3_periods_model.ipynb

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  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "u1 = np.log(y1 + q_tau * b)"
      ],
      "metadata": {
        "id": "6EyGDyfM0w9I"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def integrand(x, a, b):\n",
        "    return np.log(y2 - b) + (beta**tau) * np.log(y3)"
      ],
      "metadata": {
        "id": "Lo_QN0tOq8Aj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "# Assuming y1, q_tau, b, beta, tau, y_bar, y_underline, y3, and gamma have numerical values\n",
        "y1 = 10  # Example value\n",
        "q_tau = 0.5  # Example value\n",
        "b = 2  # Example value\n",
        "beta = 0.95  # Example value\n",
        "tau = 1  # Example value\n",
        "y_bar = 100  # Example value\n",
        "y_underline = 0  # Example value\n",
        "y3 = 50  # Example value\n",
        "gamma = 0.9  # Example value\n",
        "\n",
        "# Numerical computation for the first part of U\n",
        "U_numerical = np.log(y1 + q_tau * b)  \\\n",
        "    + (beta / (y_bar - y_underline)) * integrate(np.log(y2 - b) + (beta**tau) * np.log(y3), (y2, y_tau, y_bar)) \\\n",
        "    + (beta**tau / (y_bar - y_underline)) * integrate(np.log(gamma * y2) + (beta**tau) * np.log(gamma * y3), (y2, y_underline, y_tau))\n",
        "\n",
        "# Note: For the integral parts, you would need to use numerical integration methods since np.log cannot directly handle symbolic integration\n",
        "from scipy.integrate import quad\n",
        "def integrand(x, a, b):\n",
        "    return a*x**2 + b\n",
        "\n",
        "a = 2\n",
        "b = 1\n",
        "I = quad(integrand, 0, 1, args=(a,b))\n",
        "I"
      ],
      "metadata": {
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          "height": 220
        },
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      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "name 'integrate' is not defined",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-105-75d4eb049078>\u001b[0m in \u001b[0;36m<cell line: 15>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;31m# Numerical computation for the first part of U\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0mU_numerical\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mq_tau\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m     \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbeta\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my_bar\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbeta\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_tau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_bar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m     \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbeta\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mtau\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my_bar\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mintegrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbeta\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mtau\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_tau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'integrate' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y3 = 1.3\n",
        "gamma = 0.8\n",
        "beta = 0.9\n",
        "y_bar = 1.3\n",
        "y_underline = 1\n",
        "y1 = 1.1\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "a = 1 / (1 - gamma * np.exp(- beta * psi))\n",
        "y_tau = y_underline + (y_bar - y_underline)/2\n",
        "b = y_tau / a\n",
        "f = (((y_bar - 2 * a * b)**2) / ((r * y1 * (y_bar - y_underline)) + (b * (y_bar - a *b)))) + (beta * r) * np.log((y_bar - b) / (a * b - b))"
      ],
      "metadata": {
        "id": "otK81uYxybzm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the function to minimize\n",
        "def total_squared(params):\n",
        "    y3, gamma, beta, y_bar, y_underline, y1, r = params\n",
        "\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    a = 1 / (1 - gamma * np.exp(- beta * psi))\n",
        "    y_tau = y_underline + (y_bar - y_underline) / 2\n",
        "    b = y_tau / a\n",
        "    q = (y_bar - a * b) / (r * (y_bar - y_underline))\n",
        "\n",
        "    term_1 = ((1)/(y1 + q * b)) * (q - (a * b)/(r * (y_bar - y_underline)))\n",
        "    term_2 = ((-1 * beta) / (y_bar - y_underline)) * np.log((y_bar - b)/(y_tau - b))\n",
        "    term_3 = ((-1 * beta * a)/(y_bar - y_underline)) * (np.log(y_tau - b) + beta * np.log(y3))\n",
        "    term_4 = ((beta * a)/(y_bar - y_underline)) * (np.log(gamma * y_tau) + beta * np.log(gamma * y3))\n",
        "\n",
        "    total = term_1 + term_2 + term_3 + term_4\n",
        "\n",
        "    return total**2\n",
        "\n",
        "# Define bounds for each parameter\n",
        "bounds = [\n",
        "    (10, 20),      # y3\n",
        "    (0.5, 0.9),  # gamma\n",
        "    (0.7, 0.9),  # beta\n",
        "    (10, 20),      # y_bar\n",
        "    (10, 12),  # y_underline\n",
        "    (10, 20),      # y1\n",
        "    (1, 2)       # r\n",
        "]\n",
        "\n",
        "# Parameter names\n",
        "param_names = ['y3', 'gamma', 'beta', 'y_bar', 'y_underline', 'y1', 'r']\n",
        "\n",
        "# Calculate initial guesses as the midpoint of bounds\n",
        "initial_guess = [(low + high) / 2 for low, high in bounds]\n",
        "\n",
        "# Run the minimization with bounds\n",
        "result = minimize(total_squared, initial_guess, bounds=bounds)\n",
        "\n",
        "# Check if the optimization was successful\n",
        "if result.success:\n",
        "    optimized_params = result.x\n",
        "    minimized_value = result.fun\n",
        "    print(\"Optimized parameters:\")\n",
        "    for name, value in zip(param_names, optimized_params):\n",
        "        print(f\"{name}: {value}\")\n",
        "    print(f\"Minimized total**2: {minimized_value}\")\n",
        "else:\n",
        "    print(\"Optimization failed:\", result.message)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tw5OkLw10yw6",
        "outputId": "78edab2d-49b3-4c1f-a7b7-16374948ee03"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimized parameters:\n",
            "y3: 14.999993151151083\n",
            "gamma: 0.9\n",
            "beta: 0.7\n",
            "y_bar: 20.0\n",
            "y_underline: 10.0\n",
            "y1: 20.0\n",
            "r: 2.0\n",
            "Minimized total**2: 0.0022794123035090263\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the function to minimize\n",
        "def total_squared(params):\n",
        "    y3, gamma, beta, y_bar, y_underline, y1, r = params\n",
        "\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    a = 1 / (1 - gamma * np.exp(- beta * psi))\n",
        "    y_tau = y_underline + (y_bar - y_underline) / 2\n",
        "    b = y_tau / a\n",
        "    q = (y_bar - a * b) / (r * (y_bar - y_underline))\n",
        "\n",
        "    term_1 = ((1)/(y1 + q * b)) * (q - (a * b)/(r * (y_bar - y_underline)))\n",
        "    term_2 = ((-1 * beta) / (y_bar - y_underline)) * np.log((y_bar - b)/(y_tau - b))\n",
        "    term_3 = ((-1 * beta * a)/(y_bar - y_underline)) * (np.log(y_tau - b) + beta * np.log(y3))\n",
        "    term_4 = ((beta * a)/(y_bar - y_underline)) * (np.log(gamma * y_tau) + beta * np.log(gamma * y3))\n",
        "\n",
        "    total = term_1 + term_2 + term_3 + term_4\n",
        "\n",
        "    return total**2\n",
        "\n",
        "# Define bounds for each parameter\n",
        "bounds = [\n",
        "    (1, 1000),      # y3\n",
        "    (0.5, 0.9),  # gamma\n",
        "    (0.7, 0.9),  # beta\n",
        "    (500, 1000),      # y_bar\n",
        "    (300, 600),  # y_underline\n",
        "    (1, 1000),      # y1\n",
        "    (1, 2)       # r\n",
        "]\n",
        "\n",
        "# Parameter names\n",
        "param_names = ['y3', 'gamma', 'beta', 'y_bar', 'y_underline', 'y1', 'R']\n",
        "\n",
        "# Calculate initial guesses as the midpoint of bounds\n",
        "initial_guess = [(low + high) / 2 for low, high in bounds]\n",
        "\n",
        "# Run the minimization with bounds\n",
        "result = minimize(total_squared, initial_guess, bounds=bounds)\n",
        "\n",
        "# Check if the optimization was successful and meets the target\n",
        "if result.success:\n",
        "    optimized_params = result.x\n",
        "    minimized_value = result.fun\n",
        "    print(\"Optimized parameters:\")\n",
        "    for name, value in zip(param_names, optimized_params):\n",
        "        print(f\"{name}= {value}\")\n",
        "    print(f\"Minimized total**2: {minimized_value}\")\n",
        "\n",
        "    # Check if the minimized value meets the target\n",
        "    if minimized_value <= 0.000001:\n",
        "        print(\"The target of reaching at least 0.000001 for minimized total**2 has been achieved.\")\n",
        "    else:\n",
        "        print(\"The target of reaching at least 0.000001 for minimized total**2 has not been achieved. Consider revising the model or constraints.\")\n",
        "else:\n",
        "    print(\"Optimization failed:\", result.message)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vDA3IIYbi6zH",
        "outputId": "61281c29-74b7-4ab8-f69c-b89c6b919640"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimized parameters:\n",
            "y3= 500.5\n",
            "gamma= 0.7\n",
            "beta= 0.8\n",
            "y_bar= 750.0\n",
            "y_underline= 450.0\n",
            "y1= 500.5\n",
            "R= 1.5\n",
            "Minimized total**2: 7.379455323025469e-06\n",
            "The target of reaching at least 0.000001 for minimized total**2 has not been achieved. Consider revising the model or constraints.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import differential_evolution\n",
        "\n",
        "# Function to calculate f with regularization to avoid division by zero\n",
        "def f(params):\n",
        "    gamma, beta, y_bar, y_underline, y3, y1, r = params  # Include r as a parameter\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    a = 1 / (1 - gamma * np.exp(- beta * psi))\n",
        "    y_tau = y_underline + 1 * (y_bar - y_underline) / 7\n",
        "    b = y_tau / a\n",
        "    epsilon = 1e-8  # Small regularization term\n",
        "    f_value = (((y_bar - 2 * a * b) ** 2) / ((r * y1 * (y_bar - y_underline)) + (b * (y_bar - a * b)) + epsilon)) + (beta * r) * np.log((y_bar - b + epsilon) / (a * b - b + epsilon))\n",
        "    return f_value**2\n",
        "\n",
        "# Objective function for differential_evolution\n",
        "def objective(params):\n",
        "    return f(params)\n",
        "\n",
        "# Bounds for the parameters, including r in the range [0.8, 1.2]\n",
        "bounds = [(0.5, 0.9), (0.85, 0.99), (3, 5), (2, 3), (1, 5), (1, 5), (1, 3)]\n",
        "\n",
        "# Use differential_evolution to find the parameters that make |f| as close to zero as possible\n",
        "result = differential_evolution(objective, bounds)\n",
        "\n",
        "# Print the optimized parameters\n",
        "gamma_opt, beta_opt, y_bar_opt, y_underline_opt, y3_opt, y1_opt, r_opt = result.x\n",
        "print(f\"Optimized gamma: {gamma_opt}\")\n",
        "print(f\"Optimized beta: {beta_opt}\")\n",
        "print(f\"Optimized y_bar: {y_bar_opt}\")\n",
        "print(f\"Optimized y_underline: {y_underline_opt}\")\n",
        "print(f\"Optimized y3: {y3_opt}\")\n",
        "print(f\"Optimized y1: {y1_opt}\")\n",
        "print(f\"Optimized r: {r_opt}\")  # Print the optimized r value\n",
        "\n",
        "# Verify by calculating f with the obtained parameters\n",
        "f_at_optimized_r = f(result.x)\n",
        "print(f\"Absolute f at optimized r: {f_at_optimized_r}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iIjjl2wX2uSk",
        "outputId": "5ad5de07-f6ac-4741-a364-7065770fd31e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimized gamma: 0.9\n",
            "Optimized beta: 0.85\n",
            "Optimized y_bar: 3.5782453359146764\n",
            "Optimized y_underline: 2.0\n",
            "Optimized y3: 2.364848658253469\n",
            "Optimized y1: 5.0\n",
            "Optimized r: 1.0\n",
            "Absolute f at optimized r: 0.31422773548092214\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the parameters - adjust these as necessary\n",
        "gamma = 0.5\n",
        "beta = 0.1\n",
        "y_bar = 100\n",
        "y_underline = 50\n",
        "y3 = 75\n",
        "y1 = 60\n",
        "R = 1.05\n",
        "\n",
        "# Function to calculate psi\n",
        "def calc_psi(y3, gamma):\n",
        "    return np.log(y3) - np.log(gamma * y3)\n",
        "\n",
        "# Function to calculate b_bar and b_underline\n",
        "def calc_b_bars(y_bar, y_underline, beta, psi, gamma):\n",
        "    b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "    b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "    return b_bar, b_underline\n",
        "\n",
        "# Function to calculate y_tau\n",
        "def calc_y_tau(b, psi, gamma, beta):\n",
        "    return b / (1 - gamma * np.exp(-beta * psi))\n",
        "\n",
        "# Function to calculate q_tau\n",
        "def calc_q_tau(y_bar, y_underline, y_tau, R):\n",
        "    return (1 / R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "\n",
        "# Utility function u_total\n",
        "def u_total(b, gamma, beta, y_bar, y_underline, y3, y1, R):\n",
        "    psi = calc_psi(y3, gamma)\n",
        "    y_tau = calc_y_tau(b, psi, gamma, beta)\n",
        "    q_tau = calc_q_tau(y_bar, y_underline, y_tau, R)\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta ** 2) / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta ** 2) / (y_bar - y_underline)) * np.log(gamma * y3) * (y_tau - y_underline)\n",
        "    return -(term1 + term2 + term3 + term4 + term5)  # Negative for maximization\n",
        "\n",
        "# Secondary objective function\n",
        "def objective(b, b_bar, b_underline):\n",
        "    return (b - (b_underline + b_bar) / 2) ** 2\n",
        "\n",
        "# Optimization to maximize u_total\n",
        "result = minimize(u_total, x0=[y_bar/2], args=(gamma, beta, y_bar, y_underline, y3, y1, R), bounds=[(y_underline, y_bar)])\n",
        "\n",
        "# If successful, proceed with secondary optimization\n",
        "if result.success:\n",
        "    b_opt = result.x[0]\n",
        "    psi = calc_psi(y3, gamma)\n",
        "    b_bar, b_underline = calc_b_bars(y_bar, y_underline, beta, psi, gamma)\n",
        "\n",
        "    # Secondary optimization\n",
        "    result_secondary = minimize(objective, x0=[b_opt], args=(b_bar, b_underline), bounds=[(y_underline, y_bar)])\n",
        "\n",
        "    if result_secondary.success:\n",
        "        b_final = result_secondary.x[0]\n",
        "    else:\n",
        "        b_final = None\n",
        "else:\n",
        "    b_final = None\n",
        "\n",
        "# Print all parameters and final calculated values\n",
        "print(f\"gamma: {gamma}, beta: {beta}, y_bar: {y_bar}, y_underline: {y_underline}, y3: {y3}, y1: {y1}, R: {R}\")\n",
        "print(f\"Final b value: {b_final}\")\n",
        "if b_final is not None:\n",
        "    print(f\"b_bar_final: {b_bar}, b_underline_final: {b_underline}\")\n",
        "    print(f\"psi_final: {psi}\")\n",
        "    y_tau_final = calc_y_tau(b_final, psi, gamma, beta)\n",
        "    q_tau_final = calc_q_tau(y_bar, y_underline, y_tau_final, R)\n",
        "    print(f\"y_tau_final: {y_tau_final}, q_tau_final: {q_tau_final}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wQgW4JnVOAJP",
        "outputId": "4b3570bb-2940-4529-ec9e-5d571dd31b03"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "gamma: 0.5, beta: 0.1, y_bar: 100, y_underline: 50, y3: 75, y1: 60, R: 1.05\n",
            "Final b value: 50.0\n",
            "b_bar_final: 53.34835042315963, b_underline_final: 26.674175211579815\n",
            "psi_final: 0.693147180559945\n",
            "y_tau_final: 93.72361020237649, q_tau_final: 0.11955028185949539\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "psi = np.log(y_3) - np.log(gamma * y_3)\n",
        "y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "\n",
        "term1 = np.log(y_1 + q_tau * b)\n",
        "term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y_3) * (y_bar - y_tau)\n",
        "term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y_3) * (y_tau - y_underline)\n",
        "\n",
        "u =  term1 + term2 + term3 + term4 + term5"
      ],
      "metadata": {
        "id": "WnWPuFUEC2gk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1\n",
        "y1 = 1\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.2\n",
        "y_underline = 0.8\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values = np.linspace(0, 1, num_points)\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "\n",
        "# Initialize arrays to store u values for each b\n",
        "u_values = np.zeros(num_points)\n",
        "\n",
        "# b_values_case_1\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "    q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_tau - y_underline)\n",
        "    u_values[i] = term1 + term2 + term3 + term4 + term5\n",
        "\n",
        "\n",
        "# b_values_case_2\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1/R)\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    u_values[i] = term1 + term2 + term3\n",
        "\n",
        "\n",
        "# Plotting\n",
        "plt.plot(b_values_case_2, u_values)\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u vs b')\n",
        "plt.grid(True)\n",
        "plt.xlim(-1, 1)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "o61IHtSAHo2g",
        "outputId": "36d64335-76c2-40db-f8a5-92b11d101099"
      },
      "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": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1.5\n",
        "y1 = 3\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.5\n",
        "y_underline = 0.5\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "b_values_case_3 = np.linspace(b_bar, 2, num_points)\n",
        "\n",
        "# Initialize arrays to store u values for each b\n",
        "u_values_case_1 = np.zeros(num_points)\n",
        "u_values_case_2 = np.zeros(num_points)\n",
        "u_values_case_3 = np.zeros(num_points)\n",
        "\n",
        "\n",
        "# b_values_case_1\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "    q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_tau - y_underline)\n",
        "    u_values_case_1[i] = term1 + term2 + term3 + term4 + term5\n",
        "\n",
        "# b_values_case_2\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1/R)\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    u_values_case_2[i] = term1 + term2 + term3\n",
        "\n",
        "\n",
        "# b_values_case_3\n",
        "for i, b in enumerate(b_values_case_3):\n",
        "    term1 = np.log(y1)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_bar * np.log(y_bar) - y_underline * np.log(y_underline) - (y_bar - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    u_values_case_3[i] = term1 + term4 + term5\n",
        "\n",
        "\n",
        "\n",
        "# Plotting\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "3unFp0wQTEA0",
        "outputId": "a7cf3f9f-96f9-4e9d-a625-3aa7d12c3d16"
      },
      "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": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u vs b')\n",
        "plt.grid(True)\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "# Define the x-limits for each case\n",
        "xmin_case_1, xmax_case_1 = min(b_values_case_1), max(b_values_case_1)\n",
        "xmin_case_2, xmax_case_2 = min(b_values_case_2), max(b_values_case_2)\n",
        "xmin_case_3, xmax_case_3 = min(b_values_case_3), max(b_values_case_3)\n",
        "\n",
        "# Fill the background color for each case\n",
        "plt.axvspan(xmin_case_1, xmax_case_1, color='red', alpha=0.2)\n",
        "plt.axvspan(xmin_case_2, xmax_case_2, color='blue', alpha=0.2)\n",
        "plt.axvspan(xmin_case_3, xmax_case_3, color='yellow', alpha=0.2)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "JbMTnjTBi5gR",
        "outputId": "9309d8e7-f19f-4c81-ac06-844e1efd7840"
      },
      "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": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1.3\n",
        "y1 = 1\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.5\n",
        "y_underline = 0.5\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "b_values_case_3 = np.linspace(b_bar, 2, num_points)\n",
        "\n",
        "# Initialize arrays to store u and q_tau values for each b\n",
        "u_values_case_1 = np.zeros(num_points)\n",
        "u_values_case_2 = np.zeros(num_points)\n",
        "u_values_case_3 = np.zeros(num_points)\n",
        "q_values_case_1 = np.zeros(num_points)\n",
        "q_values_case_2 = np.zeros(num_points)\n",
        "q_values_case_3 = np.zeros(num_points)\n",
        "\n",
        "# b_values_case_1\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "    q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "    q_values_case_1[i] = q_tau\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_tau - y_underline)\n",
        "    u_values_case_1[i] = term1 + term2 + term3 + term4 + term5\n",
        "\n",
        "# b_values_case_2\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1/R)\n",
        "    q_values_case_2[i] = q_tau\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    u_values_case_2[i] = term1 + term2 + term3\n",
        "\n",
        "# b_values_case_3\n",
        "for i, b in enumerate(b_values_case_3):\n",
        "    q_values_case_3[i] = np.inf  # q_tau goes to infinity for Case 3\n",
        "    term1 = np.log(y1)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_bar * np.log(y_bar) - y_underline * np.log(y_underline) - (y_bar - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    u_values_case_3[i] = term1 + term4 + term5\n",
        "\n",
        "# Plotting u vs b\n",
        "plt.figure(figsize=(12, 6))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "# Plotting q_tau vs b\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.plot(b_values_case_1, q_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, q_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, q_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('q_tau')\n",
        "plt.title('Plot of q_tau vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "vyP_nHJiX2sv",
        "outputId": "3a3ec7c9-803c-486a-cdda-7ff8416fb1c9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1.3\n",
        "y1 = 1\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.5\n",
        "y_underline = 0.5\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "b_values_case_3 = np.linspace(b_bar, 2, num_points)\n",
        "\n",
        "# Initialize arrays to store u, q_tau, and term1 values for each b\n",
        "u_values_case_1 = np.zeros(num_points)\n",
        "u_values_case_2 = np.zeros(num_points)\n",
        "u_values_case_3 = np.zeros(num_points)\n",
        "q_values_case_1 = np.zeros(num_points)\n",
        "q_values_case_2 = np.zeros(num_points)\n",
        "q_values_case_3 = np.zeros(num_points)\n",
        "term1_values_case_1 = np.zeros(num_points)\n",
        "term1_values_case_2 = np.zeros(num_points)\n",
        "term1_values_case_3 = np.zeros(num_points)\n",
        "term2_term4_values_case_1 = np.zeros(num_points)\n",
        "term2_term4_values_case_2 = np.zeros(num_points)\n",
        "term2_term4_values_case_3 = np.zeros(num_points)\n",
        "term3_term5_values_case_1 = np.zeros(num_points)\n",
        "term3_term5_values_case_2 = np.zeros(num_points)\n",
        "term3_term5_values_case_3 = np.zeros(num_points)\n",
        "y_tau_values = np.zeros(num_points)\n",
        "\n",
        "# Calculate values for each case\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta * psi))\n",
        "    y_tau_values[i] = y_tau\n",
        "    q_tau = (1 / R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "    q_values_case_1[i] = q_tau\n",
        "    term1_values_case_1[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma *y3) * (y_tau - y_underline)\n",
        "    term2_term4_values_case_1[i] = term2 + term4\n",
        "    term3_term5_values_case_1[i] = term3 + term5\n",
        "    u_values_case_1[i] = term1_values_case_1[i] + term2 + term3 + term4 + term5\n",
        "\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1 / R)\n",
        "    q_values_case_2[i] = q_tau\n",
        "    term1_values_case_2[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(\n",
        "        y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    term4 = 0\n",
        "    term5 = 0\n",
        "    term2_term4_values_case_2[i] = term2 + term4\n",
        "    term3_term5_values_case_2[i] = term3 + term5\n",
        "    u_values_case_2[i] = term1_values_case_2[i] + term2 + term3\n",
        "\n",
        "for i, b in enumerate(b_values_case_3):\n",
        "    q_values_case_3[i] = 0\n",
        "    term1_values_case_3[i] = np.log(y1)\n",
        "    term2 = 0\n",
        "    term3 = 0\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_bar * np.log(y_bar) - y_underline * np.log(y_underline) - (y_bar - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    term2_term4_values_case_3[i] = term2 + term4\n",
        "    term3_term5_values_case_3[i] = term3 + term5\n",
        "    u_values_case_3[i] = term1_values_case_3[i] + term4 + term5\n",
        "\n",
        "# Plotting u vs b\n",
        "plt.figure(figsize=(16, 8))\n",
        "\n",
        "plt.subplot(2, 3, 1)\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "# Plotting q_tau vs b\n",
        "plt.subplot(2, 3, 2)\n",
        "plt.plot(b_values_case_1, q_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, q_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, q_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('q_tau')\n",
        "plt.title('Plot of q_tau vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "plt.subplot(2, 3, 3)\n",
        "plt.plot(b_values_case_1, y_tau_values, label='Case 1')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('y_tau')\n",
        "plt.title('y_tau vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "# Plotting term1 vs b\n",
        "plt.subplot(2, 3, 4)\n",
        "plt.plot(b_values_case_1, term1_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, term1_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, term1_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('term1')\n",
        "plt.title('Plot of term1 vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "# Plotting (term2 + term4) and (term3 + term5) vs b\n",
        "plt.subplot(2, 3, 5)\n",
        "plt.plot(b_values_case_1, term2_term4_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, term2_term4_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, term2_term4_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('Values')\n",
        "plt.title('(term2 + term4) vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "plt.subplot(2, 3, 6)\n",
        "plt.plot(b_values_case_1, term3_term5_values_case_1, label='Case 1')\n",
        "plt.plot(b_values_case_2, term3_term5_values_case_2, label='Case 2')\n",
        "plt.plot(b_values_case_3, term3_term5_values_case_3, label='Case 3')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('Values')\n",
        "plt.title('(term3 + term5) vs b')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.xlim(0, 2)\n",
        "\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 807
        },
        "id": "J9DzY2DYYk9D",
        "outputId": "64661943-610d-4091-85ad-5d35057d41b2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1600x800 with 6 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Generate values for b\n",
        "b_values = np.linspace(0, 2, 100)  # Adjust the range and number of points as needed\n",
        "\n",
        "# Calculate the function values\n",
        "log_values = np.log(1.1 + b_values)\n",
        "\n",
        "# Plot\n",
        "plt.plot(b_values, log_values)\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('log(1.1 + b)')\n",
        "plt.title('Plot of log(1.1 + b) with respect to b')\n",
        "plt.grid(True)\n",
        "plt.ylim(0,0.37)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "ICzuBgvxnnEX",
        "outputId": "cc48ff28-6350-40e0-b3dd-f5cfa85f9e06"
      },
      "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": [
        "import numpy as np\n",
        "from scipy.optimize import minimize\n",
        "\n",
        "# Define the function to calculate u_total for a given b and parameters\n",
        "def calc_u_total(b, y3, y1, gamma, beta, R, y_bar, y_underline):\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "    b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta * psi))\n",
        "    q_tau = (1 / R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma * y3) * (y_tau - y_underline)\n",
        "    return term1 + term2 + term3 + term4 + term5\n",
        "\n",
        "# Modified inner optimization to return the optimal b value along with the maximum u_total\n",
        "def inner_optimization(params):\n",
        "    y3, y1, gamma, beta, R, y_bar, y_underline = params\n",
        "    result = minimize(lambda b: -calc_u_total(b, y3, y1, gamma, beta, R, y_bar, y_underline), x0=[(y_bar + y_underline) / 2], bounds=[(y_underline, y_bar)])\n",
        "    if result.success:\n",
        "        optimal_b = result.x[0]\n",
        "        max_u_total = -result.fun\n",
        "        return max_u_total, optimal_b\n",
        "    else:\n",
        "        return np.nan, None  # Optimization failed\n",
        "\n",
        "# Outer optimization remains unchanged\n",
        "def outer_objective(params):\n",
        "    max_u_total, optimal_b = inner_optimization(params)\n",
        "    return -max_u_total  # Negate because we are maximizing\n",
        "\n",
        "\n",
        "# Initial guesses for the parameters\n",
        "initial_params = [75, 60, 0.5, 0.1, 1.05, 100, 50]  # Example: [y3, y1, gamma, beta, R, y_bar, y_underline]\n",
        "\n",
        "# Parameter bounds\n",
        "bounds = [(50, 100), (40, 80), (0.1, 1), (0.01, 0.5), (1, 2), (80, 120), (30, 70)]  # Example bounds\n",
        "\n",
        "# Run the outer optimization\n",
        "result = minimize(outer_objective, initial_params, bounds=bounds)\n",
        "\n",
        "if result.success:\n",
        "    optimized_params = result.x\n",
        "    max_u_total, optimal_b = inner_optimization(optimized_params)\n",
        "    y3, y1, gamma, beta, R, y_bar, y_underline = optimized_params\n",
        "    psi_optimal = np.log(y3) - np.log(gamma * y3)\n",
        "    b_bar_optimal = (1 - gamma * np.exp(- beta * psi_optimal)) * y_bar\n",
        "    b_underline_optimal = (1 - gamma * np.exp(- beta * psi_optimal)) * y_underline\n",
        "\n",
        "    # Check if optimal_b is within the range\n",
        "    in_range = b_underline_optimal <= optimal_b <= b_bar_optimal\n",
        "\n",
        "    # Print optimized parameters with names\n",
        "    param_names = [\"y3\", \"y1\", \"gamma\", \"beta\", \"R\", \"y_bar\", \"y_underline\"]\n",
        "    print(\"Optimized parameters:\")\n",
        "    for name, value in zip(param_names, optimized_params):\n",
        "        print(f\"{name}: {value:.4f}\")\n",
        "\n",
        "    print(f\"Maximum u_total: {max_u_total:.4f}\")\n",
        "    print(f\"Optimal b: {optimal_b:.4f}\")\n",
        "    print(f\"b_bar (Optimal): {b_bar_optimal:.4f}\")\n",
        "    print(f\"b_underline (Optimal): {b_underline_optimal:.4f}\")\n",
        "    print(f\"The optimal b is within the range of b_bar to b_underline: {'Yes' if in_range else 'No'}\")\n",
        "else:\n",
        "    print(\"Optimization failed.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Q7cua1gUav6",
        "outputId": "4f65138e-f572-4d41-96ac-e6965ac8001e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-84-7a2802bbdfba>:12: RuntimeWarning: invalid value encountered in log\n",
            "  term1 = np.log(y1 + q_tau * b)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimized parameters:\n",
            "y3: 100.0000\n",
            "y1: 80.0000\n",
            "gamma: 0.3211\n",
            "beta: 0.5000\n",
            "R: 1.0000\n",
            "y_bar: 120.0000\n",
            "y_underline: 49.8992\n",
            "Maximum u_total: 7.6518\n",
            "Optimal b: 49.8992\n",
            "b_bar (Optimal): 98.1634\n",
            "b_underline (Optimal): 40.8190\n",
            "The optimal b is within the range of b_bar to b_underline: Yes\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "\n",
        "# Assign hypothetical values to the parameters\n",
        "y1 = 10\n",
        "beta = 0.9\n",
        "y_bar = 20\n",
        "y_underline = 5\n",
        "gamma = 0.8\n",
        "y3 = 15\n",
        "R = 1\n",
        "\n",
        "# Define a simple function for y^tau(b)\n",
        "def y_tau_b_function(b, gamma, beta, y3):\n",
        "    return b / (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))  # This is a simplistic function for demonstration\n",
        "\n",
        "# Define the function for q as a function of y^tau(b)\n",
        "def q_function(y_tau_b, R, y_bar, y_underline):\n",
        "    return (1/R) * (y_bar - y_tau_b) / (y_bar - y_underline)\n",
        "\n",
        "y_tau_b = y_tau_b_function(b, gamma, beta, y3)\n",
        "q = q_function(y_tau_b, R, y_bar, y_underline)  # Calculate q based on y_tau_b\n",
        "\n",
        "b_bar = y_bar * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "b_underline = y_underline * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "\n",
        "\n",
        "# Define the function for the first part of the equation\n",
        "def first_part(y1, q, b):\n",
        "    return np.log(y1 + q * b)\n",
        "\n",
        "# Define the function for the second part of the integral\n",
        "def second_part(y2, b, beta, y3):\n",
        "    return np.log(y2 - b) + beta * np.log(y3)\n",
        "\n",
        "# Define the function for the third part of the integral\n",
        "def third_part(y2, gamma, beta, y3):\n",
        "    return np.log(gamma * y2) + beta * np.log(gamma * y3)\n",
        "\n",
        "# Compute the integrals\n",
        "integral_1, _ = quad(second_part, y_tau_b, y_bar, args=(b, beta, y3))\n",
        "integral_2, _ = quad(third_part, y_underline, y_tau_b, args=(gamma, beta, y3))\n",
        "\n",
        "# Calculate the utility U\n",
        "U = first_part(y1, q, b) + (beta / (y_bar - y_underline)) * integral_1 + (beta / (y_bar - y_underline)) * integral_2\n",
        "\n",
        "print(\"The value of U is:\", U)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "272cEBCPs96j",
        "outputId": "ca71e5fb-4918-4538-8731-ceb4abd1edd2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The value of U is: 6.521327751791066\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Assign hypothetical values to the parameters\n",
        "y1 = 10\n",
        "beta = 0.9\n",
        "y_bar = 20\n",
        "y_underline = 10\n",
        "y3 = 10\n",
        "R = 1\n",
        "gamma = 0.85\n",
        "\n",
        "# Define a function for y^tau(b)\n",
        "def y_tau_b_function(b, gamma, beta, y3):\n",
        "    return b / (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "\n",
        "# Define the function for q as a function of y^tau(b)\n",
        "def q_function(y_tau_b, R, y_bar, y_underline):\n",
        "    return (1 / R) * (y_bar - y_tau_b) / (y_bar - y_underline)\n",
        "\n",
        "# Define the function for the first part of the equation\n",
        "def first_part(y1, q, b):\n",
        "    return np.log(y1 + q * b)\n",
        "\n",
        "# Define the functions for the second and third parts of the integral\n",
        "def second_part(y2, b, beta, y3):\n",
        "    return np.log(y2 - b) + beta * np.log(y3)\n",
        "\n",
        "def third_part(y2, gamma, beta, y3):\n",
        "    return np.log(gamma * y2) + beta * np.log(gamma * y3)\n",
        "\n",
        "# Function to calculate U for a given b\n",
        "def calculate_U(b, gamma, beta, y3, R, y1, y_bar, y_underline):\n",
        "    y_tau_b = y_tau_b_function(b, gamma, beta, y3)\n",
        "    q = q_function(y_tau_b, R, y_bar, y_underline)\n",
        "    integral_1, _ = quad(second_part, y_tau_b, y_bar, args=(b, beta, y3))\n",
        "    integral_2, _ = quad(third_part, y_underline, y_tau_b, args=(gamma, beta, y3))\n",
        "    U = first_part(y1, q, b) + (beta / (y_bar - y_underline)) * integral_1 + (beta / (y_bar - y_underline)) * integral_2\n",
        "    return U\n",
        "\n",
        "# Calculate b_bar and b_underline\n",
        "b_bar = y_bar * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "b_underline = y_underline * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "\n",
        "# Generate b values\n",
        "b_values = np.linspace(b_underline, b_bar, 100)\n",
        "\n",
        "# Calculate U for each b value\n",
        "U_values = [calculate_U(b, gamma, beta, y3, R, y1, y_bar, y_underline) for b in b_values]\n",
        "\n",
        "# Plotting\n",
        "plt.plot(b_values, U_values, label='U vs b')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('Utility (U)')\n",
        "plt.title('Utility Function U as a function of b')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "bZ_gYPm-v6DN",
        "outputId": "c0b903e0-5221-4b87-fccb-517b36e06d01"
      },
      "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": [
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "from scipy.optimize import minimize_scalar\n",
        "\n",
        "# Define parameter ranges\n",
        "y1_values = np.linspace(5, 15, 10)\n",
        "beta_values = np.linspace(0.5, 1.5, 10)\n",
        "gamma_values = np.linspace(0.5, 0.95, 10)\n",
        "y3_values = np.linspace(5, 15, 10)\n",
        "R_values = np.linspace(0.5, 1.5, 10)\n",
        "y_bar_values = np.linspace(15, 25, 10)\n",
        "y_underline_values = np.linspace(5, 15, 10)\n",
        "\n",
        "epsilon = 0.01  # Small value to check inside the interval\n",
        "\n",
        "best_params = None\n",
        "max_U = -np.inf\n",
        "\n",
        "                            # Define the function to calculate U for the current set of parameters\n",
        "def calculate_U(b):\n",
        "    y_tau_b = y_tau_b_function(b, gamma, beta, y3)\n",
        "    q = q_function(y_tau_b, R, y_bar, y_underline)\n",
        "    integral_1, _ = quad(second_part, y_tau_b, y_bar, args=(b, beta, y3))\n",
        "    integral_2, _ = quad(third_part, y_underline, y_tau_b, args=(gamma, beta, y3))\n",
        "    return -first_part(y1, q, b) - (beta / (y_bar - y_underline)) * (integral_1 + integral_2)\n",
        "\n",
        "# Nested loops for parameter exploration\n",
        "for y1 in y1_values:\n",
        "    for beta in beta_values:\n",
        "        for gamma in gamma_values:\n",
        "            for y3 in y3_values:\n",
        "                for R in R_values:\n",
        "                    for y_bar in y_bar_values:\n",
        "                        for y_underline in y_underline_values:\n",
        "                            if y_underline >= y_bar:  # Ensure y_underline is less than y_bar\n",
        "                                continue\n",
        "\n",
        "                            # Calculate b_bar and b_underline for the current set of parameters\n",
        "                            b_bar = y_bar * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "                            b_underline = y_underline * (1 - gamma * np.exp(-1 * beta * (np.log(y3) - np.log(gamma * y3))))\n",
        "                            result = minimize_scalar(calculate_U, bounds=(b_underline + epsilon, b_bar - epsilon), method='bounded')\n",
        "\n",
        "                            # Update the best parameters if the current maximum U is greater than the previous maximum\n",
        "                            if -result.fun > max_U:\n",
        "                                max_U = -result.fun\n",
        "                                best_params = {\n",
        "                                    'y1': y1, 'beta': beta, 'gamma': gamma, 'y3': y3, 'R': R,\n",
        "                                    'y_bar': y_bar, 'y_underline': y_underline, 'b_at_max_U': result.x\n",
        "                                }\n",
        "\n",
        "# Output the best parameters and the corresponding maximum U value\n",
        "print(f\"Best parameters: {best_params}\")\n",
        "print(f\"Maximum U: {max_U}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        },
        "id": "y7v0GvSEy8do",
        "outputId": "bdca25ca-c9a2-4a03-9cdf-98153505a528"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-133-f316f44b281c>\u001b[0m in \u001b[0;36m<cell line: 28>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     39\u001b[0m                             \u001b[0mb_bar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my_bar\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mbeta\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m                             \u001b[0mb_underline\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my_underline\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mbeta\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m                             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminimize_scalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcalculate_U\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb_underline\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb_bar\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'bounded'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m                             \u001b[0;31m# Update the best parameters if the current maximum U is greater than the previous maximum\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize_scalar\u001b[0;34m(fun, bracket, bounds, args, method, tol, options)\u001b[0m\n\u001b[1;32m    933\u001b[0m             raise ValueError('The `bounds` parameter is mandatory for '\n\u001b[1;32m    934\u001b[0m                              'method `bounded`.')\n\u001b[0;32m--> 935\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_minimize_scalar_bounded\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    936\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'golden'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    937\u001b[0m         res = _recover_from_bracket_error(_minimize_scalar_golden,\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/optimize/_optimize.py\u001b[0m in \u001b[0;36m_minimize_scalar_bounded\u001b[0;34m(func, bounds, args, xatol, maxiter, disp, **unknown_options)\u001b[0m\n\u001b[1;32m   2336\u001b[0m         \u001b[0msi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mrat\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2337\u001b[0m         \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mxf\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msi\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmaximum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2338\u001b[0;31m         \u001b[0mfu\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2339\u001b[0m         \u001b[0mnum\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2340\u001b[0m         \u001b[0mfmin_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfu\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-133-f316f44b281c>\u001b[0m in \u001b[0;36mcalculate_U\u001b[0;34m(b)\u001b[0m\n\u001b[1;32m     22\u001b[0m     \u001b[0mq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mq_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_tau_b\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_bar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0mintegral_1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msecond_part\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_tau_b\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_bar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m     \u001b[0mintegral_2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mquad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthird_part\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_tau_b\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mfirst_part\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mbeta\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0my_bar\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mintegral_1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mintegral_2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/integrate/_quadpack_py.py\u001b[0m in \u001b[0;36mquad\u001b[0;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points, weight, wvar, wopts, maxp1, limlst, complex_func)\u001b[0m\n\u001b[1;32m    463\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    464\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mweight\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 465\u001b[0;31m         retval = _quad(func, a, b, args, full_output, epsabs, epsrel, limit,\n\u001b[0m\u001b[1;32m    466\u001b[0m                        points)\n\u001b[1;32m    467\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/integrate/_quadpack_py.py\u001b[0m in \u001b[0;36m_quad\u001b[0;34m(func, a, b, args, full_output, epsabs, epsrel, limit, points)\u001b[0m\n\u001b[1;32m    575\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mpoints\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    576\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0minfbounds\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 577\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_qagse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    578\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    579\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0m_quadpack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_qagie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbound\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0minfbounds\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsabs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepsrel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlimit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-130-df8135e5eece>\u001b[0m in \u001b[0;36mthird_part\u001b[0;34m(y2, gamma, beta, y3)\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     32\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mthird_part\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 33\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mbeta\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     34\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     35\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mcalculate_U\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_bar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_underline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from google.colab import files\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "y3= 300\n",
        "y1= 70\n",
        "gamma= 0.95\n",
        "beta= 0.96\n",
        "R= 1.05\n",
        "y_bar= 180\n",
        "y_underline= 140\n",
        "\n",
        "\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "b_values_case_3 = np.linspace(b_bar, 150, num_points)\n",
        "\n",
        "# Initialize arrays to store u, q_tau, and term1 values for each b\n",
        "u_values_case_1 = np.zeros(num_points)\n",
        "u_values_case_2 = np.zeros(num_points)\n",
        "u_values_case_3 = np.zeros(num_points)\n",
        "q_values_case_1 = np.zeros(num_points)\n",
        "q_values_case_2 = np.zeros(num_points)\n",
        "q_values_case_3 = np.zeros(num_points)\n",
        "term1_values_case_1 = np.zeros(num_points)\n",
        "term1_values_case_2 = np.zeros(num_points)\n",
        "term1_values_case_3 = np.zeros(num_points)\n",
        "term2_term4_values_case_1 = np.zeros(num_points)\n",
        "term2_term4_values_case_2 = np.zeros(num_points)\n",
        "term2_term4_values_case_3 = np.zeros(num_points)\n",
        "term3_term5_values_case_1 = np.zeros(num_points)\n",
        "term3_term5_values_case_2 = np.zeros(num_points)\n",
        "term3_term5_values_case_3 = np.zeros(num_points)\n",
        "y_tau_values = np.zeros(num_points)\n",
        "\n",
        "# Calculate values for each case\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta * psi))\n",
        "    y_tau_values[i] = y_tau\n",
        "    q_tau = (1 / R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "    q_values_case_1[i] = q_tau\n",
        "    term1_values_case_1[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma *y3) * (y_tau - y_underline)\n",
        "    term2_term4_values_case_1[i] = term2 + term4\n",
        "    term3_term5_values_case_1[i] = term3 + term5\n",
        "    u_values_case_1[i] = term1_values_case_1[i] + term2 + term3 + term4 + term5\n",
        "\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1 / R)\n",
        "    q_values_case_2[i] = q_tau\n",
        "    term1_values_case_2[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(\n",
        "        y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    term4 = 0\n",
        "    term5 = 0\n",
        "    term2_term4_values_case_2[i] = term2 + term4\n",
        "    term3_term5_values_case_2[i] = term3 + term5\n",
        "    u_values_case_2[i] = term1_values_case_2[i] + term2 + term3\n",
        "\n",
        "for i, b in enumerate(b_values_case_3):\n",
        "    q_values_case_3[i] = 0\n",
        "    term1_values_case_3[i] = np.log(y1)\n",
        "    term2 = 0\n",
        "    term3 = 0\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_bar * np.log(gamma * y_bar) - y_underline * np.log(gamma * y_underline) - (y_bar - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma * y3) * (y_bar - y_underline)\n",
        "    term2_term4_values_case_3[i] = term2 + term4\n",
        "    term3_term5_values_case_3[i] = term3 + term5\n",
        "    u_values_case_3[i] = term1_values_case_3[i] + term4 + term5\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "\n",
        "plt.subplot(1, 1, 1)\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.title('Total Utility')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 15)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "\n",
        "plt.tight_layout()\n",
        "#plt.savefig('case2.png', dpi=300, bbox_inches='tight')\n",
        "plt.show()\n",
        "#files.download('case2.png')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 407
        },
        "id": "2MfaTr7a3mUZ",
        "outputId": "a6f556ab-7826-4732-afab-9debca7e6de9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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N3ZEIL0dARERElKtcbZy2bduGVatWIRQKQSmFTZs2Dbnt17/+dSil8OCDD56y+oiIiIhSudo4dXR0YM6cOdiwYcOw223cuBGvvfYaQqHQCT+XUjy4lkopA8XFU5lLCmYiYy4y5iJjLk7MRGYohanFxTA8turd1aVmy5cvx/Lly4fd5uDBg7juuuuwZcsWrFy58oSfSynzhL82Fyllory81u0ysgozkTEXGXORMRcnZiIzlUJtebnbZWQsq9tfy7KwZs0a3HLLLZg9e/aoHourGey0TuDYsbeZSwpmImMuMuYiYy5OzESW0BpvHzvmuVV1WX1xo/vuuw8+nw/XX3992l8Ti8UQi8WSt9va2gAAlhWDZfUA6D1sqpQJrRO2VQ7945YVB6BTxk0oZQwz3mOrof+aUVrH0xo3jAJobQ36T6VgGL5hxuXa052T1hai0QMoLZ0Fw/ClbO/dOY12P1lWD6LRAwgGZ8MwjJyY00jj6cypP5fS0lnw+YpyYk7O8cznZFndfbnMhGkW5sScxmI/JRKxZC6GUZATcxrtfgK0LRMvzsnScWjDQlxbiFsWfIYBS2tb06PQe22mhNa2lXKGUjCVcowntMaBaBSzSkvhMwaO45hKwVAKcctCakvVP95j2Vcn+vre6osPasCGGi8Qao9b6a94zNrG6a233sIPfvAD7Ny5M6Orfq9fvx533XWXY/z48Tp0dxcDAIqLp6K8vBbh8DuIRg8ktwkEZiIYnIWjR3cgFjuSHC8rm4uSkmk4fHgb4vFIcryycj4KCyfi0KHnbd9s1dWLYZpFaGzcbKshFFqBRKITzc11yTGlfJg8eSVisRa0tNQnx32+AGpqliAa/QjhcENy3O+vQlXVArS17UEksjs5numcgsFzAQAtLdsRj7fnxJzGaj9pHUc83pVTcxqL/RQO70RV1cKcmtNY7Kempq05NyfgxPdTU9PWZC65MqfR7qeJEz9ry8SLczrWUQ/MBuo6gEDMhyU1NfgoGkVDOJzcvsrvx4KqKuxpa8PuyEAtU4uLUVtejnfCYRyIRpPjM8aPBwDsDIfRknLAY25ZGaaVlGDb4cOIxAdqn19ZiYmFhXj+0CFbM7S4uhpFponNjY22Oa0IhdCZSKCuuXlgfyiFlZMnoyUWQ31LS3Lc6O5GupTW2XGMTCmFjRs3YvXq1QCABx98EOvWrYOR0oUmEgkYhoEpU6bgww8/FB9HOuI0ZcoUbN58CJWVFX3PlZ0d/ak+4nTo0O9RU7OMR5xSjjg1NW3FpEnL++r3/pxGGk/3iFNT01bU1CzjEadBR5x6c/k8jzil1J5IdCZz4RGn3toBjcbGzclMvDinzuMdaN/xHhbOi6M4OG7MjjhtOXQIy2pqXD/iFGlvR8WSJWhtbUVpaSmGk7VHnNasWYOlS5faxi6++GKsWbMGV1999ZBf5/f74ff7HeOG4U/5hu3V+43lPGk8tZFIb7xAHFcq/fHe/xTOU86GHpdrT3dOWicQCMyEaY4bYnvvzWnk8eFrV8pAIDAThmFCKZUTc0pnfKQ59edimuOGrd1Lc3KOZz4npVRfLv7kY3p9TpJM52Sa/pRcBp7Hy3Ma7X4a+Hnrd9TplTkZygdlGfApI9nkGH2NzGBmX6M00rihNWYGAhhnmuL2qc1UqoKhxod4d0oaH1z7UM8lcbVxam9vx969e5O39+3bh4aGBpSXl2Pq1KmoqKiwbV9QUICamhrMnDkz4+fiqjo7pUwEg7PcLiOrMBMZc5ExFxlzcWImMlMpzAoG3S4jY66uqnvzzTdRW1uL2treZZrr1q1DbW0tbr/99jF/rsGHH/OdZcVx5Mj2vsO7BDCToTAXGXORMRcnZiKLWxa2HzmS0YnZ2cDVI06LFi1CJqdYDXVeUzqy5FSuLKL7TjBkLgOYiYy5yJiLjLk4MROJBnAkFvNcKll9HSciIiKibMLGiYiIiChNedM48eRwO6VMlJXNZS4pmImMuciYi4y5ODETmakU5paViSvqslnWXo5grPHDFe2UMlBSMs3tMrIKM5ExFxlzkTEXJ2YiM5TCtJISt8vIWN50E1xVZ2dZcTQ1vcRVHimYiYy5yJiLjLk4MRNZ3LLwUlOT51bV5VHj5LXz9k823Xd5fuYygJnImIuMuciYixMzkWgAkXjcc6nkTeNERERENFpsnIiIiIjSlDeNE1cz2CllorJyPnNJwUxkzEXGXGTMxYmZyEylML+ykqvqshVX1dkpZaCwcKLbZWQVZiJjLjLmImMuTsxEZiiFiYWFbpeRsbzpJiyrx+0Ssopl9eDgwd8ylxTMRMZcZMxFxlycmImsx7Lw24MH0cNVdeQVvESDEzORMRcZc5ExFydmIot7cMU7GyciIiKiNLFxIiIiIkpT3jROSuXNefBpUcqH6urFzCUFM5ExFxlzkTEXJ2Yi8ymFxdXV8HlsVV3eNE7kZJpFbpeQdZiJjLnImIuMuTgxE1mR6b1LNORN48QT8+y0jqOxcTNzScFMZMxFxlxkzMWJmcjiWmNzY6PnThDPm8aJiIiIaLTYOBERERGliY0TERERUZrypnHiagY7pXwIhVYwlxTMRMZcZMxFxlycmInMpxRWhEJcVUfekUh0ul1C1mEmMuYiYy4y5uLETGSdiYTbJWQsbxonrmaw0zqO5uY65pKCmciYi4y5yJiLEzORxbVGXXMzV9URERER5So2TkRERERpYuOUx3iiohMzkTEXGXORMRcnZiLz2onhAKC09tibixlqa2tDMBjEli2tqKgodbscIiIiz+k63olI/bu4cH4cxRPGuV3OmGtrb0dw0SK0traitHT4XiFvjjhpbbldQlbR2kJX12HmkoKZyJiLjLnImIsTM5FZWuNwVxcsjx2/yaPGyXtLHk8mrRNoaalnLimYiYy5yJiLjLk4MRNZQmvUt7QgwcaJiIiIKDexcSIiIiJKU940TsqDZ+6fXAo+XwAAcxnATGTMRcZcZMzFiZlIFICAz+e5VPJmfSSXgtoZhg81NUvcLiOrMBMZc5ExFxlzcWImMp9hYElNjdtlZCxvjjhxNYOd1hY6OvYzlxTMRMZcZMxFxlycmInM0hr7Ozq4qi5bcTWDndYJhMMNzCUFM5ExFxlzkTEXJ2YiS2iNhnCYq+qIiIiIchUbJyIiIqI05U3jxFV1gyn4/VXgKo9UzETGXGTMRcZcnJiJRAGo8vs9l0reLDXjqjo7w/ChqmqB22VkFWYiYy4y5iJjLk7MROYzDCyoqnK7jIzlzREnnpRnp3UCra27mEsKZiJjLjLmImMuTsxEltAau1pbeXJ4tuIyUDutLUQiu5lLCmYiYy4y5iJjLk7MRGZpjd2RCC9HkIlt27Zh1apVCIVCUEph06ZNtvvvvPNOzJo1CyUlJSgrK8PSpUvx+uuvu1MsERER5T1XG6eOjg7MmTMHGzZsEO8/88wz8cgjj+CPf/wjXn31VZx22mlYtmwZjhw5coorJSIiInL55PDly5dj+fLlQ97/D//wD7bbDzzwAH7yk5/gnXfewUUXXZTRcymVN+9KpkUpA8XFU5lLCmYiYy4y5iJjLk7MRGYohanFxTA8turdM0vNuru78fjjjyMYDGLOnDlDbheLxRCLxZK329raAPS+x2xZPQB6v4mVMqF1wvaec/+4ZcUB6JRxE0oZw4z32GroX8GndTytccMogNbWoBMHFQzDN8y4XHsmcyovr4VlxaF1j23cy3Ma7X6aMOEcAAa01jkzp+HG053ThAnnQGsNpZAzc7KPn9icenOxAKicmZOz9kznZCVz0drKkTmNfj+Vlc0ZVKe35mTpOLRhIa4txC0LPsOApbXtxG6F3pVyCa1t5y0ZSsFUShyvLS9H3LLQkzJuKgVDKcQtC6lnP/WP91j2c8V8fY1XfNC5UkONFwi1x630zz/L+sbpueeew+WXX45oNIpJkyZh69atqKysHHL79evX46677nKMh8PPIxYrBgAUF09FeXktwuF3EI0eSG4TCMxEMDgLR4/uQCw28HZgWdlclJRMw+HD2xCPR5LjlZXzUVg4EYcOPW/7ZquuXgzTLEJj42ZbDaHQCiQSnWhurkuOKeXD5MkrEYu1oKWlPjnu8wVQU7ME0ehHCIcbkuN+fxWqqhagrW0PIpHdyfFM5zRhwifQ3X0c3d3HEI+358Scxmo/TZp0MSyrO6fmlIv7iXPinLwyp+rqz+HIke3o7j7m2Tkd66gHZgN1HUAg5sOSmhp8FI2iIRxObl/l92NBVRX2tLVhd2SglqnFxagtL8c74TAORKPJ8TMCAcQSCXQmEjiScsBjblkZppWUYNvhw4jEB2qfX1mJiYWFeP7QIVsztLi6GkWmic2NjbY5rQiF0JlIoK65eWB/KIWVkyejJRZDfUtLctzo7ka6lNbZcTq7UgobN27E6tWrbeMdHR04dOgQWlpa8OMf/xgvvfQSXn/9dUycOFF8HOmI05QpU7B58yFUVlb0PVd2dvSn8jcvrS0cOvR71NQsg2H4Urb37pxGu58sqwdNTVsxadLyvvq9P6eRxtOZU38uNTXL4PMV5cScnOOZz8myuvty+TxMszAn5jQW+ymR6EzmYhgFOTGn0e4nQKOxcXMyEy/OqfN4B9p3vIeF8+IoDo4bkyNOCa2x5dAhLKupgc8YeBvTjSNOkfZ2VCxZgtbWVpSWlmI4WX/EqaSkBDNmzMCMGTPw6U9/GmeccQZ+8pOf4F/+5V/E7f1+P/x+v2NcqYKUb9j+MRNKmY5tUxuJ9MYLxHGl0h/v/U/hfP976HG59nTn1P+fyTB8Yv1enNPI4+nVrpTq+5M7cxpuPN059deQS3MaGD+ROelkvf2P6f05OWU6p/5xw7D/zPXynEa7nwZ+3qb/OpRtczKUD8oy4FNGsskx+hqZwcy+RmnE8b4GyGcYKDCc+9snjAEQtwWAgiHOlZLGB9c+1HNJPHemmmVZtiNKRERERKeKq0ec2tvbsXfv3uTtffv2oaGhAeXl5aioqMA999yDSy65BJMmTUJLSws2bNiAgwcP4ktf+lLGz8XVDHZKGQgEZjKXFMxExlxkzEXGXJyYicxQCjMDAa6qy8Sbb76JxYsXJ2+vW7cOALB27Vo89thj2LVrF372s5+hpaUFFRUVOP/88/GHP/wBs2fPzvi5pEOe+UwpE8HgLLfLyCrMRMZcZMxFxlycmInMVAqzgkG3y8iYq43TokWLMNy56c8888yYPdfgE97ynWXFcfToDlRUzBvyvfF8w0xkzEXGXGTMxYmZyOKWhR1Hj2JeRUVG5xi5zTuVjlKWLB7MIrpvSStzGcBMZMxFxlxkzMWJmUg0gCOxmOdSyZvGiYiIiGi02DgRERERpSlvGieeHG6nlImysrnMJQUzkTEXGXORMRcnZiIzlcLcsjLxmk/ZLG/OUuMyUDulDJSUTHO7jKzCTGTMRcZcZMzFiZnIDKUwraTE7TIyljfdBFfV2VlWHE1NL/Vdpp8AZjIU5iJjLjLm4sRMZHHLwktNTRl9wG42yKPGyWvn7Z9suu8DIZnLAGYiYy4y5iJjLk7MRKIBROJxz6WSN40TERER0WixcSIiIiJKU940TlzNYKeUicrK+cwlBTORMRcZc5ExFydmIjOVwvzKSq6qy1ZcVWenlIHCwolul5FVmImMuciYi4y5ODETmaEUJhYWul1GxvKmm7CsHrdLyCqW1YODB3/LXFIwExlzkTEXGXNxYiayHsvCbw8eRA9X1ZFX8BINTsxExlxkzEXGXJyYiSzuwRXvbJyIiIiI0sTGiYiIiChNedM4KZU358GnRSkfqqsXM5cUzETGXGTMRcZcnJiJzKcUFldXw+exVXV50ziRk2kWuV1C1mEmMuYiYy4y5uLETGRFpvcu0ZA3jRNPzLPTOo7Gxs3MJQUzkTEXGXORMRcnZiKLa43NjY2eO0E8bxonIiIiotFi40RERESUJjZORERERGnKm8aJqxnslPIhFFrBXFIwExlzkTEXGXNxYiYyn1JYEQpxVR15RyLR6XYJWYeZyJiLjLnImIsTM5F1JhJul5CxvGmcuJrBTus4mpvrmEsKZiJjLjLmImMuTsxEFtcadc3NXFVHRERElKvYOBERERGliY1THuOJik7MRMZcZMxFxlycmInMayeGA4DS2mNvLmaora0NwWAQW7a0oqKi1O1yiIiIPKfreCci9e/iwvlxFE8Y53Y5Y66tvR3BRYvQ2tqK0tLhe4W8OeKkteV2CVlFawtdXYeZSwpmImMuMuYiYy5OzERmaY3DXV2wPHb8Jo8aJ+8teTyZtE6gpaWeuaRgJjLmImMuMubixExkCa1R39KCBBsnIiIiotzExomIiIgoTXnTOCkPnrl/cin4fAEAzGUAM5ExFxlzkTEXJ2YiUQACPp/nUsmb9ZFcCmpnGD7U1Cxxu4yswkxkzEXGXGTMxYmZyHyGgSU1NW6XkbG8OeLE1Qx2Wlvo6NjPXFIwExlzkTEXGXNxYiYyS2vs7+jgqrpsxdUMdlonEA43MJcUzETGXGTMRcZcnJiJLKE1GsJhrqojIiIiylVsnIiIiIjSlDeNE1fVDabg91eBqzxSMRMZc5ExFxlzcWImEgWgyu/3XCp5s9SMq+rsDMOHqqoFbpeRVZiJjLnImIuMuTgxE5nPMLCgqsrtMjLm6hGnbdu2YdWqVQiFQlBKYdOmTcn7enp6cOutt+Lcc89FSUkJQqEQrrzySjQ2Np7Qc/GkPDutE2ht3cVcUjATGXORMRcZc3FiJrKE1tjV2sqTwzPR0dGBOXPmYMOGDY77otEodu7cidtuuw07d+7EM888g927d+OSSy45oefiMlA7rS1EIruZSwpmImMuMuYiYy5OzERmaY3dkYjnLkfg6vtXy5cvx/Lly8X7gsEgtm7daht75JFHMG/ePBw4cABTp049FSUSERERJXnqxJ/W1lYopTBhwoQht4nFYojFYsnbbW1tAACte2BZPQAApQwoZULrhO03gP5xy4oD0CnjJpQyhhnvsdXQfz6V1vG0xg2jAFpbgw7jKhiGb5hxufZ059S/Te94ao3endNo91P//Vrrvj/en9NI4+nMqf85LCvet7335+Qcz3xOA7n05MycxmI/peaSK3Ma7X7qZ398b83J0nFow0JcW4hbFnyGAUtr29tsCr3nLSW0th1FMpSCqZRjvP9r45b9SJypFAylELcsaGG8Z9D2vr7FX/FBR66GGi8Qah9cw3A80zh1dXXh1ltvxRVXXIHS0tIht1u/fj3uuusux/jx43Xo7i4GABQXT0V5eS3C4XcQjR5IbhMIzEQwOAtHj+5ALHYkOV5WNhclJdNw+PA2xOOR5Hhl5XwUFk7EoUPP277ZqqsXwzSL0Ni42VZDKLQCiUQnmpvrkmNK+TB58krEYi1oaalPjvt8AdTULEE0+hHC4YbkuN9fhaqqBWhr24NIZHdyPNM5TZjwCRQXT0VLy3bE4+05Maex2k+AhXg8klNzGov9FA6/nXNzGov91NS0NefmBJz4fmpq2prMJVfmNNr9VF39OYwbV57MxItzOtZRD8wG6jqAQMyHJTU1+CgaRUM4nNy+yu/Hgqoq7Glrw+7IQC1Ti4tRW16Od8JhHIhGk+NnBAKYWlyMt8NhHEk54DG3rAzTSkqw7fBhROIDtc+vrMTEwkI8f+iQrRlaXF2NItPE5kHnQK8IhdCZSKCuuXlgfyiFlZMnoyUWQ31LS3Lc6O5GupTW2fHmolIKGzduxOrVqx339fT04O/+7u/w17/+FS+//PKwjZN0xGnKlCn43e9aUFFR2vdc2dnR58NvXpwT58Q5cU6ck/fm1Hm8A+073sPCeXEUB8eNyRGn/vGhjiydyiNOkfZ2VCxZgtbW1mF7DMADR5x6enpw2WWXYf/+/XjppZdGnJDf74ff73eMK2XAMAoGjZlQynRsaxhyLEOPF4jjSqU/3vufwnmu/tDjcu3pzknrBI4dextlZZ9I/oexb++9OY08PnztvR+L8E5fJmZOzCmd8ZHmlJrLcLV7aU7O8cznZP9+MZLjEq/MSZLpnADD9v9o4Hm9O6fR7qfBP1vSqT3b5mQoH5RlwKcM+Iy+7/e+RmYws68hGmk8oTXePnYMnygrSzY5qfqfZ7CCocaHuF6jND649qGeS5LVF8Dsb5r27NmDF154ARUVFSf8WFzNYKe1hWj0AHNJwUxkzEXGXGTMxYmZyCytcSAa5aq6TLS3t2Pv3r3J2/v27UNDQwPKy8sxadIkXHrppdi5cyeee+45JBIJNDU1AQDKy8sxbtw4t8omIiKiPOVq4/Tmm29i8eLFydvr1q0DAKxduxZ33nknnn32WQDA3LlzbV9XV1eHRYsWnaoyiYiIiAC43DgtWrQIw52bPpbnrUvvl+czpQwEAjOZSwpmImMuMuYiYy5OzERmKIWZgYB4nlQ2y/qTw8eKdJJdPlPKRDA4y+0ysgozkTEXGXORMRcnZiIzlcKsYNDtMjKWN+3v4CWW+c6y4jhyZLvjApj5jJnImIuMuciYixMzkcUtC9uPHMno4pPZII8aJ2+dtX/y6b6LqDGXAcxExlxkzEXGXJyYiUQDOBKLeS6VvGmciIiIiEYro3OcysrKoISTuILBIM4880x885vfxOc///kxK46IiIgom2TUOD344IPi+PHjx/HWW2/hC1/4An79619j1apVY1HbmOLJ4XZKmSgrm8tcUjATGXORMRcZc3FiJjJTKcwtKxOvMp7NMmqc1q5dO+z9c+fOxfr167O0ceK7kqmUMlBSMs3tMrIKM5ExFxlzkTEXJ2YiM5TCtJISt8vI2Jh2E1/4whewa9eusXzIMcNVdXaWFUdT00tc5ZGCmciYi4y5yJiLEzORxS0LLzU15fequlgslrUfhcJVdYNpxOMRcJVHKmYiYy4y5iJjLk7MRKIBROJxz6Uypo3TT37yE8fHoxARERHliozOcer/LLnBWltbsXPnTrz//vvYtm3bmBRGRERElG0yapzefvttcby0tBSf//zn8cwzz2D69OljUthY42oGO6VMVFbOZy4pmImMuciYi4y5ODETmakU5ldW5vaqurq6upNVx0nHVXV2ShkoLJzodhlZhZnImIuMuciYixMzkRlKYWJhodtlZCxvugnL6nG7hKxiWT04ePC3zCUFM5ExFxlzkTEXJ2Yi67Es/PbgQfTk86o68hZeosGJmciYi4y5yJiLEzORxT244p2NExEREVGa2DgRERERpSlvGielMjoPPucp5UN19WLmkoKZyJiLjLnImIsTM5H5lMLi6mr4PLaqLm8aJ3IyzSK3S8g6zETGXGTMRcZcnJiJrMj03iUa8qZx4ol5dlrH0di4mbmkYCYy5iJjLjLm4sRMZHGtsbmx0XMniOdN40REREQ0WmyciIiIiNLExomIiIgoTXnTOHE1g51SPoRCK5hLCmYiYy4y5iJjLk7MROZTCitCIa6qI+9IJDrdLiHrMBMZc5ExFxlzcWImss5Ewu0SMpY3jRNXM9hpHUdzcx1zScFMZMxFxlxkzMWJmcjiWqOuuZmr6oiIiIhyFRsnIiIiojSxccpjPFHRiZnImIuMuciYixMzkXntxHAAUFp77M3FDLW1tSEYDGLLllZUVJS6XQ4REZHndB3vRKT+XVw4P47iCePcLmfMtbW3I7hoEVpbW1FaOnyvkDdHnLS23C4hq2htoavrMHNJwUxkzEXGXGTMxYmZyCytcbirC5bHjt/kUePkvSWPJ5PWCbS01DOXFMxExlxkzEXGXJyYiSyhNepbWpBg40RERESUm9g4EREREaUpbxon5cEz908uBZ8vAIC5DGAmMuYiYy4y5uLETCQKQMDn81wqebM+kktB7QzDh5qaJW6XkVWYiYy5yJiLjLk4MROZzzCwpKbG7TIyljdHnLiawU5rCx0d+5lLCmYiYy4y5iJjLk7MRGZpjf0dHVxVl624msFO6wTC4QbmkoKZyJiLjLnImIsTM5EltEZDOMxVdURERES5io0TERERUZpcbZy2bduGVatWIRQKQSmFTZs22e5/5plnsGzZMlRUVEAphYaGhhN+Lq6qG0zB768CV3mkYiYy5iJjLjLm4sRMJApAld/vuVRcbZw6OjowZ84cbNiwYcj7P/OZz+C+++4b9XNxVZ2dYfhQVbUAhsFc+jETGXORMRcZc3FiJjKfYWBBVRV8hrfe/HJ1Ly5fvhzLly8f8v41a9YAAD788MNRPxdPyrPTOoG2tj0oLT0DSplul5MVmImMuciYi4y5ODETWUJr7GlrwxmlpTA99K6Qt9q8UeAyUDutLUQiu5lLCmYiYy4y5iJjLk7MRGZpjd2RiOcuR5Bzxw1jsRhisVjydltbGwBA6x5YVg8AQCkDSpnQOmH7Ru4ft6w4AJ0ybkIpY5jxHlsN/W8Lah1Pa9wwCqC1NeiomIJh+IYZl2tPd0792/SOp9bo3TmNdj/136+17vvj/TmNNJ7OnPqfw7Lifdt7f07O8cznNJBLT87MaSz2U2ouuTKn0e6nfvbH99acLB2HNizEtYW4ZcFnGLC0tl1KQKH37beE1rZmyFAKplKO8f6vjVv2htJUCoZSiFsWtDDeM2h7X9/RqvigBmyo8QKh9sE1DCfnGqf169fjrrvucowfP16H7u5iAEBx8VSUl9ciHH4H0eiB5DaBwEwEg7Nw9OgOxGJHkuNlZXNRUjINhw9vQzweSY5XVs5HYeFEHDr0vO2brbp6MUyzCI2Nm201hEIrkEh0orm5LjmmlA+TJ69ELNaClpb65LjPF0BNzRJEox8hHG5Ijvv9VaiqWoC2tj2IRHYnxzOdUzB4LgCgpWU74vH2nJjTWO0nreOIx7tyak5jsZ/C4Z2oqlqYU3Mai/3U1LQ15+YEnPh+amramswlV+Y02v00ceJnbZl4cU7HOuqB2UBdBxCI+bCkpgYfRaNoCIeT21f5/VhQVYU9bW3YHRmoZWpxMWrLy/FOOIwD0WhyfMb48QCAneEwWlIOeMwtK8O0khJsO3wYkfhA7fMrKzGxsBDPHzpka4YWV1ejyDSxubHRNqcVoRA6EwnUNTcP7A+lsHLyZLTEYqhvaUmOG93dSJfSOjuOkSmlsHHjRqxevdpx34cffojp06fj7bffxty5c4d9HOmI05QpU7B5czMqK8v6nis7O/pT+ZsXABw//i6CwbOhlJGyvXfnNNr9pHUCx4//CWVlc/qe1/tzGmk8nTn15zJhwjkwTX9OzMk5nvmctI735TIbhjEuJ+Y0NkecYslcerf1/pxGu5+UUjh27P8wYcLZGDjHyVtz6jzegfYd72HhvDiKg+PG5IiTBvCn48dxdjAII+UcJzeOOEXa21GxZAlaW1tRWlqK4eTcESe/3w+/3+8YN81CGEaBbaz3G8t5ot5QKx+GHi8Qx5VKf7z3P4XzlLOhx+XaM5lTeXmtWF/v9t6c0/DjI9VegIqKTwnjqdt6bU4jj488p8G55MKcBo+fyJx8tlwGxp28MyenTOdkmoWOXHqf17tzGov9VFHxySEewxtzMpQPyjLgU0ZyFZzR18gMZvY1SumM15aXi3UAGHK1XcFQ40OcYC6ND649k5V9rp4c3t7ejoaGhuT1mfbt24eGhgYcONB7ePLYsWNoaGjAe++9BwDYvXs3Ghoa0NTUlPFzcVWdndYJHDv2NnNJwUxkzEXGXGTMxYmZyBJa4+1jx/iRK5l48803UVtbi9ra3iMf69atQ21tLW6//XYAwLPPPova2lqsXLkSAHD55ZejtrYWjz32WMbPxdUMdlpbiEYPMJcUzETGXGTMRcZcnJiJzNIaB6JRrqrLxKJFizDcKVZXXXUVrrrqqlNXEBEREdEw8uY6TkRERESjlTeNk3SyXj5TykAgMJO5pGAmMuYiYy4y5uLETGSGUpgZCIgnmGeznFtVNxRe5t5OKRPB4Cy3y8gqzETGXGTMRcZcnJiJzFQKs4JBt8vIWN60v4OvTZHvLCuOI0e2O64cns+YiYy5yJiLjLk4MRNZ3LKw/ciRjK7anQ3yqHHy1ln7J5/uu/oscxnATGTMRcZcZMzFiZlINIAjsZjnUsmbxomIiIhotNg4EREREaUpbxonnhxup5SJsrK5zCUFM5ExFxlzkTEXJ2YiM5XC3LIy8eNZslkerarLmx4xLUoZKCmZ5nYZWYWZyJiLjLnImIsTM5EZSmFaSYnbZWQsb7oJrqqzs6w4mppe4iqPFMxExlxkzEXGXJyYiSxuWXipqYmr6rIVV9UNphGPR8BVHqmYiYy5yJiLjLk4MROJBhCJxz2XSt40TkRERESjxcaJiIiIKE150zhxNYOdUiYqK+czlxTMRMZcZMxFxlycmInMVArzKyu5qi5bcVWdnVIGCgsnul1GVmEmMuYiYy4y5uLETGSGUphYWOh2GRnLm27CsnrcLiGrWFYPDh78LXNJwUxkzEXGXGTMxYmZyHosC789eBA9XFVHXsFLNDgxExlzkTEXGXNxYiayuAdXvLNxIiIiIkoTGyciIiKiNOVN46RU3pwHnxalfKiuXsxcUjATGXORMRcZc3FiJjKfUlhcXQ2fx1bV5U3jRE6mWeR2CVmHmciYi4y5yJiLEzORFZneu0RD3jROPDHPTus4Ghs3M5cUzETGXGTMRcZcnJiJLK41Njc2eu4E8bxpnIiIiIhGi40TERERUZrYOBERERGlKW8aJ65msFPKh1BoBXNJwUxkzEXGXGTMxYmZyHxKYUUoxFV15B2JRKfbJWQdZiJjLjLmImMuTsxE1plIuF1CxvKmceJqBjut42hurmMuKZiJjLnImIuMuTgxE1lca9Q1N3NVHREREVGuYuNERERElCY2TnmMJyo6MRMZc5ExFxlzcWImMq+dGA4ASmuPvbmYoba2NgSDQWzZ0oqKilK3yyEiIvKcruOdiNS/iwvnx1E8YZzb5Yy5tvZ2BBctQmtrK0pLh+8V8uaIk9aW2yVkFa0tdHUdZi4pmImMuciYi4y5ODETmaU1Dnd1wfLY8Zs8apy8t+TxZNI6gZaWeuaSgpnImIuMuciYixMzkSW0Rn1LCxJsnIiIiIhyExsnIiIiojTlTeOkPHjm/sml4PMFADCXAcxExlxkzEXGXJyYiUQBCPh8nkslb9ZHcimonWH4UFOzxO0ysgozkTEXGXORMRcnZiLzGQaW1NS4XUbG8uaIE1cz2GltoaNjP3NJwUxkzEXGXGTMxYmZyCytsb+jg6vqshVXM9hpnUA43MBcUjATGXORMRcZc3FiJrKE1mgIh7mqjoiIiChXudo4bdu2DatWrUIoFIJSCps2bbLdr7XG7bffjkmTJqGoqAhLly7Fnj173CmWiIiI8p6rjVNHRwfmzJmDDRs2iPfff//9eOihh/DYY4/h9ddfR0lJCS6++GJ0dXVl/FxcVTeYgt9fBa7ySMVMZMxFxlxkzMWJmUgUgCq/33OpZM1n1SmlsHHjRqxevRpA79GmUCiEm2++Gd/85jcBAK2traiursYTTzyByy+/PK3H5WfVERERjQ4/q25A1q7R37dvH5qamrB06dLkWDAYxAUXXID6+vohG6dYLIZYLJa83dbWBgBIJLpgWUUAAKUMKGVC64RtlUP/uGXFAeiUcRNKGcOM99hq6L/0gdbxtMYNowBaW4NOHFQwDN8w43Lt6c4JACKRv2D8+OlQykjZ3rtzGu1+0jqBSOQvKC2d2fe83p/TSOPpzKk/l0BgBkzTnxNzco5nPiet4325nA7DGJcTcxqL/WRZsWQuvdt6f06j3U9KKbS2vo9AYDqUMj05J0vHoQ0LcW0hblnwGQYsrW0ndiv0XmIgobVtpZyhFEylHOMawAeRCKaPHw8j5V0hUykYSiFuWbZXrf7xHsu+OtHX97XxQceBhhovEGqPW+mveMzaxqmpqQkAUF1dbRuvrq5O3idZv3497rrrLsf48eMvoru7GABQXDwV5eW1CIffQTR6ILlNIDATweAsHD26A7HYkeR4WdlclJRMw+HD2xCPR5LjlZXzUVg4EYcOPW/7ZquuXgzTLEJj42ZbDaHQCiQSnWhurkuOKeXD5MkrEYu1oKWlPjnu8wVQU7ME0ehHCIcbkuN+fxWqqhagrW0PIpHdyfFM5xQMnotIZDc6Ow8iHm/PiTmN1X4aP346tI7n1JzGYj/19BxHVdXCnJrTWOyn9va9OTcn4MT306FDW5K55MqcRrufJk78LNrb30d7+/uendOxjnpgNlDXAQRiPiypqcFH0SgawuHk9lV+PxZUVWFPWxt2RwZqmVpcjNrycrwTDuNANJocnzF+PPa2t+NodzdaUg54zC0rw7SSEmw7fBiR+EDt8ysrMbGwEM8fOmRrhhZXV6PINLG5sdE2pxWhEDoTCdQ1Nw/sD6WwcvJktMRiqG9pSY4b3d1IV9a+Vbd9+3YsXLgQjY2NmDRpUnK7yy67DEop/PKXvxQfRzriNGXKFGzefAiVlRV9z5WdHf2p/M1LawuHDv0eNTXLYBi+lO29O6fR7ifL6kFT01ZMmrS8r37vz2mk8XTm1J9LTc0y+HxFOTEn53jmc7Ks7r5cPg/TLMyJOY3FfkokOpO5GEZBTsxptPsJ0Ghs3JzMxItz6jzegfYd72HhvDiKg+PG5IhTQmtsOXQIy2pq4DMG3vlw44hTpL0dFUuWePutupq+q4k2NzfbGqfm5mbMnTt3yK/z+/3w+/2OcaUKUr5h+8fMlMOmA1IbifTGC8RxpdIf7/1P4TxXf+hxufZ059T/n8kwfGL9XpzTyOPp1a6U6vuTO3MabjzdOfXXkEtzGhg/kTnpZL39j+n9OTllOqf+ccOw/8z18pxGu58Gft6m/zqUbXMylA/KMuBTRrLJMfoamcHMvkZpxPG+BshnGCgwnPvbJ4wBELcFgIIhFoFJ44NrH+q5JFl7Hafp06ejpqYGL774YnKsra0Nr7/+OubPn5/x40n/CfOZUgaKi6cylxTMRMZcZMxFxlycmInMUApTi4vF5iubuXrEqb29HXv37k3e3rdvHxoaGlBeXo6pU6fixhtvxN13340zzjgD06dPx2233YZQKJR8Oy8TUueez5QyUV5e63YZWYWZyJiLjLnImIsTM5GZSqG2vNztMjLmavv75ptvora2FrW1vd9Q69atQ21tLW6//XYAwD//8z/juuuuwzXXXIPzzz8f7e3t+P3vf4/CwsKMn4uXurfTOoFjx95mLimYiYy5yJiLjLk4MRNZQmu8fewYP3IlE4sWLYLW2vHniSeeANB7rsm//du/oampCV1dXXjhhRdw5plnntBz8cMV7bS2EI0eYC4pmImMuciYi4y5ODETmaU1DkSj/JBfIiIiolzFxomIiIgoTXnTOHE1g51SBgKBmcwlBTORMRcZc5ExFydmIjOUwsxAgKvqshVX1dkpZSIYnOV2GVmFmciYi4y5yJiLEzORmUphVjDodhkZy5v2d/DVUPOdZcVx5Mj2vqvNEsBMhsJcZMxFxlycmIksblnYfuRIRp8Tlw3yqHHy1ln7J5/u+7wj5jKAmciYi4y5yJiLEzORaABHYjHPpZI3jRMRERHRaLFxIiIiIkpT3jROPDncTikTZWVzmUsKZiJjLjLmImMuTsxEZiqFuWVl4gcCZ7M8WlWXNz1iWpQyUFIyze0ysgozkTEXGXORMRcnZiIzlMK0khK3y8hY3nQTXFVnZ1lxNDW9xFUeKZiJjLnImIuMuTgxE1ncsvBSUxNX1WUrrqobTCMej4CrPFIxExlzkTEXGXNxYiYSDSASj3sulbxpnIiIiIhGi40TERERUZrypnHiagY7pUxUVs5nLimYiYy5yJiLjLk4MROZqRTmV1ZyVV224qo6O6UMFBZOdLuMrMJMZMxFxlxkzMWJmcgMpTCxsNDtMjKWN92EZfW4XUJWsaweHDz4W+aSgpnImIuMuciYixMzkfVYFn578CB6uKqOvIKXaHBiJjLmImMuMubixExkcQ+ueGfjRERERJQmNk5EREREacqbxkmpvDkPPi1K+VBdvZi5pGAmMuYiYy4y5uLETGQ+pbC4uho+j62qy5vGiZxMs8jtErIOM5ExFxlzkTEXJ2YiKzK9d4mGvGmceGKendZxNDZuZi4pmImMuciYi4y5ODETWVxrbG5s9NwJ4nnTOBERERGNFhsnIiIiojSxcSIiIiJKU940TlzNYKeUD6HQCuaSgpnImIuMuciYixMzkfmUwopQiKvqyDsSiU63S8g6zETGXGTMRcZcnJiJrDORcLuEjOVN48TVDHZax9HcXMdcUjATGXORMRcZc3FiJrK41qhrbuaqOiIiIqJcxcaJiIiIKE1snPIYT1R0YiYy5iJjLjLm4sRMZF47MRwAlNYee3MxQ21tbQgGg9iypRUVFaVul0NEROQ5Xcc7Eal/FxfOj6N4wji3yxlzbe3tCC5ahNbWVpSWDt8r5E0LrLXldglZRWsLsVgL/P5KKMUDjwAzGQpzkTEXGXNx8nomf/3rX/D3f38uCowCBIrHobioEEV+f++fwpR/p/4pLERx333FQ/y70O9Hl1KYXFqK8UVFyfvMLP/8ujxqnLy35PFk0jqBlpb6vmuLeO8/8snATGTMRcZcZMzFyeuZdHVFEYt1IoZOtJ+CqyqMKyhASV8jVdLXTBUXFg6Mpfzdf//44uLk7ZKiouSf8f1/991f5PdDjfLtwbxpnIiIiChz06bNxP/3X3/Gsdffweyzo0BBAp2xGLq6u9EZi6Gzq6v371gM0ZR/99+OdnWhs6sL0f77+7bp6OxEa2cn4n2P06+7pwfdPT0It7WN+VwMw+httPqaqf7GqnBc+m8/snEiIiKiIRUUjMOkmmkYPzGC2jPG7hynHsvC5sbG5NXDUxutaFcXOjo7xb/7/90x6L72zs7e8f4//ePRaLIxsywL7dEo2qNR4OjRE6o7bxqn0R6ayz0KPl8AAHMZwExkzEXGXGTMxYmZSBSAgM8Hhd7X6P635E4Gy7JsDVWkowPtfU1VR2cnDofD+Kd///f06uaqOiIiIhoOV9UN8N5ZaieIq+rstLbQ0bGfuaRgJjLmImMuMubixExkltbY39EBy2PHb7K+cYpEIrjxxhsxbdo0FBUVYcGCBXjjjTcyfhyuqrPTOoFwuIG5pGAmMuYiYy4y5uLETGQJrdEQDiPBxmlsfe1rX8PWrVvx5JNP4o9//COWLVuGpUuX4uDBg26XRkRERHkmqxunzs5O/M///A/uv/9+XHjhhZgxYwbuvPNOzJgxA48++qjb5REREVGeyepVdfF4HIlEAoWDzrIvKirCq6++Kn5NLBZDLOV6EG1914HQOg7L6gEAKGVAKRNaJ2zvOfePW1YcgE4ZN6GUMcx4j62G/s8k0jqe1rhhFEBra9BhXAXD8A0zLtee7py01vD7q2BZ9kPHXp7TaPeTZcUxblwFtO7NJxfmNNJ4OnPqz8WyEn3be39OzvHM5zSQSzxn5jQW+yk1l1yZ02j3E6AwblxlMhMvzsnScWjDQlxbiFsWfIYBS2vb22wKgM8wkNDadt6SoRRMpRzjltao8vuRsOznfplKwVAKccuCFsZ7Bm3f/3l38UFv+Q01XiDUHrfSP/8sqxunQCCA+fPn4zvf+Q7OOussVFdX4+mnn0Z9fT1mzJghfs369etx1113OcaPH38J3d3FAIDi4qkoL69FOPwOotEDKc83E8HgLBw9ugOx2JHkeFnZXJSUTMPhw9sQj0eS45WV81FYOBGHDj1v+2arrl4M0yxCY+NmWw2h0AokEp1obq5Ljinlw+TJKxGLtaClpT457vMFUFOzBNHoRwiHG5Ljfn8VqqoWoK1tDyKR3cnxE5lTVdUCNDW9lFNzGov9pBQQj0dyak5jsZ/C4Z05N6ex2E9NTc/n3JyAE99PTU3PJ3PJlTmNxX4qKflYMhMvzulYRz0wG6jrAAIxH5bU1OCjaBQN4XBy+yq/HwuqqrCnrQ27IwO1TC0uRm15Od4Jh3EgGk2OzwwEsKCqCtuPHMGRlAMec8vKMK2kBNsOH0YkPlD7/MpKTCwsxPOHDtmaocXV1SgyTWxubLTNaUUohM5EAnXNzQP7QymsnDwZLbEY6ltakuNGdzfSlfWXI/jLX/6Cr371q9i2bRtM08QnP/lJnHnmmXjrrbfw5z//2bG9dMRpypQp2Ly5GZWVZQCyt6M/lb95AUAk8heMHz/d9hEAXp7TaPeT1glEIn9BaenMvuf1/pxGGk9nTv25BAIzYJr+nJiTczzzOWkd78vldBjGuJyY09gccYolc+nd1vtzGu1+UkqhtfV9BALToZSZHPfSnDqPd6B9x3tYOC+O4uC4MTnipAF8EIlg+vjxMFKutejGEadIezsqlizJjQ/5Pf300/HKK6+go6MDbW1tmDRpEv7+7/8eH//4x8Xt/X4//H6/Y1wpE4ZR4Bgb+CYeYBhyLEOPF4jjSqU/3vufwnnK2dDjcu3pzsmyehCJ7O77oe+sx4tzGnl8+NotC2hv34vS0jOhlMqJOaUzPtKcUnMZrnYvzck5nvmcLEunfL8YyXGJV+YkyXxOZjKX1G28PafR7SfL6kF7+/soLZ2R9utQts3JUD4oy4BPGfAZfd/vfY3MYGZfozTSeI9lYXckgtMDARQYzv3tE8YAiNsCQMEQF7qWxgfXPtRzSbL65PBUJSUlmDRpEsLhMLZs2YIvfvGLbpdEREREeSbrjzht2bIFWmvMnDkTe/fuxS233IJZs2bh6quvdrs0IiIiyjNZf8SptbUV1157LWbNmoUrr7wSn/nMZ7BlyxYUFMiHGYciHfbNZ0oZKC6eylxSMBMZc5ExFxlzcWImMkMpTC0uFt/uy2ZZf3L4aPGz6oiIiEaHn1U3IG/aX17q3k7rBI4de5u5pGAmMuYiYy4y5uLETGQJrfH2sWP8yJVsxQ9XtNPaQjR6gLmkYCYy5iJjLjLm4sRMZJbWOBCN8kN+iYiIiHJV1q+qG63+U7iOH48MeT2LfGRZPYhGozh6tI259GEmMuYiYy4y5uKUC5nEIp3o7mpHWziKeGJs5tBjWYhGo2g7enTIazOdKm0dHQAGeobh5HzjdPToUQDAFVdMd7kSIiIiymaRSATBYHDYbXK+cSovLwcAHDhwYMQw8kn/R9F89NFHI64gyBfMRMZcZMxFxlycmIksm3LRWiMSiSAUCo24bc43Tkbf4b9gMOj6jslGpaWlzGUQZiJjLjLmImMuTsxEli25pHtwhSeHExEREaWJjRMRERFRmnK+cfL7/bjjjjvg9/vdLiWrMBcnZiJjLjLmImMuTsxE5tVccv4jV4iIiIjGSs4fcSIiIiIaK2yciIiIiNLExomIiIgoTTnfOG3YsAGnnXYaCgsLccEFF2DHjh1ul+Sa9evX4/zzz0cgEMDEiROxevVq7N692+2yss6///u/QymFG2+80e1SXHfw4EF85StfQUVFBYqKinDuuefizTffdLssVyUSCdx2222YPn06ioqKcPrpp+M73/lOWh/VkCu2bduGVatWIRQKQSmFTZs22e7XWuP222/HpEmTUFRUhKVLl2LPnj3uFHsKDZdLT08Pbr31Vpx77rkoKSlBKBTClVdeicbGRvcKPkVG+n5J9fWvfx1KKTz44IOnrL5M5XTj9Mtf/hLr1q3DHXfcgZ07d2LOnDm4+OKLcfjwYbdLc8Urr7yCa6+9Fq+99hq2bt2Knp4eLFu2DB19n9FDwBtvvIEf/ehH+MQnPuF2Ka4Lh8NYuHAhCgoK8Lvf/Q7vvfcevve976GsrMzt0lx133334dFHH8UjjzyCP//5z7jvvvtw//334+GHH3a7tFOmo6MDc+bMwYYNG8T777//fjz00EN47LHH8Prrr6OkpAQXX3wxurq6TnGlp9ZwuUSjUezcuRO33XYbdu7ciWeeeQa7d+/GJZdc4kKlp9ZI3y/9Nm7ciNdeey2tq3e7SuewefPm6WuvvTZ5O5FI6FAopNevX+9iVdnj8OHDGoB+5ZVX3C4lK0QiEX3GGWforVu36s997nP6hhtucLskV9166636M5/5jNtlZJ2VK1fqr371q7axv/3bv9Vf/vKXXarIXQD0xo0bk7cty9I1NTX6u9/9bnLs+PHj2u/366efftqFCt0xOBfJjh07NAC9f//+U1NUFhgql7/+9a968uTJ+t1339XTpk3T3//+9095benK2SNO3d3deOutt7B06dLkmGEYWLp0Kerr612sLHu0trYCGPg8v3x37bXXYuXKlbbvmXz27LPP4rzzzsOXvvQlTJw4EbW1tfjxj3/sdlmuW7BgAV588UW8//77AID/+7//w6uvvorly5e7XFl22LdvH5qammz/j4LBIC644AL+7B2ktbUVSilMmDDB7VJcZVkW1qxZg1tuuQWzZ892u5wR5exn1bW0tCCRSKC6uto2Xl1djV27drlUVfawLAs33ngjFi5ciHPOOcftclz33//939i5cyfeeOMNt0vJGh988AEeffRRrFu3Dv/6r/+KN954A9dffz3GjRuHtWvXul2ea771rW+hra0Ns2bNgmmaSCQSuOeee/DlL3/Z7dKyQlNTEwCIP3v77yOgq6sLt956K6644oqs+Jw2N913333w+Xy4/vrr3S4lLTnbONHwrr32Wrz77rt49dVX3S7FdR999BFuuOEGbN26FYWFhW6XkzUsy8J5552He++9FwBQW1uLd999F4899lheN06/+tWv8NRTT+EXv/gFZs+ejYaGBtx4440IhUJ5nQulr6enB5dddhm01nj00UfdLsdVb731Fn7wgx9g586dUEq5XU5acvatusrKSpimiebmZtt4c3MzampqXKoqO3zjG9/Ac889h7q6OnzsYx9zuxzXvfXWWzh8+DA++clPwufzwefz4ZVXXsFDDz0En8+HRCLhdomumDRpEs4++2zb2FlnnYUDBw64VFF2uOWWW/Ctb30Ll19+Oc4991ysWbMGN910E9avX+92aVmh/+crf/bK+pum/fv3Y+vWrXl/tOkPf/gDDh8+jKlTpyZ//u7fvx8333wzTjvtNLfLE+Vs4zRu3Dh86lOfwosvvpgcsywLL774IubPn+9iZe7RWuMb3/gGNm7ciJdeegnTp093u6SscNFFF+GPf/wjGhoakn/OO+88fPnLX0ZDQwNM03S7RFcsXLjQcbmK999/H9OmTXOpouwQjUZhGPYfnaZpwrIslyrKLtOnT0dNTY3tZ29bWxtef/31vP3Z26+/adqzZw9eeOEFVFRUuF2S69asWYN33nnH9vM3FArhlltuwZYtW9wuT5TTb9WtW7cOa9euxXnnnYd58+bhwQcfREdHB66++mq3S3PFtddei1/84hf4zW9+g0AgkDzfIBgMoqioyOXq3BMIBBzneZWUlKCioiKvz/+66aabsGDBAtx777247LLLsGPHDjz++ON4/PHH3S7NVatWrcI999yDqVOnYvbs2Xj77bfxwAMP4Ktf/arbpZ0y7e3t2Lt3b/L2vn370NDQgPLyckydOhU33ngj7r77bpxxxhmYPn06brvtNoRCIaxevdq9ok+B4XKZNGkSLr30UuzcuRPPPfccEolE8mdweXk5xo0b51bZJ91I3y+DG8iCggLU1NRg5syZp7rU9Li9rO9ke/jhh/XUqVP1uHHj9Lx58/Rrr73mdkmuASD++elPf+p2aVmHlyPo9b//+7/6nHPO0X6/X8+aNUs//vjjbpfkura2Nn3DDTfoqVOn6sLCQv3xj39cf/vb39axWMzt0k6Zuro68WfJ2rVrtda9lyS47bbbdHV1tfb7/fqiiy7Su3fvdrfoU2C4XPbt2zfkz+C6ujq3Sz+pRvp+GSzbL0egtM6jy90SERERjULOnuNERERENNbYOBERERGliY0TERERUZrYOBERERGliY0TERERUZrYOBERERGliY0TERERUZrYOBERERGliY0TEeWFRYsW4cYbb3S7DCLyODZORERERGli40RERESUJjZORJQ34vE4vvGNbyAYDKKyshK33XYb+HGdRJQJNk5ElDd+9rOfwefzYceOHfjBD36ABx54AP/5n//pdllE5CFK89ctIsoDixYtwuHDh/GnP/0JSikAwLe+9S08++yzeO+991yujoi8gkeciChvfPrTn042TQAwf/587NmzB4lEwsWqiMhL2DgRERERpYmNExHljddff912+7XXXsMZZ5wB0zRdqoiIvIaNExHljQMHDmDdunXYvXs3nn76aTz88MO44YYb3C6LiDzE53YBRESnypVXXonOzk7MmzcPpmnihhtuwDXXXON2WUTkIVxVR0RERJQmvlVHRERElCY2TkRERERpYuNERERElCY2TkRERERpYuNERERElCY2TkRERERpYuNERERElCY2TkRERERpYuNERERElCY2TkRERERpYuNERERElCY2TkRERERp+v8BDyKy6OhvNdgAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from google.colab import files\n",
        "import numpy as np\n",
        "\n",
        "y3= 3\n",
        "y1= 100\n",
        "gamma= 0.98\n",
        "beta= 0.9\n",
        "R= 1\n",
        "y_bar= 120\n",
        "y_underline= 90\n",
        "\n",
        "\n",
        "\n",
        "psi = np.log(y3) - np.log(gamma * y3)\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "b_values_case_3 = np.linspace(b_bar, 150, num_points)\n",
        "\n",
        "# Initialize arrays to store u, q_tau, and term1 values for each b\n",
        "u_values_case_1 = np.zeros(num_points)\n",
        "u_values_case_2 = np.zeros(num_points)\n",
        "u_values_case_3 = np.zeros(num_points)\n",
        "q_values_case_1 = np.zeros(num_points)\n",
        "q_values_case_2 = np.zeros(num_points)\n",
        "q_values_case_3 = np.zeros(num_points)\n",
        "term1_values_case_1 = np.zeros(num_points)\n",
        "term1_values_case_2 = np.zeros(num_points)\n",
        "term1_values_case_3 = np.zeros(num_points)\n",
        "term2_term4_values_case_1 = np.zeros(num_points)\n",
        "term2_term4_values_case_2 = np.zeros(num_points)\n",
        "term2_term4_values_case_3 = np.zeros(num_points)\n",
        "term3_term5_values_case_1 = np.zeros(num_points)\n",
        "term3_term5_values_case_2 = np.zeros(num_points)\n",
        "term3_term5_values_case_3 = np.zeros(num_points)\n",
        "y_tau_values = np.zeros(num_points)\n",
        "\n",
        "# Calculate values for each case\n",
        "for i, b in enumerate(b_values_case_1):\n",
        "    y_tau = b / (1 - gamma * np.exp(-beta * psi))\n",
        "    y_tau_values[i] = y_tau\n",
        "    q_tau = (1 / R) * (y_bar - y_tau) / (y_bar - y_underline) - 0.05\n",
        "    #q_tau = (1 / R)\n",
        "    q_values_case_1[i] = q_tau\n",
        "    term1_values_case_1[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma *y3) * (y_tau - y_underline)\n",
        "    #term3 = term5 = 0\n",
        "    term2_term4_values_case_1[i] = term2 + term4\n",
        "    term3_term5_values_case_1[i] = term3 + term5\n",
        "    u_values_case_1[i] = term1_values_case_1[i] + term2 + term3 + term4 + term5\n",
        "\n",
        "\n",
        "for i, b in enumerate(b_values_case_2):\n",
        "    q_tau = (1 / R)\n",
        "    #q_values_case_2[i] =(1 / R) * (y_bar - 0.9*y_tau) / (y_bar - y_underline)\n",
        "    q_values_case_2[i] = q_tau\n",
        "    term1_values_case_2[i] = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(\n",
        "        y_underline - b) - (y_bar - y_underline))\n",
        "    term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "    term4 = 0\n",
        "    term5 = 0\n",
        "    #term3 = term5 = 0\n",
        "    term2_term4_values_case_2[i] = term2 + term4\n",
        "    term3_term5_values_case_2[i] = term3 + term5\n",
        "    u_values_case_2[i] = term1_values_case_2[i] + term2 + term3\n",
        "\n",
        "\n",
        "for i, b in enumerate(b_values_case_3):\n",
        "    q_values_case_3[i] = 0\n",
        "    #q_values_case_3[i] = (1 / R) * (y_bar - 0.9*y_tau) / (y_bar - y_underline) - 0.09\n",
        "    q_values_case_3[i] = (1 / R)-0.09\n",
        "    term1_values_case_3[i] = np.log(y1)\n",
        "    term2 = 0\n",
        "    term3 = 0\n",
        "    term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_bar * np.log(gamma * y_bar) - y_underline * np.log(gamma * y_underline) - (y_bar - y_underline))\n",
        "    term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma * y3) * (y_bar - y_underline)\n",
        "    #term3 = term5 = 0\n",
        "    term2_term4_values_case_3[i] = term2 + term4\n",
        "    term3_term5_values_case_3[i] = term3 + term5\n",
        "    u_values_case_3[i] = term1_values_case_3[i] + term4 + term5\n",
        "\n",
        "\n",
        "plt.figure(figsize=(12, 14))\n",
        "\n",
        "plt.subplot(3, 2, 1)\n",
        "plt.plot(b_values_case_1, u_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, u_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, u_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U')\n",
        "plt.title('Total Utility')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 15)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "plt.text(0.03, plt.ylim()[0] + 0.07 * (plt.ylim()[1] - plt.ylim()[0]), 'Never Default', color='black', fontsize=8)\n",
        "plt.text(1.23, plt.ylim()[0] + 0.07 * (plt.ylim()[1] - plt.ylim()[0]), 'Always Default', color='black', fontsize=8)\n",
        "\n",
        "\n",
        "plt.subplot(3, 2, 2)\n",
        "plt.plot(b_values_case_1, y_tau_values, label='Case 1', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('$y^{\\\\tau}$')\n",
        "plt.title('$y^{\\\\tau}(b)$ in Indifferent Situation')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 100)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "plt.axhline(y_bar, color='gray', linestyle='--')\n",
        "plt.axhline(y_underline, color='gray', linestyle='--')\n",
        "plt.text(1.22, plt.ylim()[0] + 0.07 * (plt.ylim()[1] - plt.ylim()[0]), 'y2 Lower Bound', color='gray', fontsize=8)\n",
        "plt.text(1.22, plt.ylim()[0] + 0.92 * (plt.ylim()[1] - plt.ylim()[0]), 'y2 Upper Bound', color='gray', fontsize=8)\n",
        "\n",
        "\n",
        "plt.subplot(3, 2, 3)\n",
        "plt.plot(b_values_case_1, q_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, q_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, q_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('$q^{\\\\tau}$')\n",
        "plt.title('Bond Price ($q^{\\\\tau}$)')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 100)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "\n",
        "plt.subplot(3, 2, 4)\n",
        "plt.plot(b_values_case_1, term1_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, term1_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, term1_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U1')\n",
        "plt.title('Utility in Period 1')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 100)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "plt.subplot(3, 2, 5)\n",
        "plt.plot(b_values_case_1, term2_term4_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, term2_term4_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, term2_term4_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U2')\n",
        "plt.title('Expected Utility in Period 2')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 100)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "plt.subplot(3, 2, 6)\n",
        "plt.plot(b_values_case_1, term3_term5_values_case_1, label='Case 1', color='black')\n",
        "plt.plot(b_values_case_2, term3_term5_values_case_2, label='Case 2', color='black')\n",
        "plt.plot(b_values_case_3, term3_term5_values_case_3, label='Case 3', color='black')\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('U3')\n",
        "plt.title('Expected Utility in Period 3')\n",
        "plt.grid(True, linestyle='--')\n",
        "plt.xlim(0, 100)\n",
        "plt.axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "plt.axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "plt.tight_layout()\n",
        "#plt.savefig('case2.png', dpi=300, bbox_inches='tight')\n",
        "plt.show()\n",
        "#files.download('case2.png')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "x6uDRkDBjzLz",
        "outputId": "cf65da66-8dcd-4c46-ec24-dcf22a404a78"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1400 with 6 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Constants\n",
        "y1 = 1.1\n",
        "gamma = 0.8\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.3\n",
        "y_underline = 1\n",
        "y3 = 1.3\n",
        "\n",
        "\n",
        "\n",
        "# Define function to calculate utility values\n",
        "def calculate_utility(y_bar):\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "    b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "    # Generate array of b values within the range [0, 0.1]\n",
        "    num_points = 100\n",
        "    b_values_case_1 = np.linspace(b_underline, b_bar, num_points)\n",
        "    b_values_case_2 = np.linspace(0, b_underline, num_points)\n",
        "    b_values_case_3 = np.linspace(b_bar, 2, num_points)\n",
        "\n",
        "    # Initialize arrays to store u values for each case\n",
        "    u_values_case_1 = np.zeros(num_points)\n",
        "    u_values_case_2 = np.zeros(num_points)\n",
        "    u_values_case_3 = np.zeros(num_points)\n",
        "\n",
        "    # Calculate values for each case\n",
        "    for i, b in enumerate(b_values_case_1):\n",
        "        y_tau = b / (1 - gamma * np.exp(-beta * psi))\n",
        "        q_tau = (1 / R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "        term1 = np.log(y1 + q_tau * b)\n",
        "        term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "        term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "        term4 = (beta / (y_bar - y_underline)) * (\n",
        "                    y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "        term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma *y3) * (y_tau - y_underline)\n",
        "        u_values_case_1[i] = term1 + term2 + term3 + term4 + term5\n",
        "\n",
        "    for i, b in enumerate(b_values_case_2):\n",
        "        q_tau = (1 / R)\n",
        "        term1 = np.log(y1 + q_tau * b)\n",
        "        term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_underline - b) * np.log(\n",
        "            y_underline - b) - (y_bar - y_underline))\n",
        "        term3 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_underline)\n",
        "        u_values_case_2[i] = term1 + term2 + term3\n",
        "\n",
        "    for i, b in enumerate(b_values_case_3):\n",
        "        term1 = np.log(y1)\n",
        "        term4 = (beta / (y_bar - y_underline)) * (\n",
        "                y_bar * np.log(gamma * y_bar) - y_underline * np.log(gamma * y_underline) - (y_bar - y_underline))\n",
        "        term5 = ((beta) ** 2 / (y_bar - y_underline)) * np.log(gamma * y3) * (y_bar - y_underline)\n",
        "        u_values_case_3[i] = term1 + term4 + term5\n",
        "\n",
        "    return b_values_case_1, u_values_case_1, b_values_case_2, u_values_case_2, b_values_case_3, u_values_case_3\n",
        "\n",
        "# Plotting\n",
        "y3_values = [1.1, 1.3, 1.4]\n",
        "fig, axes = plt.subplots(1, 3, figsize=(12, 4))\n",
        "\n",
        "for i, y3_value in enumerate(y3_values):\n",
        "    b_values_case_1, u_values_case_1, b_values_case_2, u_values_case_2, b_values_case_3, u_values_case_3 = calculate_utility(y3_value)\n",
        "\n",
        "    axes[i].plot(b_values_case_1, u_values_case_1, label='Case 1', color='black')\n",
        "    axes[i].plot(b_values_case_2, u_values_case_2, label='Case 2', color='black')\n",
        "    axes[i].plot(b_values_case_3, u_values_case_3, label='Case 3', color='black')\n",
        "    axes[i].set_xlabel('b')\n",
        "    axes[i].set_ylabel('U')\n",
        "    axes[i].set_title(f'Total Utility (y upper bound$= {y3_value}$)')\n",
        "    axes[i].grid(True, linestyle='--')\n",
        "    axes[i].set_xlim(0, 1.5)\n",
        "    axes[i].axvspan(min(b_values_case_1), max(b_values_case_1), color='red', alpha=0.2)\n",
        "    axes[i].axvspan(min(b_values_case_2), max(b_values_case_2), color='blue', alpha=0.2)\n",
        "    axes[i].axvspan(min(b_values_case_3), max(b_values_case_3), color='yellow', alpha=0.2)\n",
        "\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.savefig('y_bar.png', dpi=300, bbox_inches='tight')\n",
        "plt.show()\n",
        "files.download('y_bar.png')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 407
        },
        "id": "EDh6KDl1jWQd",
        "outputId": "a6431812-3f4b-4b62-f842-64be48a9ad59"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ],
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ],
            "application/javascript": [
              "download(\"download_aff25d4b-d441-4ab6-aeca-7e30d8cdc48b\", \"y_bar.png\", 191701)"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1\n",
        "y1 = 1\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.05\n",
        "y_underline = 0.95\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values = np.linspace(0, 1, num_points)\n",
        "\n",
        "# Initialize arrays to store u values for each b\n",
        "u_values = np.zeros(num_points)\n",
        "\n",
        "# Calculate u for each b\n",
        "for i, b in enumerate(b_values):\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "    q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_tau - y_underline)\n",
        "\n",
        "    u_values[i] = term1\n",
        "\n",
        "# Plotting\n",
        "plt.plot(b_values, u_values)\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('u')\n",
        "plt.title('Plot of u1 vs b')\n",
        "plt.grid(True)\n",
        "plt.xlim(-1, 1)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 655
        },
        "id": "81O09ELJRyhH",
        "outputId": "2756779e-4482-4029-f8e3-0eb36f953709"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-64-1e19924da863>:27: RuntimeWarning: divide by zero encountered in log\n",
            "  term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
            "<ipython-input-64-1e19924da863>:27: RuntimeWarning: invalid value encountered in scalar multiply\n",
            "  term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
            "<ipython-input-64-1e19924da863>:29: RuntimeWarning: divide by zero encountered in log\n",
            "  term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
            "<ipython-input-64-1e19924da863>:29: RuntimeWarning: invalid value encountered in scalar multiply\n",
            "  term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
            "<ipython-input-64-1e19924da863>:26: RuntimeWarning: invalid value encountered in log\n",
            "  term1 = np.log(y1 + q_tau * b)\n"
          ]
        },
        {
          "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": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Constants\n",
        "y3 = 1\n",
        "y1 = 1\n",
        "gamma = 0.5\n",
        "beta = 0.9\n",
        "R = 1\n",
        "y_bar = 1.2\n",
        "y_underline = 0.8\n",
        "\n",
        "b_bar = (1 - gamma * np.exp(- beta * psi)) * y_bar\n",
        "b_underline = (1 - gamma * np.exp(- beta * psi)) * y_underline\n",
        "\n",
        "# Generate array of b values within the range [0, 0.1]\n",
        "num_points = 100\n",
        "b_values = np.linspace(0, 1, num_points)\n",
        "\n",
        "# Initialize arrays to store u values for each b\n",
        "u_values = np.zeros(num_points)\n",
        "\n",
        "# Calculate u for each b\n",
        "for i, b in enumerate(b_values):\n",
        "    psi = np.log(y3) - np.log(gamma * y3)\n",
        "    y_tau =  b / (1 - gamma * np.exp(- beta * psi))\n",
        "    q_tau = (1/R) * (y_bar - y_tau) / (y_bar - y_underline)\n",
        "\n",
        "    term1 = np.log(y1 + q_tau * b)\n",
        "    term2 = (beta / (y_bar - y_underline)) * ((y_bar - b) * np.log(y_bar - b) - (y_tau - b) * np.log(y_tau - b) - (y_bar - y_tau))\n",
        "    term3 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_bar - y_tau)\n",
        "    term4 = (beta / (y_bar - y_underline)) * (y_tau * np.log(gamma * y_tau) - y_underline * np.log(gamma * y_underline) - (y_tau - y_underline))\n",
        "    term5 = ((beta)**2 / (y_bar - y_underline)) * np.log(y3) * (y_tau - y_underline)\n",
        "\n",
        "    u_values[i] = y_tau\n",
        "\n",
        "# Plotting\n",
        "plt.plot(b_values, u_values)\n",
        "plt.xlabel('b')\n",
        "plt.ylabel('y_tau')\n",
        "plt.title('Plot of y_tau vs b')\n",
        "plt.grid(True)\n",
        "plt.xlim(-1, 1)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "Ldjay6ctTomR",
        "outputId": "f5253a1f-8135-4df5-baf4-5ea8d735a3ea"
      },
      "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": {}
        }
      ]
    }
  ]
}