Separating_Equilibrium.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Initial conditions"
      ],
      "metadata": {
        "id": "WdIcXQizCzbM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Distribution choice (triangular or uniform or normal)?\n",
        "distribution_choice = 'triangular'\n",
        "beta_e = 0.9\n",
        "beta_p = 0.8\n",
        "gamma = 0.97\n",
        "R = 1.05\n",
        "y_lower = 800\n",
        "y_upper = 4800\n",
        "y_3 = 1300\n",
        "y_1 = 1100\n",
        "y_mode = 2800 # triangular\n",
        "y_mean = 1300\n",
        "sigma = 100000 # normal"
      ],
      "metadata": {
        "id": "VD8QeIZWlkcx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "distribution_choice = 'uniform'\n",
        "beta_e = 0.7\n",
        "beta_p = 0.8\n",
        "gamma = 0.95\n",
        "R = 1.18\n",
        "y_lower = 8300\n",
        "y_upper = 14000\n",
        "y_3 = 5200\n",
        "y_1 = 9600\n",
        "y_mode = 28000 # triangular\n",
        "y_mean = 28000 # normal\n",
        "sigma = 1000000 # normal"
      ],
      "metadata": {
        "id": "kEeyoFmTiRCJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Different distributions, PDF, and CDF"
      ],
      "metadata": {
        "id": "P4mAaEG0C3T3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "from scipy.optimize import fsolve\n",
        "import pandas as pd\n",
        "from google.colab import files"
      ],
      "metadata": {
        "id": "Ewo_AL11GsiK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sigma = np.sqrt(sigma) # normal\n",
        "psi = np.log(y_3) - np.log(gamma * y_3)\n",
        "\n",
        "b_upper_e = (1 - gamma * np.exp(- beta_e * psi)) * y_upper\n",
        "b_lower_e = (1 - gamma * np.exp(- beta_e * psi)) * y_lower\n",
        "b_upper_p = (1 - gamma * np.exp(- beta_p * psi)) * y_upper\n",
        "b_lower_p = (1 - gamma * np.exp(- beta_p * psi)) * y_lower\n",
        "\n",
        "print(f\"debt level where default starts for E type = {b_lower_e:.3f}\")\n",
        "print(f\"debt level with always default for E type = {b_upper_e:.3f}\")\n",
        "print(f\"debt level where default starts for P type = {b_lower_p:.3f}\")\n",
        "print(f\"debt level with always default for P type = {b_upper_p:.3f}\")"
      ],
      "metadata": {
        "id": "cQbnIaPBDS79",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d3e24d78-4bba-4407-eb59-f3f81eb2b6da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "debt level where default starts for E type = 44.984\n",
            "debt level with always default for E type = 269.903\n",
            "debt level where default starts for P type = 42.681\n",
            "debt level with always default for P type = 256.083\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "uniform_pdf = lambda y: 1 / (y_upper - y_lower) if y_lower <= y <= y_upper else 0\n",
        "\n",
        "def normal_pdf(y):\n",
        "    normalization_constant = norm.cdf(y_upper, y_mean, sigma) - norm.cdf(y_lower, y_mean, sigma)\n",
        "\n",
        "    if y_lower <= y <= y_upper:\n",
        "        pdf_at_y = norm.pdf(y, y_mean, sigma)\n",
        "        truncated_pdf = pdf_at_y / normalization_constant\n",
        "        return truncated_pdf\n",
        "    else:\n",
        "        return 0\n",
        "\n",
        "def triangular_pdf(y):\n",
        "    if y_lower <= y <= y_mode:\n",
        "        return 2 * (y - y_lower) / ((y_upper - y_lower) * (y_mode - y_lower))\n",
        "    elif y_mode < y <= y_upper:\n",
        "        return 2 * (y_upper - y) / ((y_upper - y_lower) * (y_upper - y_mode))\n",
        "    else:\n",
        "        return 0"
      ],
      "metadata": {
        "id": "semoyiMf0vUj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "c = 0.001\n",
        "def modify_triangular_pdf(y):\n",
        "    # Original triangular PDF without the shift\n",
        "    if y_lower <= y <= y_mode:\n",
        "        original_pdf = 2 * (y - y_lower) / ((y_upper - y_lower) * (y_mode - y_lower))\n",
        "    elif y_mode < y <= y_upper:\n",
        "        original_pdf = 2 * (y_upper - y) / ((y_upper - y_lower) * (y_upper - y_mode))\n",
        "    else:\n",
        "        original_pdf = 0\n",
        "\n",
        "    # Total width of the distribution\n",
        "    width = y_upper - y_lower\n",
        "\n",
        "    # Adjustment needed to maintain total area = 1\n",
        "    # Total area is the area under the original PDF plus the area added by the constant c\n",
        "    area_under_original_pdf = 1  # By definition of PDF\n",
        "    area_added_by_c = c * width\n",
        "    total_area = area_under_original_pdf + area_added_by_c\n",
        "\n",
        "    # Normalization factor to adjust the PDF so that the total area remains 1\n",
        "    normalization_factor = 1 / total_area\n",
        "\n",
        "    # Shifted and normalized PDF\n",
        "    shifted_pdf = (original_pdf + c) * normalization_factor\n",
        "\n",
        "    return shifted_pdf"
      ],
      "metadata": {
        "id": "Rqnb1GOtqTgZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def normal_cdf(y):\n",
        "    cdf_at_y = norm.cdf(y, y_mean, sigma)\n",
        "    cdf_at_y_lower = norm.cdf(y_lower, y_mean, sigma)\n",
        "    cdf_at_y_upper = norm.cdf(y_upper, y_mean, sigma)\n",
        "    if y < y_lower:\n",
        "        return 0\n",
        "    elif y > y_upper:\n",
        "        return 1\n",
        "    else:\n",
        "        return (cdf_at_y - cdf_at_y_lower) / (cdf_at_y_upper - cdf_at_y_lower)\n",
        "\n",
        "def uniform_cdf(y):\n",
        "    if y < y_lower:\n",
        "        return 0\n",
        "    elif y_lower <= y <= y_upper:\n",
        "        return (y - y_lower) / (y_upper - y_lower)\n",
        "    else:\n",
        "        return 1\n",
        "\n",
        "def triangular_cdf(y):\n",
        "    if y < y_lower:\n",
        "        return 0\n",
        "    elif y_lower <= y < y_mode:\n",
        "        return ((y - y_lower)**2) / ((y_upper - y_lower) * (y_mode - y_lower))\n",
        "    elif y_mode <= y <= y_upper:\n",
        "        return 1 - ((y_upper - y)**2) / ((y_upper - y_lower) * (y_upper - y_mode))\n",
        "    else:\n",
        "        return 1"
      ],
      "metadata": {
        "id": "EUG476Ba7wBw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y_values = np.linspace(y_lower - 0.1, y_upper + 0.1, 1000)\n",
        "pdf_values_triangular = [triangular_pdf(y) for y in y_values]\n",
        "pdf_values_triangular_modify = [modify_triangular_pdf(y) for y in y_values]\n",
        "pdf_values_uniform = [uniform_pdf(y) for y in y_values]\n",
        "pdf_values_normal = [normal_pdf(y) for y in y_values]\n",
        "\n",
        "plt.plot(y_values, pdf_values_triangular_modify, label='Triangular with an upward shift')\n",
        "plt.plot(y_values, pdf_values_triangular, label='Triangular')\n",
        "#plt.plot(y_values, pdf_values_uniform, label='Uniform')\n",
        "#plt.plot(y_values, pdf_values_normal, label='Normal')\n",
        "plt.title('PDF of y2 distribution')\n",
        "plt.xlabel('y2')\n",
        "plt.ylim(0,0.0006)\n",
        "plt.ylabel('Probability Density')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "#plt.savefig('pdf.png')\n",
        "plt.show()\n",
        "#files.download('pdf.png')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "KEksx89x9rbk",
        "outputId": "4072f1b5-f30a-44cb-d414-91b51836846a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if distribution_choice == 'triangular':\n",
        "    chosen_cdf = triangular_cdf\n",
        "    chosen_pdf = triangular_pdf\n",
        "elif distribution_choice == 'uniform':\n",
        "    chosen_cdf = uniform_cdf\n",
        "    chosen_pdf = uniform_pdf\n",
        "elif distribution_choice == 'normal':\n",
        "    chosen_cdf = normal_cdf\n",
        "    chosen_pdf = normal_pdf"
      ],
      "metadata": {
        "id": "zPLFReDr7t5M"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Calculating $b^E$"
      ],
      "metadata": {
        "id": "6APHZRt0bCGe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# def Total_U_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "#     y_tau = b / (1 - gamma * np.exp(-beta_e * psi))\n",
        "#     cdf = cdf(y_tau)\n",
        "#     q_e = (1 / R) * (1 - cdf)\n",
        "#     integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2), y_lower, y_upper)\n",
        "#     def integrand_case_2_1(y_2):\n",
        "#         return np.log(y_2 - b) * pdf(y_2)\n",
        "#     def integrand_case_2_2(y_2):\n",
        "#         return np.log(gamma * y_2) * pdf(y_2)\n",
        "#     integral_case_2_1, _ = quad(integrand_case_2_1, y_tau, y_upper)\n",
        "#     integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "#     integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "#     U_period_1 = np.log(y_1 + q_e * b)\n",
        "#     U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "#                  (beta_e * integral_case_2_1 + beta_e * integral_case_2_2) +\n",
        "#                  (1 if y_tau < y_lower else 0) * (beta_e * integral_case_1) +\n",
        "#                  (1 if y_tau > y_upper else 0) * (beta_e * integral_case_3))\n",
        "#     U_period_3 = ((beta_e ** 2) * np.log(y_3) * (1 - cdf) +\n",
        "#                   (beta_e ** 2) * np.log(gamma * y_3) * cdf)\n",
        "#     U_total = U_period_1 + U_period_2 + U_period_3\n",
        "#     return U_total"
      ],
      "metadata": {
        "id": "36FpdSgGldf9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def Total_U_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta_e * psi))\n",
        "    cdf_value = cdf(y_tau)\n",
        "    q_e = (1 / R) * (1 - cdf_value)\n",
        "\n",
        "    # Initialize integral_case_1 to 0 to ensure it has a value even if not calculated\n",
        "    integral_case_1 = 0\n",
        "\n",
        "    # Compute integral_case_1 only if b is less than y_lower\n",
        "    if b < y_lower:\n",
        "        integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0, y_lower, y_upper)\n",
        "\n",
        "    def integrand_case_2_1(y_2):\n",
        "        return np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0  # Ensure logarithm is computed for valid values only\n",
        "\n",
        "    def integrand_case_2_2(y_2):\n",
        "        return np.log(gamma * y_2) * pdf(y_2)\n",
        "\n",
        "    integral_case_2_1, _ = quad(integrand_case_2_1, max(y_tau, b), y_upper)  # Ensure y_2 > b\n",
        "    integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "    integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "\n",
        "    U_period_1 = np.log(y_1 + q_e * b)\n",
        "    U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "                  (beta_e * integral_case_2_1 + beta_e * integral_case_2_2) +\n",
        "                  (1 if y_tau <= y_lower else 0) * (beta_e * integral_case_1) +  # Use <= to include equality\n",
        "                  (1 if y_tau > y_upper else 0) * (beta_e * integral_case_3))\n",
        "    U_period_3 = ((beta_e ** 2) * np.log(y_3) * (1 - cdf_value) +\n",
        "                  (beta_e ** 2) * np.log(gamma * y_3) * cdf_value)\n",
        "\n",
        "    U_total = U_period_1 + U_period_2 + U_period_3\n",
        "    return U_total"
      ],
      "metadata": {
        "id": "TKs7euveR5qU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b_values = np.linspace(0, 1.5 * b_upper_e, 500)\n",
        "U_values_uniform_e = []\n",
        "U_values_uniform_p = []\n",
        "\n",
        "for b in b_values:\n",
        "    U_uniform_e = Total_U_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, chosen_cdf, chosen_pdf)\n",
        "    U_values_uniform_e.append(U_uniform_e)"
      ],
      "metadata": {
        "id": "5LILX7zP3b81"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "max_index_uniform_e = np.argmax(U_values_uniform_e)\n",
        "max_b_uniform_e = b_values[max_index_uniform_e]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, U_values_uniform_e, label='Uniform', alpha=1, color='gray')\n",
        "plt.title('Extravagant\\'s Total Utility')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.xlim(0, 1.5*b_upper_e)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.scatter(max_b_uniform_e, U_values_uniform_e[max_index_uniform_e], color='green', zorder=2)\n",
        "plt.axvspan(0, b_lower_e, color='blue', alpha=0.2)\n",
        "plt.axvspan(b_lower_e, b_upper_e, color='red', alpha=0.2)\n",
        "plt.axvspan(b_upper_e, 1.5*b_upper_e, color='yellow', alpha=0.2)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "WzVpPHsrImkZ",
        "outputId": "c356d9bc-e4a0-4807-ff2f-ffc1a214c353"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if max_b_uniform_e > 1.01 * b_lower_e:\n",
        "    print(\"b_E in red area\")\n",
        "else:\n",
        "    print(\"b_E in blue area\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uu0LeKjnl2t5",
        "outputId": "35808aef-b6ca-4f98-d6e9-591f7202b1a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b_E in red area\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Calculating $\\hat{b^E}$"
      ],
      "metadata": {
        "id": "t4-6z0zd3vsJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# def calculate_U_uniform_for_b_hat_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "#     y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "#     cdf_uniform = cdf(y_tau)\n",
        "#     q_uniform_e = (1 / R) * (1 - cdf_uniform)\n",
        "#     integral_case_1_uniform, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2), y_lower, y_upper)\n",
        "#     def integrand_case_2_1_uniform(y_2):\n",
        "#         return np.log(y_2 - b) * pdf(y_2)\n",
        "#     def integrand_case_2_2_uniform(y_2):\n",
        "#         return np.log(gamma * y_2) * pdf(y_2)\n",
        "#     integral_case_2_1_uniform, _ = quad(integrand_case_2_1_uniform, y_tau, y_upper)\n",
        "#     integral_case_2_2_uniform, _ = quad(integrand_case_2_2_uniform, y_lower, y_tau)\n",
        "#     integral_case_3_uniform, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "#     U_period_1 = np.log(y_1 + q_uniform_e * b)\n",
        "#     U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "#                  (beta_e * integral_case_2_1_uniform + beta_e * integral_case_2_2_uniform) +\n",
        "#                  (1 if y_tau < y_lower else 0) * (beta_e * integral_case_1_uniform) +\n",
        "#                  (1 if y_tau > y_upper else 0) * (beta_e * integral_case_3_uniform))\n",
        "#     U_period_3 = ((beta_e ** 2) * np.log(y_3) * (1 - cdf_uniform) +\n",
        "#                   (beta_e ** 2) * np.log(gamma * y_3) * cdf_uniform)\n",
        "#     U_uniform_for_b_hat_e = U_period_1 + U_period_2 + U_period_3\n",
        "#     return U_uniform_for_b_hat_e"
      ],
      "metadata": {
        "id": "_zuV5K_iMChX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def calculate_U_uniform_for_b_hat_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "    cdf_uniform = cdf(y_tau)\n",
        "    q_uniform_e = (1 / R) * (1 - cdf_uniform)\n",
        "\n",
        "    # Initialize integral_case_1_uniform to 0 to ensure it has a value even if not calculated\n",
        "    integral_case_1_uniform = 0\n",
        "\n",
        "    # Compute integral_case_1_uniform only if b is less than y_lower\n",
        "    if b < y_lower:\n",
        "        integral_case_1_uniform, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0, y_lower, y_upper)\n",
        "\n",
        "    def integrand_case_2_1_uniform(y_2):\n",
        "        return np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0  # Ensure logarithm is computed for valid values only\n",
        "\n",
        "    def integrand_case_2_2_uniform(y_2):\n",
        "        return np.log(gamma * y_2) * pdf(y_2)\n",
        "\n",
        "    integral_case_2_1_uniform, _ = quad(integrand_case_2_1_uniform, max(y_tau, b), y_upper)  # Ensure y_2 > b\n",
        "    integral_case_2_2_uniform, _ = quad(integrand_case_2_2_uniform, y_lower, y_tau)\n",
        "    integral_case_3_uniform, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "\n",
        "    U_period_1 = np.log(y_1 + q_uniform_e * b)\n",
        "    U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "                  (beta_e * integral_case_2_1_uniform + beta_e * integral_case_2_2_uniform) +\n",
        "                  (1 if y_tau <= y_lower else 0) * (beta_e * integral_case_1_uniform) +  # Use <= to include equality\n",
        "                  (1 if y_tau > y_upper else 0) * (beta_e * integral_case_3_uniform))\n",
        "    U_period_3 = ((beta_e ** 2) * np.log(y_3) * (1 - cdf_uniform) +\n",
        "                  (beta_e ** 2) * np.log(gamma * y_3) * cdf_uniform)\n",
        "\n",
        "    U_uniform_for_b_hat_e = U_period_1 + U_period_2 + U_period_3\n",
        "    return U_uniform_for_b_hat_e"
      ],
      "metadata": {
        "id": "yJzdkLdcSii7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b_values = np.linspace(0, 1.5 * b_upper_e, 500)\n",
        "U_values_uniform_for_b_hat_e = []\n",
        "\n",
        "for b in b_values:\n",
        "    U_uniform_for_b_hat_e = calculate_U_uniform_for_b_hat_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, chosen_cdf, chosen_pdf)\n",
        "    U_values_uniform_for_b_hat_e.append(U_uniform_for_b_hat_e)"
      ],
      "metadata": {
        "id": "Xl1_1zJE3oj9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "difference = np.array(U_values_uniform_e)[max_index_uniform_e] - np.array(U_values_uniform_for_b_hat_e)\n",
        "crossings = np.where(np.diff(np.sign(difference)))[0]\n",
        "regions = zip([0] + list(crossings), list(crossings) + [len(difference) - 1])\n",
        "nearest_zero_indices = [np.argmin(np.abs(difference[start:end+1])) + start for start, end in regions]\n",
        "nearest_zero_indices = list(set(nearest_zero_indices))\n",
        "b_nearest_zeros = b_values[nearest_zero_indices]\n",
        "differences_nearest_zeros = difference[nearest_zero_indices]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, difference, label='Uniform', alpha=1, color='gray')\n",
        "plt.scatter(b_nearest_zeros, differences_nearest_zeros, color='red', zorder=5, label='Nearest to 0')  # Mark the nearest points to 0\n",
        "plt.axhline(0, color='black', linewidth=0.5)  # Zero line for reference\n",
        "plt.title('$U(τ = E, q^{E}(b^E), b^E) - U(τ = E, q^{P}(\\hat{b^E}), \\hat{b^E})$')\n",
        "plt.xlabel('b')\n",
        "#plt.ylabel('U')\n",
        "#plt.legend(loc='center', bbox_to_anchor=(0.5, -0.15), ncol=3)\n",
        "plt.xlim(0, 1.5 * b_upper_e)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 575
        },
        "id": "c5NsF8FNO9NP",
        "outputId": "5979af51-a996-47b4-c9e0-3fca73b24c21"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "threshold = 0.01 * b_upper_e\n",
        "b_nearest_zeros_sorted = np.sort(b_nearest_zeros)\n",
        "grouped_b_values = [b_nearest_zeros_sorted[0]]\n",
        "for b in b_nearest_zeros_sorted[1:]:\n",
        "    if b - grouped_b_values[-1] > threshold:\n",
        "        grouped_b_values.append(b)\n",
        "    else:\n",
        "        grouped_b_values[-1] = (grouped_b_values[-1] + b) / 2\n",
        "\n",
        "print('b_hat_e:')\n",
        "for b_val in grouped_b_values:\n",
        "    print(b_val)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bCJwJAPYWdCs",
        "outputId": "025a5531-06af-457e-bfab-5b9076296a32"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b_hat_e:\n",
            "689.6310847909402\n",
            "868.1238361485954\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Calculating $b^P$"
      ],
      "metadata": {
        "id": "xWIlP-Tbcigx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# def Total_U_p(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "#     y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "#     cdf = cdf(y_tau)\n",
        "#     q_p = (1 / R) * (1 - cdf)\n",
        "#     integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2), y_lower, y_upper)\n",
        "#     def integrand_case_2_1(y_2):\n",
        "#         return np.log(y_2 - b) * pdf(y_2)\n",
        "#     def integrand_case_2_2(y_2):\n",
        "#         return np.log(gamma * y_2) * pdf(y_2)\n",
        "#     integral_case_2_1, _ = quad(integrand_case_2_1, y_tau, y_upper)\n",
        "#     integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "#     integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "#     U_period_1 = np.log(y_1 + q_p * b)\n",
        "#     U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "#                  (beta_p * integral_case_2_1 + beta_p * integral_case_2_2) +\n",
        "#                  (1 if y_tau < y_lower else 0) * (beta_p * integral_case_1) +\n",
        "#                  (1 if y_tau > y_upper else 0) * (beta_p * integral_case_3))\n",
        "#     U_period_3 = ((beta_p ** 2) * np.log(y_3) * (1 - cdf) +\n",
        "#                   (beta_p ** 2) * np.log(gamma * y_3) * cdf)\n",
        "#     U_total = U_period_1 + U_period_2 + U_period_3\n",
        "#     return U_total"
      ],
      "metadata": {
        "id": "k7o9tZZGRcCt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def Total_U_p(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "    cdf_value = cdf(y_tau)\n",
        "    q_p = (1 / R) * (1 - cdf_value)\n",
        "    integral_case_1 = 0\n",
        "    if b < y_lower:\n",
        "        integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2), y_lower, y_upper)\n",
        "    def integrand_case_2_1(y_2):\n",
        "        return np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0  # Add conditional to handle y_2 <= b\n",
        "    def integrand_case_2_2(y_2):\n",
        "        return np.log(gamma * y_2) * pdf(y_2)\n",
        "    integral_case_2_1, _ = quad(integrand_case_2_1, max(y_tau, b), y_upper)  # Ensure y_2 > b\n",
        "    integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "    integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "    U_period_1 = np.log(y_1 + q_p * b)\n",
        "    U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "                  (beta_p * integral_case_2_1 + beta_p * integral_case_2_2) +\n",
        "                  (1 if y_tau <= y_lower else 0) * (beta_p * integral_case_1) +  # Use <= to include equality\n",
        "                  (1 if y_tau > y_upper else 0) * (beta_p * integral_case_3))\n",
        "    U_period_3 = ((beta_p ** 2) * np.log(y_3) * (1 - cdf_value) +\n",
        "                  (beta_p ** 2) * np.log(gamma * y_3) * cdf_value)\n",
        "    U_total = U_period_1 + U_period_2 + U_period_3\n",
        "    return U_total"
      ],
      "metadata": {
        "id": "opil3aFMPJR_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b_values = np.linspace(0, 1.5 * b_upper_p, 500)\n",
        "U_values_uniform_p = []\n",
        "\n",
        "for b in b_values:\n",
        "    U_uniform_p = Total_U_p(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, chosen_cdf, chosen_pdf)\n",
        "    U_values_uniform_p.append(U_uniform_p)"
      ],
      "metadata": {
        "id": "uQDztYZ43s8b"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "max_index_uniform_p = np.argmax(U_values_uniform_p)\n",
        "max_b_uniform_p = b_values[max_index_uniform_p]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, U_values_uniform_p, alpha=1, color='black')\n",
        "plt.title('Prudent\\'s Total Utility')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "#plt.xlim(100, 110)\n",
        "plt.xlim(0, 1.5*b_upper_p)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.scatter(max_b_uniform_p, U_values_uniform_p[max_index_uniform_p], color='red', zorder=2)\n",
        "plt.axvspan(0, b_lower_p, color='blue', alpha=0.2)\n",
        "plt.axvspan(b_lower_p, b_upper_p, color='red', alpha=0.2)\n",
        "plt.axvspan(b_upper_p, 1.5*b_upper_p, color='yellow', alpha=0.2)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "Lfu6myRtVV3_",
        "outputId": "21073a62-37ef-4b2b-df97-ba3f18c728f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if max_b_uniform_p > 1.01 * b_lower_p:\n",
        "    print(\"b_P in red area\")\n",
        "else:\n",
        "    print(\"b_P in blue area\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R4QC--yHm0jP",
        "outputId": "fe26da67-b40b-4cdb-f141-f4f01943162e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b_P in red area\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Calculating $b^{P*}$"
      ],
      "metadata": {
        "id": "2vv5_oe_eNat"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "min_values = [min(b_val, max_b_uniform_p) for b_val in grouped_b_values]\n",
        "overall_min_value = min(min_values)\n",
        "print(\"Overall minimum value:\", overall_min_value)\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, U_values_uniform_p, label='U for Type P', alpha=1, color='black')\n",
        "plt.title('Prudent\\'s Total Utility')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.legend(loc='center', bbox_to_anchor=(0.5, -0.15), ncol=3)\n",
        "plt.xlim(0, 1.5 * b_upper_p)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.scatter(max_b_uniform_p, U_values_uniform_p[max_index_uniform_p], color='red', zorder=2, label='$U(b^P)$')\n",
        "plt.axvspan(0, b_lower_p, color='blue', alpha=0.2)\n",
        "plt.axvspan(b_lower_p, b_upper_p, color='red', alpha=0.2)\n",
        "plt.axvspan(b_upper_p, 1.5 * b_upper_p, color='yellow', alpha=0.2)\n",
        "\n",
        "min_value_index = np.argmin(np.abs(b_values - overall_min_value))\n",
        "U_at_min_value = U_values_uniform_p[min_value_index]\n",
        "\n",
        "plt.scatter(overall_min_value, U_at_min_value, color='blue', zorder=3, label='$U(b^{P*})$')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 581
        },
        "id": "sXHk-itpZAO6",
        "outputId": "d162664c-39a5-4b6f-9342-92ffbbf39d94"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Overall minimum value: 689.6310847909402\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Checking whether $U^P(b^{P*_{lower}})$ > $U^P(b^{P*_{upper}})$"
      ],
      "metadata": {
        "id": "3iDafQ16bYNI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "overall_max_value2 = min(grouped_b_values)\n",
        "overall_max_value = max(grouped_b_values)\n",
        "\n",
        "min_value_index2 = np.argmin(np.abs(b_values - overall_max_value2))\n",
        "U_at_min_value2 = U_values_uniform_p[min_value_index2]\n",
        "\n",
        "max_value_index = np.argmin(np.abs(b_values - overall_max_value))\n",
        "U_at_max_value = U_values_uniform_p[max_value_index]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, U_values_uniform_p, label='U for Type P', alpha=1, color='black')\n",
        "plt.title('Prudent\\'s Total Utility')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.legend(loc='center', bbox_to_anchor=(0.5, -0.15), ncol=3)\n",
        "plt.xlim(0, 1.5 * b_upper_p)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.scatter(max_b_uniform_p, U_values_uniform_p[max_index_uniform_p], color='red', zorder=2, label='$U(b^P)$')\n",
        "plt.axvspan(0, b_lower_p, color='blue', alpha=0.2)\n",
        "plt.axvspan(b_lower_p, b_upper_p, color='red', alpha=0.2)\n",
        "plt.axvspan(b_upper_p, 1.5 * b_upper_p, color='yellow', alpha=0.2)\n",
        "plt.scatter(overall_max_value2, U_at_min_value2, color='blue', zorder=3, label='$U^P(b^{P*_{lower}})$')\n",
        "plt.scatter(overall_max_value, U_at_max_value, color='orange', zorder=3, label='$U^P(b^{P*_{upper}})$')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "YI7IVvFzd22J",
        "outputId": "0770e4e1-f12b-4fb4-ec33-3c3e94a57196"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if U_at_min_value2 > U_at_max_value:\n",
        "    print(\"Prudent government prefers lower b_P*\")\n",
        "else:\n",
        "    print(\"Prudent government prefers upper b_P*\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RnJTTvnxgvZa",
        "outputId": "2d3d855d-91b5-43c8-c9a9-bad046a71f96"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prudent government prefers lower b_P*\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Calculating $U^P(q^E)$, checking whether P deviates from $b^{P*}$"
      ],
      "metadata": {
        "id": "DZVGyV9-Pm6L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# def Total_U_p_with_price_q_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "#     y_tau_e = b / (1 - gamma * np.exp(-beta_e * psi))\n",
        "#     y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "#     cdf = cdf(y_tau_e)\n",
        "#     q_e = (1 / R) * (1 - cdf)\n",
        "#     integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2), y_lower, y_upper)\n",
        "#     def integrand_case_2_1(y_2):\n",
        "#         return np.log(y_2 - b) * pdf(y_2)\n",
        "#     def integrand_case_2_2(y_2):\n",
        "#         return np.log(gamma * y_2) * pdf(y_2)\n",
        "#     integral_case_2_1, _ = quad(integrand_case_2_1, y_tau, y_upper)\n",
        "#     integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "#     integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "#     U_period_1 = np.log(y_1 + q_e * b)\n",
        "#     U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "#                  (beta_p * integral_case_2_1 + beta_p * integral_case_2_2) +\n",
        "#                  (1 if y_tau < y_lower else 0) * (beta_p * integral_case_1) +\n",
        "#                  (1 if y_tau > y_upper else 0) * (beta_p * integral_case_3))\n",
        "#     U_period_3 = ((beta_p ** 2) * np.log(y_3) * (1 - cdf) +\n",
        "#                   (beta_p ** 2) * np.log(gamma * y_3) * cdf)\n",
        "#     U_total = U_period_1 + U_period_2 + U_period_3\n",
        "#     return U_total"
      ],
      "metadata": {
        "id": "QB19MigDPsw7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def Total_U_p_with_price_q_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, cdf, pdf):\n",
        "    y_tau_e = b / (1 - gamma * np.exp(-beta_e * psi))\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta_p * psi))\n",
        "    cdf_value = cdf(y_tau_e)\n",
        "    q_e = (1 / R) * (1 - cdf_value)\n",
        "\n",
        "    # Initialize integral_case_1 to 0 to ensure it has a value even if not calculated\n",
        "    integral_case_1 = 0\n",
        "\n",
        "    # Compute integral_case_1 only if b is less than y_lower\n",
        "    if b < y_lower:\n",
        "        integral_case_1, _ = quad(lambda y_2: np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0, y_lower, y_upper)\n",
        "\n",
        "    def integrand_case_2_1(y_2):\n",
        "        return np.log(y_2 - b) * pdf(y_2) if y_2 > b else 0  # Ensure logarithm is computed for valid values only\n",
        "\n",
        "    def integrand_case_2_2(y_2):\n",
        "        return np.log(gamma * y_2) * pdf(y_2)\n",
        "\n",
        "    integral_case_2_1, _ = quad(integrand_case_2_1, max(y_tau, b), y_upper)  # Ensure y_2 > b\n",
        "    integral_case_2_2, _ = quad(integrand_case_2_2, y_lower, y_tau)\n",
        "    integral_case_3, _ = quad(lambda y_2: np.log(gamma * y_2) * pdf(y_2), y_lower, y_upper)\n",
        "\n",
        "    U_period_1 = np.log(y_1 + q_e * b)\n",
        "    U_period_2 = ((1 if y_lower < y_tau < y_upper else 0) *\n",
        "                  (beta_p * integral_case_2_1 + beta_p * integral_case_2_2) +\n",
        "                  (1 if y_tau <= y_lower else 0) * (beta_p * integral_case_1) +  # Use <= to include equality\n",
        "                  (1 if y_tau > y_upper else 0) * (beta_p * integral_case_3))\n",
        "    U_period_3 = ((beta_p ** 2) * np.log(y_3) * (1 - cdf_value) +\n",
        "                  (beta_p ** 2) * np.log(gamma * y_3) * cdf_value)\n",
        "\n",
        "    U_total = U_period_1 + U_period_2 + U_period_3\n",
        "    return U_total\n"
      ],
      "metadata": {
        "id": "Sy2-UN02TgS_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "b_values = np.linspace(0, 1.5 * b_upper_p, 500)\n",
        "U_values_uniform_p_with_price_q = []\n",
        "\n",
        "for b in b_values:\n",
        "    U_uniform_p_with_price_q = Total_U_p_with_price_q_e(b, gamma, beta_e, beta_p, psi, R, y_1, y_3, y_lower, y_upper, chosen_cdf, chosen_pdf)\n",
        "    U_values_uniform_p_with_price_q.append(U_uniform_p_with_price_q)"
      ],
      "metadata": {
        "id": "CSxt_Yjt4Ray"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "max_index_uniform_p_with_price_q = np.argmax(U_values_uniform_p_with_price_q)\n",
        "max_b_uniform_p_with_price_q = b_values[max_index_uniform_p_with_price_q]\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(b_values, U_values_uniform_p, label='U for Type P', alpha=0.7, color='black')\n",
        "plt.plot(b_values, U_values_uniform_p_with_price_q, label='U for Type P with price q', linestyle='--', alpha=1, color='gray')\n",
        "plt.title('Prudent\\'s Total Utility')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.legend(loc='center', bbox_to_anchor=(0.5, -0.15), ncol=3)\n",
        "plt.xlim(0, 1.5 * b_upper_p)\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.scatter(max_b_uniform_p, U_values_uniform_p[max_index_uniform_p], color='red', zorder=2, label='$U(b^P,q^P)$')\n",
        "plt.axvspan(0, b_lower_p, color='blue', alpha=0.2)\n",
        "plt.axvspan(b_lower_p, b_upper_p, color='red', alpha=0.2)\n",
        "plt.axvspan(b_upper_p, 1.5 * b_upper_p, color='yellow', alpha=0.2)\n",
        "\n",
        "min_value_index = np.argmin(np.abs(b_values - overall_min_value))\n",
        "U_at_min_value = U_values_uniform_p[min_value_index]\n",
        "plt.scatter(max_b_uniform_p_with_price_q, U_values_uniform_p_with_price_q[max_index_uniform_p_with_price_q], color='green', zorder=2, label='$U(b^P,q^E)$')\n",
        "plt.scatter(overall_min_value, U_at_min_value, color='blue', zorder=3, label='$U(b^{P*})$')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "svYmoscxR6lE",
        "outputId": "0f154e73-f830-411b-d3fb-6ac61bf69cae"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "if U_at_min_value > U_values_uniform_p_with_price_q[max_index_uniform_p_with_price_q]:\n",
        "    print(\"Prudent government doesn't want to deviate from b_P*\")\n",
        "else:\n",
        "    print(\"Prudent government is happy that the market misunderstands him with Extravagant and he is happy that the market applies q_E to him\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dqHnl6qZWnkW",
        "outputId": "713c6840-b237-45a3-b069-69b24a8493ce"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prudent government doesn't want to deviate from b_P*\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Summary of results"
      ],
      "metadata": {
        "id": "53EVB9ogo1q4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Distribution choice:\", distribution_choice)\n",
        "print(\"beta_e =\", beta_e)\n",
        "print(\"beta_p =\", beta_p)\n",
        "print(\"gamma =\", gamma)\n",
        "print(\"R =\", R)\n",
        "print(\"y_lower =\", y_lower)\n",
        "print(\"y_upper =\", y_upper)\n",
        "print(\"y_3 =\", y_3)\n",
        "print(\"y_1 =\", y_1)\n",
        "print(\"y_mode (triangular) =\", y_mode)\n",
        "print(\"y_mean (normal) =\", y_mean)\n",
        "print(\"sigma (normal) =\", sigma)\n",
        "print(\"-----------------------------------------------------------------------------\")\n",
        "print(f\"debt level where default starts for P type = {b_lower_p:.1f}\")\n",
        "print(f\"debt level with always default for P type = {b_upper_p:.1f}\")\n",
        "print(\"b_P:\", f\"{max_b_uniform_p:.1f}\")\n",
        "if max_b_uniform_p > 1.01 * b_lower_p:\n",
        "    print(\"b_P in red area\")\n",
        "else:\n",
        "    print(\"b_P in blue area\")\n",
        "print(\"-----------------------------------------------------------------------------\")\n",
        "print(f\"debt level where default starts for E type = {b_lower_e:.1f}\")\n",
        "print(f\"debt level with always default for E type = {b_upper_e:.1f}\")\n",
        "print(\"b_E:\", f\"{max_b_uniform_e:.1f}\")\n",
        "if max_b_uniform_e > 1.01 * b_lower_e:\n",
        "    print(\"b_E in red area\")\n",
        "else:\n",
        "    print(\"b_E in blue area\")\n",
        "print(\"-----------------------------------------------------------------------------\")\n",
        "print('b_hat_e:')\n",
        "for b_val in grouped_b_values:\n",
        "    print(f\"{b_val:.1f}\")\n",
        "print(\"b_P*:\", f\"{overall_min_value:.1f}\")\n",
        "print(\"-----------------------------------------------------------------------------\")\n",
        "print(\"Checking whether U^P(b_P*_lower) > U^P(b_P*_upper):\")\n",
        "if U_at_min_value2 > U_at_max_value:\n",
        "    print(\"Prudent government prefers lower b_P*\")\n",
        "else:\n",
        "    print(\"Prudent government prefers upper b_P*\")\n",
        "print(\"-----------------------------------------------------------------------------\")\n",
        "print(\"Calculating U_P(q_E), Checking whether Prudent government deviates from b_P*:\")\n",
        "if U_at_min_value > U_values_uniform_p_with_price_q[max_index_uniform_p_with_price_q]:\n",
        "    print(\"Prudent government doesn't deviate from b_P*\")\n",
        "else:\n",
        "    print(\"Prudent government is happy that the market misunderstands him with Extravagant and the market applies q_E\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ivGvyzTppZoc",
        "outputId": "40955d8b-1f9e-4fd0-f2f8-88167c86af94"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Distribution choice: triangular\n",
            "beta_e = 0.9\n",
            "beta_p = 0.95\n",
            "gamma = 0.97\n",
            "R = 1\n",
            "y_lower = 8000\n",
            "y_upper = 48000\n",
            "y_3 = 13000\n",
            "y_1 = 11000\n",
            "y_mode (triangular) = 15900\n",
            "y_mean (normal) = 13000\n",
            "sigma (normal) = 1000.0\n",
            "-----------------------------------------------------------------------------\n",
            "debt level where default starts for P type = 461.3\n",
            "debt level with always default for P type = 2768.0\n",
            "b_P: 765.5\n",
            "b_P in red area\n",
            "-----------------------------------------------------------------------------\n",
            "debt level where default starts for E type = 449.8\n",
            "debt level with always default for E type = 2699.0\n",
            "b_E: 762.7\n",
            "b_E in red area\n",
            "-----------------------------------------------------------------------------\n",
            "b_hat_e:\n",
            "689.6\n",
            "868.1\n",
            "b_P*: 689.6\n",
            "-----------------------------------------------------------------------------\n",
            "Checking whether U^P(b_P*_lower) > U^P(b_P*_upper):\n",
            "Prudent government prefers lower b_P*\n",
            "-----------------------------------------------------------------------------\n",
            "Calculating U_P(q_E), Checking whether Prudent government deviates from b_P*:\n",
            "Prudent government doesn't deviate from b_P*\n"
          ]
        }
      ]
    }
  ]
}