigma1 = sym.var('x, mu1, sigma1')\n",
      "skill_cdf = 0.5 + 0.5 * sym.erf((sym.log(x) - mu1) / sym.sqrt(2 * sigma1**2))\n",
      "skill_params = {'mu1': 0.0, 'sigma1': 1e0}\n",
      "skill_bounds = [1e-3, 50.0]\n",
      "\n",
      "workers = inputs.Input(var=x,\n",
      "                       cdf=skill_cdf,\n",
      "                       params=skill_params,\n",
      "                       bounds=skill_bounds,\n",
      "                       )\n",
      "\n",
      "# define some firms\n",
      "y, mu2, sigma2 = sym.var('y, mu2, sigma2')\n",
      "productivity_cdf = 0.5 + 0.5 * sym.erf((sym.log(y) - mu2) / sym.sqrt(2 * sigma2**2))\n",
      "productivity_params = {'mu2': 0.0, 'sigma2': 1e0}\n",
      "productivity_bounds = [1e-3, 50.0]\n",
      "\n",
      "firms = inputs.Input(var=y,\n",
      "                     cdf=productivity_cdf,\n",
      "                     params=productivity_params,\n",
      "                     bounds=productivity_bounds,\n",
      "                     )\n",
      "\n",
      "# define some valid model params\n",
      "F_params = {'eta': 0.89, 'kappa': 1.0, 'gamma': 0.54, 'rho': 0.24, 'A': 1.0, 'k': 1.0}\n",
      "\n",
      "# define a valid production function\n",
      "A, k, kappa, eta, rho, l, gamma, r = sym.var('A, k, kappa, eta, rho, l, gamma, r')\n",
      "F = r * A * kappa * eta * ((k * x)**rho + (1 - eta) * (y * (l / r))**rho)**(gamma / rho)\n",
      "\n",
      "model = models.Model('negative',\n",
      "                     workers=workers,\n",
      "                     firms=firms,\n",
      "                     production=F,\n",
      "                     params=F_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver = solvers.ShootingSolver(model=model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.solve(1e0, tol=1e-4, number_knots=10000, integrator='vode',\n",
      "             atol=1e-9, rtol=1e-6, check=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exhausted firms: initial guess of 0.5 for firm size is too low.\n"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver.integrator.successful()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 110,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver._solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 111,
       "text": [
        "array([[  1.00000000e-03,   5.00000000e+01,   7.50000000e-01,\n",
        "          6.25292214e-02,   1.02985470e-01],\n",
        "       [  6.00040004e-03,   4.91355141e+01,   2.93698995e-02,\n",
        "          6.50895813e-01,   1.02614135e-01],\n",
        "       [  1.10008001e-02,   1.87728995e+01,   6.10881218e-04,\n",
        "          8.73207163e+00,   9.34543423e-02],\n",
        "       [  1.34286568e-02,   2.61227847e+06,   1.98653860e+04,\n",
        "          1.04151668e-01,   1.79568793e+03]])"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "integrat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "50.0"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}