{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The use of axes\n",
    "\n",
    "Axes are a great option to add at the scenario declaration in order to make a variable v evolves in a given interval.\n",
    "\n",
    "We'll show this opportunity with the illustration of the evolution of average rate and marginal rate of the French Income Tax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initialisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We import essential modules and initialize the tax and benefit system\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from openfisca_france import FranceTaxBenefitSystem   \n",
    "tax_benefit_system = FranceTaxBenefitSystem()  # Create an instance of French Tax and Benefit system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Income Tax Concavity : a progressive system ?\n",
    "\n",
    "Let's observe how to declare a scenario  with an income evolving between 0 euros and 100000 euros per year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scenario = tax_benefit_system.new_scenario()\n",
    "\n",
    "scenario.init_single_entity(\n",
    "    \n",
    "    # Axe declaration\n",
    "    axes = [\n",
    "        dict(                       #  in a dictionary\n",
    "            count = 100,            # 'count' : indicates the number of step\n",
    "            min = 0,\n",
    "            max = 100000,\n",
    "            name = 'salaire_de_base', # the variable you want to make evolve\n",
    "            ),\n",
    "        ],\n",
    "    \n",
    "    \n",
    "    period = 2014,\n",
    "     parent1 = dict(\n",
    "        date_naissance = '1980-01-01',\n",
    "         )\n",
    "    )\n",
    "\n",
    "simulation = scenario.new_simulation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([     0.     ,   1010.10114,   2020.2023 ,   3030.3027 ,\n",
       "         4040.4045 ,   5050.5054 ,   6060.6055 ,   7070.707  ,\n",
       "         8080.809  ,   9090.909  ,  10101.011  ,  11111.11   ,\n",
       "        12121.211  ,  13131.315  ,  14141.414  ,  15151.515  ,\n",
       "        16161.618  ,  17171.717  ,  18181.818  ,  19191.918  ,\n",
       "        20202.021  ,  21212.121  ,  22222.22   ,  23232.326  ,\n",
       "        24242.422  ,  25252.525  ,  26262.63   ,  27272.725  ,\n",
       "        28282.828  ,  29292.932  ,  30303.03   ,  31313.13   ,\n",
       "        32323.236  ,  33333.332  ,  34343.434  ,  35353.54   ,\n",
       "        36363.637  ,  37373.74   ,  38383.836  ,  39393.938  ,\n",
       "        40404.043  ,  41414.14   ,  42424.242  ,  43434.344  ,\n",
       "        44444.44   ,  45454.547  ,  46464.652  ,  47474.75   ,\n",
       "        48484.844  ,  49494.94   ,  50505.05   ,  51515.152  ,\n",
       "        52525.26   ,  53535.363  ,  54545.45   ,  55555.55   ,\n",
       "        56565.656  ,  57575.76   ,  58585.863  ,  59595.953  ,\n",
       "        60606.06   ,  61616.16   ,  62626.26   ,  63636.37   ,\n",
       "        64646.473  ,  65656.555  ,  66666.664  ,  67676.766  ,\n",
       "        68686.87   ,  69696.98   ,  70707.08   ,  71717.164  ,\n",
       "        72727.27   ,  73737.375  ,  74747.48   ,  75757.586  ,\n",
       "        76767.67   ,  77777.78   ,  78787.875  ,  79797.97   ,\n",
       "        80808.086  ,  81818.164  ,  82828.28   ,  83838.38   ,\n",
       "        84848.484  ,  85858.586  ,  86868.69   ,  87878.805  ,\n",
       "        88888.88   ,  89899.     ,  90909.09   ,  91919.19   ,\n",
       "        92929.305  ,  93939.38   ,  94949.5    ,  95959.59   ,\n",
       "        96969.69   ,  97979.805  ,  98989.88   , 100000.01   ],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulation.calculate_add('salaire_de_base', 2014)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "income_tax = - simulation.calculate('irpp', 2014)\n",
    "gross_wage = simulation.calculate_add('salaire_de_base', 2014)\n",
    "taxable_income = simulation.calculate_add('salaire_imposable', 2014)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,u'Gross Wage')"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb16ac41d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gross_wage,income_tax)\n",
    "plt.ylabel(u\"Tax Income\")\n",
    "plt.xlabel(u\"Gross Wage\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NB** : The Income Tax is flat in opposite to common opinion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Average rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   -0.         -0.         -0.         -0.         -0.         -0.\n",
      "    -0.         -0.         -0.         -0.         -0.         -0.\n",
      "    -0.         -0.         -0.         -0.         -0.         -0.\n",
      "    -0.         66.42151   272.37683   478.34143   684.29895   890.5364\n",
      "  1096.4983   1218.7299   1321.7083   1424.827    1527.8077   1630.7878\n",
      "  1733.7666   1836.8859   1939.8651   2042.8439   2145.8242   2248.9458\n",
      "  2351.9229   2528.8452   2754.0625   2979.5876   3205.1072   3430.3289\n",
      "  3655.8538   3881.073    4106.5933   4331.8145   4557.34     4782.5566\n",
      "  5008.0815   5233.305    5458.83     5684.051    5909.5723   6134.7935\n",
      "  6360.315    6585.535    6811.0566   7036.2773   7261.8057   7487.3247\n",
      "  7712.5405   7938.068    8163.287    8388.814    8614.031    8839.561\n",
      "  9064.776    9290.299    9515.524    9741.038    9966.265   10191.787\n",
      " 10417.013   10642.528   10867.752   11093.281   11318.499   11544.02\n",
      " 11769.54    11994.767   12220.289   12445.505   12671.029   12896.245\n",
      " 13121.774   13346.995   13572.518   13797.74    14023.261   14248.479\n",
      " 14474.006   14699.231   14924.749   15149.965   15375.492   15600.71\n",
      " 15826.239   16112.037   16419.852   16728.053  ]\n",
      "[     0.        1010.10114   2020.2023    3030.3027    4040.4045\n",
      "   5050.5054    6060.6055    7070.707     8080.809     9090.909\n",
      "  10101.011    11111.11     12121.211    13131.315    14141.414\n",
      "  15151.515    16161.618    17171.717    18181.818    19191.918\n",
      "  20202.021    21212.121    22222.22     23232.326    24242.422\n",
      "  25252.525    26262.63     27272.725    28282.828    29292.932\n",
      "  30303.03     31313.13     32323.236    33333.332    34343.434\n",
      "  35353.54     36363.637    37373.74     38383.836    39393.938\n",
      "  40404.043    41414.14     42424.242    43434.344    44444.44\n",
      "  45454.547    46464.652    47474.75     48484.844    49494.94\n",
      "  50505.05     51515.152    52525.26     53535.363    54545.45\n",
      "  55555.55     56565.656    57575.76     58585.863    59595.953\n",
      "  60606.06     61616.16     62626.26     63636.37     64646.473\n",
      "  65656.555    66666.664    67676.766    68686.87     69696.98\n",
      "  70707.08     71717.164    72727.27     73737.375    74747.48\n",
      "  75757.586    76767.67     77777.78     78787.875    79797.97\n",
      "  80808.086    81818.164    82828.28     83838.38     84848.484\n",
      "  85858.586    86868.69     87878.805    88888.88     89899.\n",
      "  90909.09     91919.19     92929.305    93939.38     94949.5\n",
      "  95959.59     96969.69     97979.805    98989.88    100000.01   ]\n"
     ]
    }
   ],
   "source": [
    "average_rate = income_tax / gross_wage\n",
    "# the 1st value of gross_wage is zero, so there's a warning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,u'Gross Wage')"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb16ac02910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gross_wage, average_rate)\n",
    "plt.ylabel(\"Averate Tax Rate\")\n",
    "plt.xlabel(\"Gross Wage\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Marginal rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "marginal_rate =  (income_tax[:-1] - income_tax[1:]) / (taxable_income[:-1] - taxable_income[1:] ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,u'Gross Wage')"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb16ac02c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(gross_wage[:-1], marginal_rate)\n",
    "plt.ylabel(\"Marginal Tax Rate\")\n",
    "plt.xlabel(\"Gross Wage\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.12595813, 0.26981202)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marginal_rate[25], marginal_rate[90]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the step in the French Tax scale of 14% and 30% (applied after a 10% deduction on the taxable income) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notice :  dedicated fonctions in OpenFisca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Marginal and Average rate exist as functions implemented in OpenFisca. You can apply them on several income concept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from openfisca_core.rates import average_rate, marginal_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0.      ,   -74.434586,  -148.86015 ,  -223.29471 ,\n",
       "        -297.7293  ,  -372.15488 ,  -446.58942 ,  -521.024   ,\n",
       "        -595.4586  ,  -669.8843  ,  -744.3187  ,  -818.7533  ,\n",
       "        -893.17883 ,  -967.61346 , -1042.048   , -1116.4736  ,\n",
       "       -1190.9083  , -1265.3428  , -1339.7686  , -1414.203   ,\n",
       "       -1488.6375  , -1563.072   , -1637.4978  , -1711.9324  ,\n",
       "       -1786.367   , -1860.7925  , -1935.2269  , -2009.6617  ,\n",
       "       -2084.0872  , -2158.5217  , -2232.9565  , -2307.3813  ,\n",
       "       -2381.8167  , -2456.2505  , -2530.6855  , -2605.1108  ,\n",
       "       -2679.5457  , -2753.9802  , -2828.406   , -2902.84    ,\n",
       "       -2977.275   , -3051.7007  , -3126.1353  , -3200.5698  ,\n",
       "       -3275.0044  , -3349.4302  , -3423.8647  , -3498.2988  ,\n",
       "       -3572.724   , -3647.1592  , -3721.5942  , -3796.019   ,\n",
       "       -3870.4539  , -3944.8887  , -4019.3145  , -4093.7483  ,\n",
       "       -4168.183   , -4242.618   , -4317.0435  , -4391.4775  ,\n",
       "       -4465.913   , -4540.339   , -4614.773   , -4689.2065  ,\n",
       "       -4763.6333  , -4838.0674  , -4912.501   , -4986.9272  ,\n",
       "       -5061.3623  , -5135.797   , -5210.2305  , -5284.657   ,\n",
       "       -5359.0913  , -5433.5264  , -5507.951   , -5582.386   ,\n",
       "       -5656.821   , -5731.247   , -5805.68    , -5880.1157  ,\n",
       "       -5954.541   , -6028.975   , -6103.4097  , -6177.8447  ,\n",
       "       -6252.2705  , -6326.7046  , -6401.1396  , -6475.5654  ,\n",
       "       -6550.      , -6624.4346  , -6698.8604  , -6773.295   ,\n",
       "       -6847.7295  , -6922.163   , -6996.589   , -7071.024   ,\n",
       "       -7145.458   , -7219.884   , -7294.3184  , -7368.753   ],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csg = simulation.calculate_add('csg', period = 2014)\n",
    "csg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07369024, 0.07368577, 0.07368726, 0.07368797, 0.07368666,\n",
       "       0.07368726, 0.07368767, 0.07368797, 0.07368726, 0.07368755,\n",
       "       0.07368779, 0.07368726, 0.07368749, 0.07368767, 0.07368726,\n",
       "       0.07368743, 0.07368761, 0.07368726, 0.07368743, 0.07368755,\n",
       "       0.07368767, 0.07368743, 0.07368749, 0.07368767, 0.07368737,\n",
       "       0.07368749, 0.07368761, 0.07368737, 0.07368743, 0.07368755,\n",
       "       0.07368731, 0.07368743, 0.07368749, 0.07368761, 0.07368743,\n",
       "       0.07368749, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n",
       "       0.07368743, 0.07368749, 0.07368755, 0.07368761, 0.07368743,\n",
       "       0.07368749, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n",
       "       0.07368743, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n",
       "       0.07368755, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n",
       "       0.07368749, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n",
       "       0.07368749, 0.07368743, 0.07368749, 0.07368749, 0.07368755,\n",
       "       0.07368749, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n",
       "       0.07368755, 0.07368743, 0.07368749, 0.07368755, 0.07368743,\n",
       "       0.07368749, 0.07368749, 0.07368755, 0.07368749, 0.07368749,\n",
       "       0.07368755, 0.07368743, 0.07368749, 0.07368755, 0.07368743,\n",
       "       0.07368749, 0.07368749, 0.07368755, 0.07368749, 0.07368749,\n",
       "       0.07368755, 0.07368749, 0.07368749, 0.07368755], dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - average_rate(-csg[1:], gross_wage[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb16aa86650>]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb16aa86a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ylim(0,0.1)\n",
    "plt.plot(gross_wage[1:], 1-average_rate(-csg[1:], gross_wage[1:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}