notebooks/Senegal-exercices-solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exploring the senegalese tax-benefit-system with OpenFisca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt  # For graphics\n",
    "%matplotlib inline\n",
    "from openfisca_core import periods\n",
    "\n",
    "from openfisca_senegal import CountryTaxBenefitSystem as SenegalTaxBenefitSystem  # The Senegalese tax-benefits system\n",
    "from openfisca_senegal.scenarios import init_single_entity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The concepts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Tax Benefit System"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "tax_benefit_system = SenegalTaxBenefitSystem()\n",
    "tax_benefit_system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Entities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "tax_benefit_system.entities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "[entity.key for entity in tax_benefit_system.entities]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "[entity.label for entity in tax_benefit_system.entities]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Variables "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "tax_benefit_system.variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "sorted(tax_benefit_system.variables.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import inspect\n",
    "for name, variable in sorted(tax_benefit_system.variables.items()):\n",
    "    print(name)\n",
    "    if not variable.is_input_variable():\n",
    "        formula = variable.get_formula('2017')\n",
    "        source_code = inspect.getsourcelines(formula)[0]\n",
    "        print(''.join(source_code))\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "print(tax_benefit_system.parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "parameters = tax_benefit_system.parameters(2017)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "parameters.prelevements_obligatoires.impots_directs.bareme_impot_progressif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A simple test case scenario"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "scenario = tax_benefit_system.new_scenario()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "init_single_entity(\n",
    "    scenario,\n",
    "    parent1 = {\n",
    "        'salaire': 2800000,\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 1,\n",
    "        },\n",
    "    period = '2017',\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "simulation = scenario.new_simulation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "simulation.calculate('salaire', period = '2017')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "simulation.calculate('impot_revenus', period = '2017')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Application: a simple function to compute the tax gain for having a child"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def tax_gain(salaire = 0, est_marie = False, conjoint_a_des_revenus = False, nombre_enfants = 0):\n",
    "    period = '2017'\n",
    "    parent1_before = {\n",
    "        'salaire': salaire,\n",
    "        'est_marie': est_marie,\n",
    "        'conjoint_a_des_revenus': conjoint_a_des_revenus,\n",
    "        'nombre_enfants': nombre_enfants,\n",
    "        }\n",
    "    simulation_before = init_single_entity(\n",
    "        tax_benefit_system.new_scenario(),\n",
    "        parent1 = parent1_before,\n",
    "        period = period,\n",
    "        ).new_simulation()\n",
    "    parent1_after = parent1_before.copy()\n",
    "    parent1_after['nombre_enfants'] += 1\n",
    "    simulation_after = init_single_entity(\n",
    "        tax_benefit_system.new_scenario(),\n",
    "        parent1 = parent1_after,\n",
    "        period = period,\n",
    "        ).new_simulation()\n",
    "    difference = simulation_after.calculate('impot_revenus', period) - simulation_before.calculate('impot_revenus', period)\n",
    "    return -difference\n",
    "                                                                                            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "tax_gain(salaire = 2800000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "tax_gain(salaire = 2800000, nombre_enfants = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "[tax_gain(salaire = 2800000, nombre_enfants = n) for n in range(8)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n in range(8):\n",
    "    print(\"having \", n, \" children gives a tax gain of \", tax_gain(salaire = 2800000, nombre_enfants = n) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More complex scenario: varying revenue "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "year = 2017\n",
    "simulation = init_single_entity(\n",
    "    tax_benefit_system.new_scenario(),\n",
    "    parent1 = {\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 0,\n",
    "        },\n",
    "    period = year,\n",
    "    axes = [[\n",
    "        {\n",
    "            'count': 100,\n",
    "            'min': 0,\n",
    "            'max': 15e6,\n",
    "            'name': 'salaire',\n",
    "            }\n",
    "        ]],\n",
    "    ).new_simulation()\n",
    "\n",
    "\n",
    "salaire = simulation.calculate('salaire', period = year)\n",
    "reduction_impots_pour_charge_famille = simulation.calculate('reduction_impots_pour_charge_famille', period = year)\n",
    "impot_avant_reduction_famille = simulation.calculate('impot_avant_reduction_famille', period = year)\n",
    "impot_revenus = simulation.calculate('impot_revenus', period = year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(salaire, impot_avant_reduction_famille, label='avant réduction famille')\n",
    "plt.plot(salaire, reduction_impots_pour_charge_famille, label='réduction famille')\n",
    "plt.plot(salaire, impot_revenus, label='impôt revenus')\n",
    "plt.xlabel('Salaire')\n",
    "plt.legend()\n",
    "plt.title('0 enfants', fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Application: by how much the tax gain for having a child varies with revenue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def tax_gain_varying_revenue(max_salaire = 0, est_marie = False, conjoint_a_des_revenus = False, \n",
    "                             nombre_enfants = 0, count = 100):\n",
    "    period = '2017'\n",
    "    parent1_before = {\n",
    "        'est_marie': est_marie,\n",
    "        'conjoint_a_des_revenus': conjoint_a_des_revenus,\n",
    "        'nombre_enfants': nombre_enfants,\n",
    "        }\n",
    "    axes = [[\n",
    "            {\n",
    "                'count': count,\n",
    "                'min': 0,\n",
    "                'max': max_salaire,\n",
    "                'name': 'salaire',\n",
    "                }\n",
    "            ]]\n",
    "    simulation_before = init_single_entity(\n",
    "        tax_benefit_system.new_scenario(),\n",
    "        parent1 = parent1_before,\n",
    "        axes = axes,\n",
    "        period = period,\n",
    "        ).new_simulation()\n",
    "    parent1_after = parent1_before.copy()\n",
    "    parent1_after['nombre_enfants'] += 1\n",
    "    simulation_after = init_single_entity(\n",
    "        tax_benefit_system.new_scenario(),\n",
    "        parent1 = parent1_after,\n",
    "        axes = axes,\n",
    "        period = period,\n",
    "        ).new_simulation()\n",
    "    difference = simulation_after.calculate('impot_revenus', period) - simulation_before.calculate('impot_revenus', period)\n",
    "    salaire = simulation_after.calculate('salaire', period)\n",
    "    return salaire, -difference\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "salaire, gain = tax_gain_varying_revenue(max_salaire = 15e6, count = 1000)\n",
    "gain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(salaire, gain, label='Gain fiscal')\n",
    "plt.xlabel('Salaire')\n",
    "plt.legend()\n",
    "plt.title('Gain fiscal au 1er enfant', fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "#### Exercice: Write a loop to plot the gain for several children"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "for nombre_enfants in range(5):\n",
    "    salaire, gain = tax_gain_varying_revenue(max_salaire=15e6, nombre_enfants = nombre_enfants)\n",
    "    plt.plot(salaire, gain, label=f\"Enfant de rang {nombre_enfants}\")\n",
    "\n",
    "plt.xlabel('Salaire')\n",
    "plt.legend()\n",
    "plt.title(u\"Gain fiscal selon le rang de l'enfant\", fontsize=20)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Tax rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Average tax rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "simulation = init_single_entity(\n",
    "    tax_benefit_system.new_scenario(),\n",
    "    parent1 = {\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 0,\n",
    "        },\n",
    "    period = year,\n",
    "    axes = [[\n",
    "        {\n",
    "            'count': 100,\n",
    "            'min': 0,\n",
    "            'max': 18e6,\n",
    "            'name': 'salaire',\n",
    "            }\n",
    "        ]],\n",
    "    ).new_simulation()\n",
    "salaire = simulation.calculate('salaire', period = year)\n",
    "impot = simulation.calculate('impot_revenus', period = year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire, impot)\n",
    "plt.ylabel(u\"Impôt sur les revenus\")\n",
    "plt.xlabel(u\"Salaire\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "taux_moyen = impot / salaire  # Average tax rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "taux_moyen = impot / (salaire * (salaire != 0) + (salaire == 0) )  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire, taux_moyen)\n",
    "plt.ylabel(\"Taux moyen\")\n",
    "plt.xlabel(\"Salaire\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Marginal tax rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "(impot[:-1] - impot[1:]) / (salaire[:-1] - salaire[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "taux_marginal =  (impot[:-1] - impot[1:]) / (salaire[:-1] - salaire[1:] )  # We avoid the first point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "len(taux_marginal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire[:-1], taux_marginal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "#### Exercice: how marginal and average tax rate compare at infinity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(salaire, taux_moyen, label = 'average')\n",
    "plt.plot(salaire[:-1], taux_marginal, label = 'marginal')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Add a new variable and use dedicated functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Add a disposable income variable to the tax-benefit-system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from openfisca_core.model_api import *\n",
    "from openfisca_senegal.entities import Person\n",
    "\n",
    "tax_benefit_system = SenegalTaxBenefitSystem()\n",
    "\n",
    "class revenu_disponible(Variable):\n",
    "    definition_period = YEAR\n",
    "    entity = Person\n",
    "    value_type = float\n",
    "\n",
    "    def formula(person, period):\n",
    "        salaire = person('salaire', period)\n",
    "        pension_retraite = person('pension_retraite', period)\n",
    "        impot_revenus = person('impot_revenus', period)\n",
    "        return salaire + pension_retraite - impot_revenus\n",
    "\n",
    "\n",
    "tax_benefit_system.add_variable(revenu_disponible)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "simulation = init_single_entity(\n",
    "    tax_benefit_system.new_scenario(),\n",
    "    parent1 = {\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 0,\n",
    "        },\n",
    "    period = '2017',\n",
    "    axes = [[\n",
    "        {\n",
    "            'count': 1000,\n",
    "            'min': 0,\n",
    "            'max': 50e6,\n",
    "            'name': 'salaire',\n",
    "            }\n",
    "        ]],\n",
    "    ).new_simulation()\n",
    "salaire = simulation.calculate('salaire', period = year)\n",
    "impot_revenus = simulation.calculate('impot_revenus', period = year)\n",
    "revenu_disponible = simulation.calculate('revenu_disponible', period = year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire, salaire, label = 'salaire')\n",
    "plt.plot(salaire, revenu_disponible, label = 'revenu_disponible')\n",
    "plt.plot(salaire, impot_revenus, label = 'impot_revenus')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from openfisca_core.rates import average_rate, marginal_rate\n",
    "plt.plot(salaire[1:], average_rate(revenu_disponible[1:], salaire[1:]))\n",
    "plt.plot(salaire[1:], marginal_rate(revenu_disponible, salaire))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Reforming the tax-benefit system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parametric reform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def modify_parameters(parameters):\n",
    "    parameters.prelevements_obligatoires.impots_directs.bareme_impot_progressif[5].rate.update(\n",
    "        period = period(year), \n",
    "        value = .5\n",
    "        )\n",
    "    return parameters\n",
    "    \n",
    "class tax_the_rich(Reform):\n",
    "    name = u\"Tax last bracket at 50%\"\n",
    "\n",
    "    def apply(self):\n",
    "        self.modify_parameters(modifier_function = modify_parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "reformed_tax_benefit_system = tax_the_rich(tax_benefit_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "simulation = init_single_entity(\n",
    "    reformed_tax_benefit_system.new_scenario(),\n",
    "    parent1 = {\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 0,\n",
    "        },\n",
    "    period = year,\n",
    "    axes = [[\n",
    "        {\n",
    "            'count': 100,\n",
    "            'min': 0,\n",
    "            'max': 18e6,\n",
    "            'name': 'salaire',\n",
    "            }\n",
    "        ]],\n",
    "    ).new_simulation()\n",
    "salaire = simulation.calculate('salaire', period = year)\n",
    "impot = simulation.calculate('impot_revenus', period = year)\n",
    "taux_marginal =  (impot[:-1] - impot[1:]) / (salaire[:-1] - salaire[1:] )  # We avoid the first point\n",
    "plt.plot(salaire[:-1], taux_marginal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Structural Reform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Exercice: add a an amount threshold under which no tax is due"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "seuil = 10000\n",
    "tax_benefit_system = SenegalTaxBenefitSystem()\n",
    "    \n",
    "class impot_revenus(Variable):\n",
    "    def formula(person, period):\n",
    "        impot_avant_reduction_famille = person('impot_avant_reduction_famille', period)\n",
    "        reduction_impots_pour_charge_famille = person('reduction_impots_pour_charge_famille', period)\n",
    "        impot_apres_reduction_famille = impot_avant_reduction_famille - reduction_impots_pour_charge_famille\n",
    "        impot_revenus = max_(0, impot_apres_reduction_famille)\n",
    "        return impot_revenus * (impot_revenus > seuil)            \n",
    "\n",
    "class revenu_disponible(Variable):\n",
    "    definition_period = YEAR\n",
    "    entity = Person\n",
    "    value_type = float\n",
    "\n",
    "    def formula(person, period):\n",
    "        salaire = person('salaire', period)\n",
    "        impot_revenus = person('impot_revenus', period)\n",
    "        return salaire - impot_revenus\n",
    "\n",
    "class structural_reform(Reform):\n",
    "    name = f\"Seuil de non-versement: {seuil}\"\n",
    "\n",
    "    def apply(self):\n",
    "        self.update_variable(impot_revenus)\n",
    "        self.add_variable(revenu_disponible)\n",
    "\n",
    "structurally_reformed_tax_benefit_system = structural_reform(tax_benefit_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def build_structural_reform(seuil = 10000):    \n",
    "    tax_benefit_system = SenegalTaxBenefitSystem()\n",
    "    \n",
    "    class impot_revenus(Variable):\n",
    "        def formula(individu, period):\n",
    "            impot_avant_reduction_famille = individu('impot_avant_reduction_famille', period)\n",
    "            reduction_impots_pour_charge_famille = individu('reduction_impots_pour_charge_famille', period)\n",
    "            impot_apres_reduction_famille = impot_avant_reduction_famille - reduction_impots_pour_charge_famille\n",
    "            impot_revenus = max_(0, impot_apres_reduction_famille)\n",
    "            return impot_revenus * (impot_revenus > seuil)            \n",
    "\n",
    "    class revenu_disponible(Variable):\n",
    "        definition_period = YEAR\n",
    "        entity = Person\n",
    "        value_type = float\n",
    "\n",
    "        def formula(person, period):\n",
    "            salaire = person('salaire', period)\n",
    "            impot_revenus = person('impot_revenus', period)\n",
    "            return salaire - impot_revenus\n",
    "\n",
    "    class structural_reform(Reform):\n",
    "        name = f\"Seuil de non-versement: {seuil}\"\n",
    "\n",
    "        def apply(self):\n",
    "            self.update_variable(impot_revenus)\n",
    "            self.add_variable(revenu_disponible)\n",
    "\n",
    "    return structural_reform(tax_benefit_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "structural_reform = build_structural_reform(seuil = 100000)\n",
    "simulation = init_single_entity(\n",
    "    structural_reform.new_scenario(),\n",
    "    parent1 = {\n",
    "        'est_marie': True,\n",
    "        'conjoint_a_des_revenus': False,\n",
    "        'nombre_enfants': 0,\n",
    "        },\n",
    "    period = '2017',\n",
    "    axes = [[\n",
    "        {\n",
    "            'count': 100,\n",
    "            'min': 0,\n",
    "            'max': 5e6,\n",
    "            'name': 'salaire',\n",
    "            }\n",
    "        ]],\n",
    "    ).new_simulation()\n",
    "salaire = simulation.calculate('salaire', period = year)\n",
    "impot_verse = simulation.calculate('impot_revenus', period = year)\n",
    "revenu_disponible = simulation.calculate('revenu_disponible', period = year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire, impot_verse)\n",
    "plt.ylabel(u\"Impôt sur les revenus\")\n",
    "plt.xlabel(u\"Salaire\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(salaire[1:], average_rate(revenu_disponible[1:], salaire[1:]))\n",
    "plt.plot(salaire[1:], marginal_rate(revenu_disponible, salaire))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}