solow.ipynb

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        "<a href=\"https://colab.research.google.com/github/cmg777/intro-macro-models-with-python/blob/main/Solow%20Model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "#### [**NICOLAS CACHANOSKY**](http://www.ncachanosky.com) | Department of Economics | Metropolitan State University of Denver | ncachano@msudenver.edu"
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      "source": [
        "# SOLOW MODEL\n",
        "---"
      ]
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      "source": [
        "This note illustrates how to code the Solow Model in Python. The purpose of the note is to walk through Python applications, not to offer a detailed discussion of the Solow Model or to show best coding practices. The note also assumes familiarity with the Solow model and a beginner experience with Python.\n",
        "\n",
        "For a more complete and detailed discussion of Python applications see the material in [Quant Econ](https://quantecon.org/).\n",
        "\n",
        "---"
      ]
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        "# To run this notebook in Google Colab, activate and run the following\n",
        "#!pip install --q sympy==1.7.1\n",
        "#!pip install --q numpy==1.19.4\n",
        "#!pip install --q matplotlib==2.2.5\n",
        "#!pip install --q watermark"
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        "## TABLE OF CONTENTS\n",
        "1. [The production function](#1.-THE-PRODUCTION-FUNCTION)\n",
        "2. [The steady-state](#2.-THE-STEADY-STATE)\n",
        "3. [Shocks](#3.-SHOCKS)\n",
        "4. [Phase diagram and convergence](#4.-PHASE-DIAGRAM-AND-CONVERGENCE)\n",
        "5. [The golden-rule](#5.-THE-GOLDEN-RULE)\n",
        "6. [Growth accounting](#6.-GROWTH-ACCOUNTING)"
      ]
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      "source": [
        "## 1. THE PRODUCTION FUNCTION"
      ]
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        "The main component of the Solow model is a neoclassical production function, $f(x_{i})$ that satisfies the Inada conditions, where each $x_{i} \\geq 0$: \n",
        "\n",
        "1. The production function has diminishing marginal returns: $\\partial f(x)/\\partial x > 0$ and $\\partial^2/\\partial x^2 <0$\n",
        "2. If there is no input, there is no production: $f\\left(x=0\\right)=0$\n",
        "3. As the value of the input approaches to zero, the first derivative approaches to infinity: $\\lim\\limits_{x \\to 0^+} \\partial f(x)/\\partial x = +\\infty $\n",
        "4. As the value of the input approaches to infinity, the first derivative approaches to zero: $\\lim\\limits_{x \\to +\\infty} \\partial f(x)/\\partial x = 0^+$\n",
        "\n",
        "Assume a Cobb-Douglas production function in discrete time $(t)$ with Hicks-neutral techonology $(A)$, and with constant returns to scale where $\\alpha \\in (0, 1)$ is the output elasticity of capital.\n",
        "\n",
        "\\begin{equation}\n",
        "    Y_{t}\\left(K_{t}, N_{t}\\right) = A_{t} \\cdot F\\left(K_{t}, N_{t}\\right) =  A_{t} \\cdot \\left(K_{t} ^{\\alpha} N_{t}^{1-\\alpha}\\right)\n",
        "\\end{equation}\n",
        "\n",
        "The first and second derivatives with respect to capital and labor are:\n",
        "\n",
        "\\begin{equation}\n",
        "    \\frac{\\partial   Y_{t}}{\\partial K}   = \\alpha \\cdot A\\left(\\frac{N_{t}}{K_{t}}\\right)^{1-\\alpha} \n",
        "  = \\alpha \\cdot \\frac{Y_{t}}{K_{t}} > 0 \\; \\text{and} \\;\n",
        "    \\frac{\\partial^2 Y_{t}}{\\partial K^2} = -\\alpha (1-\\alpha) \\cdot A\\left(\\frac{N_{t}}{K_{t}}\\right)^{1-\\alpha} < 0\n",
        "    \\\\\n",
        "    \\frac{\\partial   Y_{t}}{\\partial N}   = (1-\\alpha) \\cdot A\\left(\\frac{K_{t}}{N_{t}}\\right)^{\\alpha} \n",
        "  = (1-\\alpha) \\cdot \\frac{Y_{t}}{N_{t}} > 0 \\; \\text{and} \\;\n",
        "    \\frac{\\partial^2 Y_{t}}{\\partial N^2} = -\\alpha (1-\\alpha) \\cdot A\\left(\\frac{K_{t}}{N_{t}}\\right)^{1-\\alpha} < 0\n",
        "\\end{equation}\n",
        "\n",
        "Python can calculate the derivatives and present them in LaTeX format. For this, Python needs the `sympy` package. The example below calculates the first partial derivative of the output function with respect to capital and prints the output in Python and LaTeX formats."
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        "\"1|IMPORT PACKAGES\"\n",
        "from sympy import Symbol\n",
        "from sympy import latex\n",
        "\n",
        "\"2|TELL PYTHON TO TREAT VARIABLES AS 'MATH' SYMBOLS\"\n",
        "A, K, N, alpha = Symbol('A'), Symbol('K'), Symbol('N'), Symbol('alpha')  \n",
        "Y = A * (K)**(alpha) * (N)**(1-alpha)                                    \n",
        "\n",
        "\"3|CALCULATE THE DERIVATIVE AND PRINT THE RESULT\"\n",
        "Yprime = Y.diff(K)   # Calculate the partial derivative with respect to K\n",
        "print(Yprime)        # Print dY/dK\n",
        "latex(Yprime)        # Print dY/dK in LaTeX format"
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            "A*K**alpha*N**(1 - alpha)*alpha/K\n"
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              "'\\\\frac{A K^{\\\\alpha} N^{1 - \\\\alpha} \\\\alpha}{K}'"
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        "$$\\frac{A \\alpha}{K} K^{\\alpha} N^{- \\alpha + 1}$$"
      ]
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        "### 1.2 PRODUCTION PER CAPITA\n",
        "\n",
        "Write the production function in *per capita* terms:\n",
        "\n",
        "\\begin{align}\n",
        "    Y_{t} &= A_{t} \\cdot \\left(K_{t}^{\\alpha}N_{t}^{1-\\alpha} \\right) \\\\\n",
        "    \\frac{Y_{t}}{N_{t}} &= A_{t} \\cdot \\left[ \\left(\\frac{K_{t}}{N_{t}} \\right)^{\\alpha} \\left(\\frac{N_{t}}{N_{t}} \\right)^{1-\\alpha} \\right] \\\\\n",
        "    y_{t} &= f\\left(k_{t}\\right) = A_{t} \\cdot k_{t}^{\\alpha}\n",
        "\\end{align}\n",
        "\n",
        "The following code plots the level of output for changes in $K$ at different levels of $A$. The first part of the code imports the required packages. The second part of the code sets the parameter values and defines a user-defined production function. The third part of the code builds the graph. To be able to plot, Python needs the 'matplotlib' package.\n",
        "\n",
        "Remember that Python numbers the first element of a vector 'V' with a zero: If the first element is 'a', then $V[0] = a$. The code sets the plot line to be a solid blue line (\"b-\") with some transparency set by the value of 'alpha'."
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        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS\"\n",
        "# Parameters\n",
        "K_size = 100                # Model domain\n",
        "A = 1                       # Total Factor Productivity\n",
        "N = K_size/2                # Labor stock\n",
        "alpha = 0.50                # Output elasticity of capital\n",
        "# Arrays\n",
        "k = np.arange(K_size)       # Create array of K\n",
        "\n",
        "\"3|CALCULATE OUTPUT VALUES\"\n",
        "def output(k, A):           # User-defined Cobb-Douglas Production Function\n",
        "    y = A * (k)**(alpha)\n",
        "    return y\n",
        "\n",
        "y  = output(k, A)\n",
        "y2 = output(k, A+1)\n",
        "y3 = output(k, A+2)\n",
        "y4 = output(k, A+3)\n",
        "y5 = output(k, A+4)\n",
        "y6 = output(k, A+5)\n",
        "\n",
        "\"4|PLOT THE PRODUCTION FUNCTION FOR DIFFERENT VALUES OF TECHNOLOGY\"\n",
        "y_max = np.max(y6)\n",
        "v = [0, K_size, 0, y_max]                       # Set the axes range\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.set(title=\"output\", xlabel=\"Capital\", ylabel=\"Output\")\n",
        "ax.grid()\n",
        "ax.plot(k, y,  \"b-\", alpha=1.00, label=\"A=1\")\n",
        "ax.plot(k, y2, \"b-\", alpha=0.85, label=\"A=2\")\n",
        "ax.plot(k, y3, \"b-\", alpha=0.70, label=\"A=3\")\n",
        "ax.plot(k, y4, \"b-\", alpha=0.55, label=\"A=4\")\n",
        "ax.plot(k, y5, \"b-\", alpha=0.40, label=\"A=5\")\n",
        "ax.plot(k, y6, \"b-\", alpha=0.25, label=\"A=6\")\n",
        "ax.legend() \n",
        "plt.axis(v)                                    # Use 'v' as the axes range\n",
        "plt.show()"
      ],
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              "<Figure size 1000x800 with 1 Axes>"
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        "---\n",
        "## 2. THE STEADY-STATE\n",
        "\n",
        "To find the steady-state (equilibrum) of the Solow model, a motion function that tracks changes in capital is needed. Investment increases the capital stock. A *break-even line* tracks how much investment is required to keep capital per capita constant.\n",
        "\n",
        "### 2.1 Increase in the Capital Stock: Investment\n",
        "\n",
        "Invesmtnt $(I)$ equals a fixed and exogenous savings rate $\\left(s \\in (0, 1) \\right)$ of income. In per capita terms $\\left(i=I/N\\right)$:\n",
        "\n",
        "\\begin{equation}\n",
        "   i_{t} = s \\cdot \\left(A \\cdot k_{t}^{\\alpha}\\right) = s \\cdot y_{t}\n",
        "\\end{equation}\n",
        "\n",
        "Since income per capita increases at a decreasing rate with capital, so does investment per capita, which is a fixed proportion $\\left(s\\right)$ of income.\n",
        "\n",
        "Assuming a closed economy with no government, consumption per capita is the difference between income and investment: $c = y - i$\n",
        "\n",
        "### 2.2 Break-Even Line: Depreciation and Dilution\n",
        "\n",
        "There are two reasons why capital per capita decreases. The first one is capital depreciation. The second one is capital dilution, which is when population grows at a faster rate than capital. *Ceteris paribus*, to keep capital per capita constant capital stock needs to grow at the same rate than population.\n",
        "\n",
        "Assume population growths at rate $n$: $N_{t+1} = (1 + n)N_{t}$\n",
        "\n",
        "Also assume that the amount of depreciation $D$ equals a fixed rate $\\left(\\delta \\in (0, 1) \\right)$ of the capital stock. In per capita values:\n",
        "\n",
        "\\begin{equation}\n",
        "   d_{t} = \\delta \\cdot k_{t}\n",
        "\\end{equation}\n",
        "\n",
        "The derivative of $k$ with respect to time yields the change in capital per capita taking into account depreciation and capital dilution. The break-even line $\\left[ \\left( \\delta + n \\right) k \\right]$ shows the investment required to just compensate for depreciation and population growth (dropping the subscript $t$ for notation simplicity):\n",
        "\n",
        "\\begin{align}\n",
        " \\frac{\\partial k}{\\partial t} &= \\frac{\\partial (K/L)}{\\partial t}                                                       \\\\[10pt]\n",
        " \\frac{\\partial k}{\\partial t} &= \\frac{1}{L} \\frac{\\partial K}{\\partial t} - \\frac{K}{L^2} \\frac{\\partial L}{\\partial t} \\\\[10pt]\n",
        " \\frac{\\partial k}{\\partial t} &= \\frac{sY - \\delta K}{L} - \\frac{K}{L} \\cdot \\frac{\\partial L}{\\partial t} \\frac{1}{L}   \\\\[10pt]\n",
        " \\frac{\\partial k}{\\partial t} &= sy - \\delta k - k n                                                                     \\\\[10pt]\n",
        " \\frac{\\partial k}{\\partial t} &= sy - \\left(\\delta + n \\right)k                                                          \\\\[10pt]\n",
        " \\frac{\\partial k}{\\partial t} &= s \\cdot Ak^{\\alpha} - \\left(\\delta + n \\right)k\n",
        "\\end{align}\n",
        "\n",
        "---\n",
        "\n",
        "The steady-state is the value $k^*$ that maintains the capital stock per capita constant $\\left(\\partial k/\\partial t =0 \\right)$. Since $K = kL$ and $L$ grows at rate $n$, $K$ is also growing at rate $n$. Since the Cobb-Douglas production function has constant returns to scale, $Y$ is also growint at rate $n$.\n",
        "\n",
        "Now let the growth rate of technology be $\\gamma$. Since at the steady-state $k$ does not change, output per capita growths at the growth rate of technology: $\\frac{\\partial y}{\\partial t}\\frac{1}{y} = \\frac{\\partial A}{\\partial t} \\cdot k^{\\alpha} \\frac{1}{y} + A \\cdot \\frac{\\partial f(k^*)}{\\partial t} \\frac{1}{y}$. Because $\\frac{\\partial f(k^*)}{\\partial t} = 0$, then $\\frac{\\partial y}{\\partial t}\\frac{1}{y} = \\frac{\\partial A}{\\partial t} \\cdot k^{\\alpha} \\frac{1}{y} = \\frac{\\partial A}{\\partial t} \\frac{1}{A} = \\gamma$\n",
        "\n",
        "Furthermore, since investment is a fixed proportion of $y$, investment also grows at rate $\\gamma$ in the steady-state. And since consumption per capita is the difference between output and investment per capita, consumption also grows at rate $\\gamma$.\n",
        "\n",
        "Solve for $k^*$ from the equilibrium condition:\n",
        "\n",
        "\\begin{align}\n",
        "  (\\delta + n)k &= s \\cdot Ak^{\\alpha}         \\\\\n",
        "  k^{1-\\alpha} &= A \\cdot \\frac{s}{\\delta + n} \\\\\n",
        "  k^* &= \\left[ A \\cdot \\frac{s}{\\delta + n} \\right]^{\\frac{1}{1-\\alpha}}\n",
        "\\end{align}\n",
        "\n",
        "Knowing $k^*$ allows to calculate the steady-state values of the other variables.\n",
        "\\begin{align}\n",
        "  y^* &= A(k^*)^{\\alpha}  \\\\\n",
        "  i^* &= sy^*             \\\\\n",
        "  c^* &= y^* - i^*        \\\\\n",
        "  d^* &= \\delta k^*\n",
        "\\end{align}\n",
        "\n",
        "The code below calculates the steady-state values and graphs the Solow model in per capita values. Steady-state values are shown in a table. For this the package `tabulate` is necessary [if you are using Anaconda, you need to first download this package in the *Environments* section]."
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      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS\"\n",
        "# Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "N = 5                            # Capital stock\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "s = 0.30                         # Savings rate\n",
        "d = 0.10                         # Depreciation rate\n",
        "#Arrays\n",
        "K = np.arange(K_size)            # Create empty array of K\n",
        "\n",
        "\"3|DEFINE FUNCTIONS\"\n",
        "def output(K):   # Cobb-Douglas Production Function\n",
        "    Y = A * (K)**(alpha) * (N)**(1-alpha)    \n",
        "    return Y\n",
        "\n",
        "\"4|POPULATE ARRAYS\"\n",
        "Y = output(K)\n",
        "D = d*K\n",
        "I = s*Y\n",
        "\n",
        "\"5|CALCULATE STEADY-STATE VALUES\"\n",
        "Kstar = ((s*A*(N)**(1-alpha))/d)**(1/(1-alpha))\n",
        "Ystar = A  *(Kstar**alpha)*((N)**(1-alpha))\n",
        "Istar = s*Ystar\n",
        "Cstar = Ystar - Istar\n",
        "Dstar = d*Kstar\n",
        "\n",
        "\"6|PLOT THE SOLOW MODEL\"\n",
        "y_max = np.max(Y)\n",
        "v = [0, K_size, 0, y_max]\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.plot(K, Y, \"k\", ls = '-', label=\"Output\")\n",
        "ax.plot(K, I, \"b\", ls = '-', label=\"Investment\")\n",
        "ax.plot(K, D, \"r\", ls = '-', label=\"Depreciation\")\n",
        "ax.set(title=\"Solow Model\", xlabel=\"Capital Stock\")\n",
        "plt.text(77, 19,  r'$Y = A \\cdot K^{\\alpha} N^{1-\\alpha}$')\n",
        "plt.text(90, 10,  r'$D = dK$')\n",
        "plt.text(90, 5.5, r'$I = sY$')\n",
        "plt.legend(loc=2)\n",
        "plt.axvline(x = Kstar, ls = \":\", color = 'k')\n",
        "plt.axhline(y = Istar, ls = \":\", color = 'k')\n",
        "plt.axhline(y = Ystar, ls = \":\", color = 'k')\n",
        "plt.axis(v)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vws1LFn0a2HD"
      },
      "source": [
        "## 3. SHOCKS\n",
        "\n",
        "Starting from the steady-state, the effect of different schocks can be analyzed. A well-known feature of the Solow model is that an increase in the savings rate $(s)$, while it does produce level effects, does not have long-run effects on the growth rate of income per capita $(y)$. The reason is that capital productivity has decreasing marginal returns while capital loss (depreciation plus dilution) has constant returns. At some point, the stock of capital is so large that it cannot produce enough income to replace capital loss and increase the stock.\n",
        "\n",
        "For each case, assume that starting in $t=0$ the model is in is steady-state and the shocks occurs in $t=10$.\n",
        "\n",
        "### 3.1. Savings Rate\n",
        "\n",
        "Let the savings rate increase from $s_1$ to $s_2$. This produces an upward shift in the investment line, but produces no change on output or on the break-even line. Now investment is more than the break-even point producing an increase in the capital stock. If the shock is permanent, then $k^*$ moves outward initiating a new convergence movemente to the **new** steady-state values. If the shock is for a one period only, then the model **returns** to its original steady-state. Note that the convergence to the steady-state (old or new) is asympthotic: $\\{k, y, i, d, c\\}_{t \\to \\infty} \\to \\{k^*, y^*, i^*, d^*, c^*\\}$.\n",
        "\n",
        "The code below plots the Solow model and the effects of a one-time and a permanent shock to the savings rate."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "B_EAtdmia2HD",
        "outputId": "83acd0bd-49eb-427e-ffb0-7d024a544b1f"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "# Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s1 = 0.35                        # Savings rate before the shock\n",
        "s2 = 0.45                        # Savings rate after the shock\n",
        "n  = 0.02                        # Population growth rate\n",
        "# Arrays\n",
        "k  = np.arange(K_size)           # Create array of k\n",
        "\n",
        "\"3|DEFINE FUNCTIONS\"\n",
        "def output(k):                   # Cobb-Douglas per capita function\n",
        "    y = A * (k)**(alpha)\n",
        "    return y\n",
        "\n",
        "y  = output(k)                   # Production function\n",
        "d  = delta*k                     # Depreciation\n",
        "i1 = s1*y                        # Investment before the shock\n",
        "i2 = s2*y                        # Investment after the shock\n",
        "d_and_i = (delta + n)*k          # Breack-even\n",
        "\n",
        "\"4|CALCULATE STEADY-STATE VALUES\"\n",
        "k_star1 = (s1/(n+delta)*A)**(1/(1-alpha))\n",
        "k_star2 = (s2/(n+delta)*A)**(1/(1-alpha))\n",
        "y_star1 = A*(k_star1**alpha)\n",
        "y_star2 = A*(k_star2**alpha)\n",
        "i_star1 = s1*y_star1\n",
        "i_star2 = s2*y_star2\n",
        "c_star1 = y_star1 - i_star1\n",
        "c_star2 = y_star2 - i_star2\n",
        "d_star1 = delta*k_star1\n",
        "d_star2 = delta*k_star2\n",
        "\n",
        "\"5|PLOT THE SOLOW MODEL\"               \n",
        "y_max = np.max(y)\n",
        "v = [0, K_size, 0, y_max]              # Axis range\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.set(title=\"SOLOW MODEL: SAVINGS RATE SHOCK\", xlabel=r'$k$')\n",
        "ax.plot(k, y      , \"k\", ls = '-', label=\"Output per capita\")\n",
        "ax.plot(k, i1     , \"k\", ls = '-', label=\"Investment before shock\")\n",
        "ax.plot(k, i2     , \"b\", ls = '-', label=\"Investment after shock\")\n",
        "ax.plot(k, d_and_i, \"k\", ls = '-', label=\"Depreciation plus dilution\")\n",
        "plt.text(87, 9.1, r'$y = A \\cdot k^{\\alpha}$', color = 'k')\n",
        "plt.text(89, 5.0, r'$(\\delta + n)k$'         , color = 'k')\n",
        "plt.text(90, 3.0, r'$i = s_{1}y$'            , color = 'k')\n",
        "plt.text(90, 4.1, r'$i = s_{2}y$'            , color = \"b\")\n",
        "plt.legend(loc=2)\n",
        "plt.axvline(x = k_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axhline(y = i_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axhline(y = y_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axvline(x = k_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "plt.axhline(y = i_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "plt.axhline(y = y_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "ax.yaxis.set_major_locator(plt.NullLocator())      # Hide ticks\n",
        "ax.xaxis.set_major_locator(plt.NullLocator())      # Hide ticks\n",
        "plt.axis(v)\n",
        "plt.show()\n",
        "\n",
        "\"6|SAVINGS RATE: ONE-PERIOD SHOCK\"\n",
        "T = 200                 # Number of periods\n",
        "t_shock = 10            # Period when shock happens\n",
        "time = np.arange(T)     # Create array of time\n",
        "s = np.zeros(T)         # Create array of s\n",
        "y = np.zeros(T)         # Create array of y\n",
        "k = np.zeros(T)         # Create array of k\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "s = np.zeros(T)\n",
        "s[0:T] = s1             # Array of savings rate\n",
        "s[t_shock] = s2         # Shock to savings rate\n",
        "\n",
        "for j in range(1, T):\n",
        "    k[j] = k[j-1] + i[j-1] - (n + delta)*k[j-1]\n",
        "    y[j] = A*k[j]**alpha\n",
        "    i[j] = s[j]*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "    \n",
        "### Plot effect on variables\n",
        "ticks = [\"\"]*T                                  # Create tick labels\n",
        "ticks[t_shock] = 'Shock'                        # Create label \"shock\" \n",
        "\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                   # Plots be next to each other\n",
        "ax1.set(title=\"ONE-PERIOD SHOCK TO SAVINGS RATE\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.text(150, 49.1, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax2.text(150, 7.01, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.text(150, 4.2, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(150, 2.7, 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                         # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks\n",
        "\n",
        "\"8|SAVINGS RATE: PERMANENT SHOCK\"\n",
        "time = np.arange(T)     # Create array of time\n",
        "s = np.zeros(T)         # Create array of s\n",
        "y = np.zeros(T)         # Create array of y\n",
        "k = np.zeros(T)         # Create array of k\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "s = np.zeros(T)\n",
        "s[0:t_shock] = s1       # Array of savings rate\n",
        "s[t_shock:T] = s2       # Shock to savings rate\n",
        "\n",
        "for j in range(1, T):\n",
        "    k[j] = k[j-1] + i[j-1] - (n + delta)*k[j-1]\n",
        "    y[j] = A*k[j]**alpha\n",
        "    i[j] = s[j]*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "    \n",
        "### Plot effect on variables\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                    # Plots be next to each other\n",
        "ax1.set(title=\"PERMANENT SHOCK TO SAVINGS RATE\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax1.text(150, 75.1, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax2.text(150, 8.7, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.text(150, 4.6, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(150, 3.7, 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                          # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DZdG0vT1a2HE"
      },
      "source": [
        "### 3.2 Population growth rate\n",
        "\n",
        "In the case of an increase in the growth rate of population $(n)$, capital per capita falls. Now investment is less than the break-even point. Capital stock cannot keep up with the higher growth rate of population. Similarly to a shock to the savings rate, a one-period shock moves the model out of its steady-state and then it **returns** to its original position. A permanent shock makes the model converge to a **new** steady-state. Note that a change in the depreciation rate produces the same effects than a change in population growth rate. \n",
        "\n",
        "The code below is similar to the previous one. The difference is that the shock is affecting $n$ instead of $s$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "gh_ylUtea2HE",
        "outputId": "bb8ac9f3-24ad-4a94-db92-222fa6be7127"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "#Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s  = 0.35                        # Savings rate\n",
        "n1 = 0.02                        # Population growth rate before the shock\n",
        "n2 = 0.05                        # Population growth rate after the shock\n",
        "# Arrays\n",
        "k  = np.arange(K_size)           # Create array of k\n",
        "\n",
        "\"3|DEFINE FUNCTIONS\"\n",
        "def output(k):   # Cobb-Douglas Production Function (per capita)\n",
        "    y = A * (k)**(alpha)    \n",
        "    return y\n",
        "\n",
        "y = output(k)\n",
        "d = delta*k\n",
        "i = s*y\n",
        "d_and_i1 = (delta + n1)*k\n",
        "d_and_i2 = (delta + n2)*k\n",
        "\n",
        "\"4|CALCULATE STEADY-STATE VALUES\"\n",
        "k_star1 = (s/(n1+delta)*A)**(1/(1-alpha))\n",
        "k_star2 = (s/(n2+delta)*A)**(1/(1-alpha))\n",
        "y_star1 = A*(k_star1**alpha)\n",
        "y_star2 = A*(k_star2**alpha)\n",
        "i_star1 = s*y_star1\n",
        "i_star2 = s*y_star2\n",
        "c_star1 = y_star1 - i_star1\n",
        "c_star2 = y_star2 - i_star2\n",
        "d_star1 = delta*k_star1\n",
        "d_star2 = delta*k_star2\n",
        "\n",
        "\"5|PLOT THE SOLOW MODEL\"\n",
        "y_max = np.max(y)\n",
        "v = [0, K_size, 0, y_max]              # Axis range\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.set(title=\"SOLOW MODEL: POPULATOIN GROWTH RATE SHOCK\", xlabel=r'$k$')\n",
        "ax.plot(k, y       , \"k\", ls='-', label=\"Output per capita\")\n",
        "ax.plot(k, i       , \"k\", ls='-', label=\"Investment\")\n",
        "ax.plot(k, d_and_i1, \"k\", ls='-', label=\"Dep. plus dilution before the shock\")\n",
        "ax.plot(k, d_and_i2, \"b\", ls='-', label=\"Dep. plus dilution after the shock\")\n",
        "plt.text(87, 9.1, r'$y = A \\cdot k^{\\alpha}$', color = 'k')\n",
        "plt.text(89, 5.0, r'$(\\delta + n_{1})k$'     , color = 'k')\n",
        "plt.text(89, 8.0, r'$(\\delta + n_{2})k$'     , color = \"b\")\n",
        "plt.text(90, 3.0, r'$i = sy$'                , color = 'k')\n",
        "plt.legend(loc=2)\n",
        "plt.axvline(x = k_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axhline(y = i_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axhline(y = y_star1, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axvline(x = k_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "plt.axhline(y = i_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "plt.axhline(y = y_star2, ls = \":\", color = 'b', alpha = 0.6)\n",
        "ax.yaxis.set_major_locator(plt.NullLocator())      # Hide ticks\n",
        "ax.xaxis.set_major_locator(plt.NullLocator())      # Hide ticks\n",
        "plt.axis(v)\n",
        "plt.show()\n",
        "\n",
        "\"6|SPOPULATION GROWTH RATE: ONE-PERIOD SHOCK\"\n",
        "T = 200                 # Number of periods\n",
        "t_shock = 10            # Period when shock happens\n",
        "time = np.arange(T)     # Create array of time\n",
        "y = np.zeros(T)         # Create array of y\n",
        "k = np.zeros(T)         # Create array of k\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "n = np.zeros(T)\n",
        "n[0:T] = n1             # Population\n",
        "n[t_shock] = n2         # Shock to population\n",
        "\n",
        "for j in range(1, T):\n",
        "    k[j] = k[j-1] + i[j-1] - (n[j] + delta)*k[j-1]\n",
        "    y[j] = A*k[j]**alpha\n",
        "    i[j] = s*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "    \n",
        "### Plot effect on variables\n",
        "ticks = [\"\"]*T                                  # Create tick labels\n",
        "ticks[t_shock] = 'Shock'                        # Create label \"shock\" \n",
        "\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                   # Plots be next to each other\n",
        "ax1.set(title=\"ONE-PERIOD SHOCK TO POPULATION GROWTH RATE\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.text(150, 48.7, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax2.text(150, 6.98, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.text(150, 4.2, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(150, 2.7, 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                         # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks\n",
        "\n",
        "\"7|POPULATION GROWTH RATE: PERMANENT SHOCK\"\n",
        "time = np.arange(T)     # Create array of time\n",
        "y = np.zeros(T)         # Create array of y\n",
        "k = np.zeros(T)         # Create array of k\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "n = np.zeros(T)\n",
        "n[0:T] = n1             # Population\n",
        "n[t_shock:T] = n2       # Population shock\n",
        "\n",
        "for j in range(1, T):\n",
        "    k[j] = k[j-1] + i[j-1] - (n[j] + delta)*k[j-1]\n",
        "    y[j] = A*k[j]**alpha\n",
        "    i[j] = s*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "    \n",
        "### Plot effect on variables\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                    # Plots be next to each other\n",
        "ax1.set(title=\"PERMANENT SHOCK TO POPULATION GROWTH RATE\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax1.text(150, 22.1, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax2.text(150, 4.7, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.text(150, 3.1, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(150, 1.7, 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                          # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oOunbTWwa2HE"
      },
      "source": [
        "### 3.3 GROWTH RATE OF TECHNOLOGY\n",
        "\n",
        "In general terms, $(A)$ captures *total factor productivity* (TFP). If $fp_{j}, j = \\{1, \\dotsc, J \\}$ are $J$ factors of production, then:\n",
        "\n",
        "$$A = \\frac{Y}{F\\left(fp_{1}, \\cdots, fp_{J}\\right)}$$\n",
        "\n",
        "\n",
        "Repeated increases in productivity produces the effect in output shown in section 2. Since output is increasing, so does investment. This produces a permanent outward shift of $k^*$. The savings rate is bounded between 0 and 1, but $A$ can grow indefinitely. Also note the exponential effect on output, investment, and consumption. Starting at the stead-state position, an increase in productivity means that investment is more than the break-even value and therefore modes starts to converge to a permanent moving steady-state position. This case of productivity gains can be described as *cutting-edge* growth. Different is the case of *catching-up growth*, which is the situation of the model approaching a fixed steady-state position (e.g. after a one-period shock).\n",
        "\n",
        "A one-time time shock to TFP moves the model out of equilibrium until it **returns** to its original position. But, a permanent increase in $\\gamma$ can produce a **continuous** growth of the steady-state values. This implies that steady-state values grow at the growth rate ot TFP, $\\gamma$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 899
        },
        "id": "v-K8G7mOa2HE",
        "outputId": "ed20c3a1-2744-4403-cfe7-3cd09a589115"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "# Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s = 0.35                         # Savings rate\n",
        "n = 0.02                         # Population growth rate\n",
        "# Arrays\n",
        "k = np.arange(K_size)            # Create array of k\n",
        "y = np.zeros(K_size)             # Create array of y\n",
        "d = np.zeros(K_size)             # Create array of d\n",
        "i = np.zeros(K_size)             # Create array of i\n",
        "c = np.zeros(K_size)             # Create array of c\n",
        "d_and_i = np.zeros(K_size)       # Break-even before the shock\n",
        "\n",
        "\"3|CALCULATE STEADY-STATE VALUES\"\n",
        "k_star1 = (s/(n+delta)*A)**(1/(1-alpha))\n",
        "k_star2 = (s/(n+delta)*A)**(1/(1-alpha))\n",
        "y_star1 = A*(k_star1**alpha)\n",
        "y_star2 = A*(k_star2**alpha)\n",
        "i_star1 = s*y_star1\n",
        "i_star2 = s*y_star2\n",
        "c_star1 = y_star1 - i_star1\n",
        "c_star2 = y_star2 - i_star2\n",
        "d_star1 = delta*k_star1\n",
        "d_star2 = delta*k_star2\n",
        "\n",
        "\"4|TOTAL FACTROR PRODUCTIVITY: ONE-PERIOD SHOCK\"\n",
        "T = 200                 # Number of periods\n",
        "t_shock = 10            # Period when shock happens\n",
        "time = np.arange(T)     # Create array of time\n",
        "alpha = 0.50            # Output elasticity of capital\n",
        "delta = 0.03            # Depreciation rate\n",
        "s = 0.35                # Savings rate\n",
        "n = 0.02                # Population growth rate before the shock\n",
        "g = 0.05                # Growth rate of TFP\n",
        "k = np.zeros(T)         # Create array of k\n",
        "y = np.zeros(T)         # Create array of y\n",
        "d = np.zeros(T)         # Create array of d\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "d_and_i = np.zeros(T)   # Depreciation plus dilution before the shock\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "TFP = np.empty(T)       # Create array of TFP including shock\n",
        "TFP[0:T] = A\n",
        "TFP[t_shock] = A*(1+g)\n",
        "\n",
        "for j in range(1, T):\n",
        "    k[j] = k[j-1] + i[j-1] - (n + delta)*k[j-1]\n",
        "    y[j] = TFP[j]*k[j]**alpha\n",
        "    i[j] = s*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "    \n",
        "### Plot effect on variables\n",
        "ticks = [\"\"]*T                                  # Create tick labels\n",
        "ticks[t_shock] = 'Shock'                        # Create label \"shock\" \n",
        "\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                   # Plots be next to each other\n",
        "ax1.set(title=\"ONE-PERIOD SHOCK TO TFP\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.text(150, 49.015, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax2.text(150, 7.03, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax3.text(150, 4.3, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(150, 2.6, 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                         # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks\n",
        "\n",
        "\"5|TOTAL FACTOR PRODUCTIVITY: PERMANENT SHOCK\"\n",
        "T = 50\n",
        "time = np.arange(T)     # Create array of time\n",
        "y = np.zeros(T)         # Create array of y\n",
        "k = np.zeros(T)         # Create array of k\n",
        "i = np.zeros(T)         # Create array of i\n",
        "c = np.zeros(T)         # Create array of c\n",
        "\n",
        "y[0] = y_star1          # Set initial value of y\n",
        "k[0] = k_star1          # Set initial value of k\n",
        "i[0] = i_star1          # Set initial value of i\n",
        "c[0] = c_star1          # Set initial value of c\n",
        "\n",
        "TFP = np.zeros(T)       # Create array of TFP including shock\n",
        "TFP[0:T] = A\n",
        "\n",
        "for j in range(1, T):\n",
        "    TFP[j] = TFP[j-1]*(1+g)\n",
        "    k[j] = k[j-1] + i[j-1] - (n + delta)*k[j-1]\n",
        "    y[j] = TFP[j]*k[j]**alpha\n",
        "    i[j] = s*y[j]\n",
        "    c[j] = y[j] - i[j]\n",
        "\n",
        "### Plot effect on variables\n",
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex=True, figsize=(10, 7))\n",
        "fig.subplots_adjust(hspace=0)                    # Plots be next to each other\n",
        "ax1.set(title=\"PERMANENT SHOCK TO TFP\")\n",
        "ax1.plot(time, k, \"k-\", alpha = 0.7)\n",
        "ax1.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax1.text(35, 400, 'Capital: '+r'$k$')\n",
        "\n",
        "ax2.plot(time, y, \"b-\", alpha = 0.7)\n",
        "ax2.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax2.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax2.text(35, 180, 'Output: '+ r'$y=f(k)$', color = \"b\")\n",
        "\n",
        "ax3.plot(time, i, \"g-\", alpha = 0.7)\n",
        "ax3.plot(time, c, \"r-\", alpha = 0.7)\n",
        "ax3.axvline(x = t_shock, color=\"k\", ls = ':', alpha = 0.6)\n",
        "ax3.yaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.xaxis.set_major_locator(plt.NullLocator())   # Hide ticks\n",
        "ax3.text(35, 170, 'Consumption: '+r'$c = (1-s)y$', color = \"r\")\n",
        "ax3.text(35, 10 , 'Investment: '+r'$i = sy$'     , color = \"g\")\n",
        "plt.xticks(time, ticks)                          # Use user-defined ticks\n",
        "plt.xlabel('Time')\n",
        "plt.tick_params(axis='both', which='both', bottom=False, top=False,\n",
        "                labelbottom=True, left=False, right=False, labelleft=True)\n",
        "                                                # Hide tick marks"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K9ILtuyda2HF"
      },
      "source": [
        "## 4. PHASE DIAGRAM AND CONVERGENCE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ptyks8bUa2HF"
      },
      "source": [
        "Note that this is a stable model with two steady states; $k_{1}^* = 0$ and $k_{2}^* = \\left[ A \\cdot \\frac{s}{\\delta + n} \\right]^{\\frac{1}{1-\\alpha}}$. Once $k$ has any positive value, the model will converge to $k_{2}^*$.\n",
        "\n",
        "This behavior of $k$ can be shown with a phase diagram that relates changes in $k$ with values of k (same function thatn section 2.2:\n",
        "\n",
        "\\begin{align}\n",
        "    \\Delta(k) &= h(k)                                 \\\\\n",
        "    \\Delta(k) &= s \\cdot Ak^{\\alpha} - (n + \\delta)k\n",
        "\\end{align}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 427
        },
        "id": "rmmYMI4Za2HF",
        "outputId": "df60170d-f409-4cee-ba00-49e163868f3a"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "# Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s = 0.35                         # Savings rate\n",
        "n = 0.02                         # Population growth rate\n",
        "# Arrays\n",
        "k = np.arange(K_size)            # Create array of k\n",
        "y = np.zeros(K_size)             # Create array of y\n",
        "d = np.zeros(K_size)             # Create array of d\n",
        "i = np.zeros(K_size)             # Create array of i\n",
        "c = np.zeros(K_size)             # Create array of c\n",
        "d_and_i = np.zeros(K_size)       # Break-even before the shock\n",
        "\n",
        "\"3|DEFINE MOTION FUNCTION|\"\n",
        "def motion(k):                   # Motion function of k\n",
        "    DeltaK = s * A*(k)**(alpha) - (n + delta)*k    \n",
        "    return DeltaK\n",
        "\n",
        "DeltaK = motion(k)               # Change in K\n",
        "\n",
        "\"4|PLOT PHASE DIAGRAM\"\n",
        "fig, ax1 = plt.subplots(figsize=(10, 7))\n",
        "ax1.set(title=\"PHASE DIAGRAM\")\n",
        "ax1.plot(k, DeltaK, \"k-\", alpha = 0.7)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.xaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.axvline(x=0, color = 'k')\n",
        "ax1.axhline(y=0, color = 'k')\n",
        "plt.box(False)                                  # Hide plot borders\n",
        "plt.text(100, -0.1, r'$k$')\n",
        "plt.text( -4,  0.6, r'$\\Delta K$')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ND3Ljqoa2HF"
      },
      "source": [
        "---\n",
        "The vertical axis is showing how much does capital per capita change for each value of $k$. In other words, the value on the vertical axis shows how much in the next period $k$ will move to the right on the horizontal axis. Then, the phase diagram is also showing the speed of convergence to $k_{2}^*$. The closer $k$ is to $k_{2}^*$ the slower capital per capita is growing. \n",
        "\n",
        "This effect is shown in the plots below with three different starting points of $k$. The *high* starting value of $k$ is at 90% of the steady-state value of $k^*$. The *medium* starting point of $k$ is at 50% of the steady-state value. And the *low* sarting value of $k$ is at 10% of the steady-state value. The first plot shows again the phase diagram with the starin position of each point. The second graph shows the evolution of $k$ for each starting point in time. The color black denotes the starting point high capital value, the blue color denotes the medium strating point, and the red color denotes the low starting point."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 923
        },
        "id": "P5Ast8tma2HF",
        "outputId": "f9e60ee8-4636-43e9-fd1e-11270c568aa6"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "# Parameters\n",
        "K_size = 101                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s = 0.35                         # Savings rate\n",
        "n = 0.02                         # Population growth rate\n",
        "# Arrays\n",
        "k = np.arange(K_size)            # Create array of k\n",
        "\n",
        "\"3|PLOT CHANGE IN CAPITAL FOR DIFFERENT STARTING POINTS\"\n",
        "T = 200\n",
        "time = np.arange(T)\n",
        "k1 = np.zeros(T)\n",
        "k2 = np.zeros(T)\n",
        "k3 = np.zeros(T)\n",
        "\n",
        "k_star = (s/(n+delta)*A)**(1/(1-alpha))\n",
        "k1[0] = k_star * 0.9\n",
        "k2[0] = k_star * 0.5\n",
        "k3[0] = k_star * 0.1\n",
        "\n",
        "def output(k):   # Cobb-Douglas Production Function (per capita)\n",
        "    y = A * (k)**(alpha)    \n",
        "    return y\n",
        "\n",
        "def motion(k):                   # Motion function of k\n",
        "    DeltaK = s * A*(k)**(alpha) - (n + delta)*k    \n",
        "    return DeltaK\n",
        "\n",
        "DeltaK = motion(k)\n",
        "\n",
        "Kdelta1 = motion(k1[0]) \n",
        "Kdelta2 = motion(k2[0])\n",
        "Kdelta3 = motion(k3[0])\n",
        "\n",
        "#### Phase Diagram\n",
        "fig, ax1 = plt.subplots(figsize=(10, 7))\n",
        "ax1.set(title=\"PHASE DIAGRAM\")\n",
        "ax1.plot(k, DeltaK, \"k-\", alpha = 0.7)\n",
        "ax1.yaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.xaxis.set_major_locator(plt.NullLocator())  # Hide ticks\n",
        "ax1.axvline(x=0, color = 'k')\n",
        "ax1.axhline(y=0, color = 'k')\n",
        "plt.box(False)                                  # Hide plot borders\n",
        "plt.text(100, -0.1, r'$k$')\n",
        "plt.text( -4,  0.6, r'$\\Delta K$')\n",
        "plt.plot(k1[0], Kdelta1, 'ko')                  # Add dot for K-high\n",
        "plt.plot(k2[0], Kdelta2, 'bo')                  # Add dot for K-medium\n",
        "plt.plot(k3[0], Kdelta3, 'ro')                  # Add for for K-low\n",
        "plt.text(k1[0]  , Kdelta1+0.05, r'$K_{H}$', color = 'k')\n",
        "plt.text(k2[0]  , Kdelta2+0.05, r'$K_{M}$', color = 'b')\n",
        "plt.text(k3[0]-2, Kdelta3+0.05, r'$K_{L}$', color = 'r')\n",
        "\n",
        "### Plot change of capital in time for each starting value (high, medium, low)\n",
        "for j in range(1, T):\n",
        "    k1[j] = k1[j-1] + s*output(k1[j-1]) - (delta + n)*k1[j-1]\n",
        "    k2[j] = k2[j-1] + s*output(k2[j-1]) - (delta + n)*k2[j-1]\n",
        "    k3[j] = k3[j-1] + s*output(k3[j-1]) - (delta + n)*k3[j-1]\n",
        "\n",
        "v = [0, T, 0, k_star*1.1]              # Axis range\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.plot(time, k1, \"k-\", label=\"High $k$ starting point\"  , alpha = 0.7)\n",
        "ax.plot(time, k2, \"b-\", label=\"Medium $k$ starting point\", alpha = 0.7)\n",
        "ax.plot(time, k3, \"r-\", label=\"Low $k$ starting point\"   , alpha = 0.7)\n",
        "ax.set(title=\"Convergence\", xlabel=r'$k$')\n",
        "plt.legend(loc=4)\n",
        "plt.axhline(y = k_star, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.axis(v)\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('k', rotation = 0)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LFjaSE5XKyqCw0L7M8G1R0d6DVPiLDv/h1H5cXGzv1VDO2RecllbzhYW3jIw999Xe9vYztbcAvngFMJEAeO8pKiqiqKiIwsJCdu/eXed+YWEhRUVFde7Xfy7UwHMMaWlptG7dmlatWlVvXbp0qfO4/vOtWrXaa2BKS0ujRYsWCkbSaKEQ7N5tx+/du/e+1T621w9ZxcUNG1lq0QJat667tWtngSl8LA9v4UBV+7b+a1q2jMCoUHOqrKz50muHqPBW+3HtgLV7d83jhvzucc6+7Fatar7I8LBd7X3h14Sfr73V/kMJf/Fx9LtHAUykEbz37N69m927d7Nz50527dq1123nzp3VrwkHqAPNUQoHp/T0dNq0aUO7du3IzMykTZs2pKenVz9XPzjVDlNpaWkKS9JsvLcgtHNnzbZr14GD1e7dBx51atkS0tNtCx+jO3XaM0y1arXnvtrH/ZR4PcpVVNR8mbt21Xzx4fv19+3ebX9AhYUHfu+0tJovPz3dQlNmZt0/kPr364en1NS4CkvNIV7/aooctPCo1I4dO9ixYwfbt2+vvl8/RIWDVbiR394452jTpk11eOrQoQNZWVnVAWp/W+vWrUmJ2yOHRKPwPKjaYWpf265dNff3NxiSlgZt2tRsmZk199PT6z5Xe0tPt+N3wvDeRpd27oTt22tud+you9UOU/sLUs7VfJlt21qA6tHDbut/0XsLVFF77jO+6De8xLXy8vI6gSocqmqHq9r79nVaLy0tjXbt2lWHqa5du9K2bdvqrfZz4X3p6em6+kwCFT6ub99uW0FBzf3aW3j/vqbjOFdzHG/XDrp3hyOOqHlce6t9bE/of0OEQjVfbn7+nmGq/ravJNuqFbRvb1uHDtYHIRys2rSp+dLbtq3Z16aNRp9iQCL/7yExrKysrLpbcX5+fvVWUFBQvS/cSXtvUlNT6dChAx06dCAjI4Ps7Gw6dOhA+/bt97ht164dqQn1z3GJdpWVdmzfts2O7du22ba3gFVevufPO2fH7YwMO6ZnZtpt+Di/t1Cl43mVkpKaUFX7tv6+qmVv9pCWVhOmOnWCww6r+dI7dKi5De9r0SKy/30SMQpgElW89xQUFJCXl0deXl6dMHWgYJWcnExGRgYdO3akR48eDBo0iIyMjOqgFQ5VHTp00NwoiVrFxTWBKrzVDlnhoFX/avikpJrjekaGDZR06FCzhcNW+Bivwdl6vLfEmpe351Y7WFWtVVlHSop9sR07QrducOSRdj8jo+Y2HKoUqKSKAphEjPeewsJC8vLy2Lp1K1u3bq0OWuHH27Zt2+M04N6CVceOHffY2rVrp1AlUS0UsuP5li2wdWvd23C42tvxPT3djuOdOlmw6tRpz619e4WqffLeRqTCX/TWrXve5ufveRowJQU6d7YvuG9fOP54C1O1g1XHjnbqT7975CApgEmTCV8RuHnzZjZv3symTZuq74cDVklJSZ2fSU5OplOnTnTu3JkjjzySLl260LlzZzp37kyXLl3o1KmTgpXEjJIS2Ly5JliFw1V4KyjYs3VCRgZ07Qq9e8Oxx+4ZrDp2tLNWsh/e2+T08Je/eXPd+1u27HnZZThcde4MRx9dc7/21q6dgpU0GwUwOShlZWV7hKvaj4uKiuq8vm3btnTr1o2srCyOPfbY6oAVvs3IyNBEdYkZ4bNUmzbBxo22he9v2mRzqWsLH+O7drVw1bUrdOlit1272nOaXthApaX2Jefm2m39oFXvH3e0aWNfcq9eNnJV+0tXuJIooAAmeygvL2fTpk3k5uayYcOGOrf5+fl1XtuiRQu6detG9+7dGThwIN26dat+3K1bN1q3bh3Qf4XIoamstGN67XAVvr9pU92BFOfsWJ6ZCSNG2G34ON+1q41u6Rh/EEpLa77w3Ny6t3l5dV/burXNt8rMhKFD7X63bjVffnp6MP8NIg2kAJagKisr2bJlS3Wwqh2ytmzZUqe3Vfv27enRowfHHnssmZmZ1eGqW7dudOjQQacHJSYVFsL69bBhQ93b3Ny6U4FatKh7nO/e3e53727HeY1gHaSKCkuy69bZl147aG3bVve17dvblz14sN326FHz5evSTIlxCmBxrqysjNzcXNauXcu6deuqbzdu3Fhnsnvr1q3p2bMnAwYMYNSoUfTs2ZMePXrQo0cP0vUvSYlR4dGscMAKh6z16+1UYlhysh3Te/WC4cOhZ0871nfvbnOwdJw/BGVlFqrWrYO1a+1LD4eu2gk3HLKGDKkJWOFb/e6ROKYAFidKS0tZv379XoNWeDTLOUePHj3IyspixIgR9OjRg549e9KzZ09NdJeY5r2doVqzpu62bl3dPlht29YNWb162datW4I3DW2MkpK6IWvtWnu8aVPNFQfOWZrNyoJhw+w2K8v+EBSyJEHpV06M8d6zdetWvvrqK7766itWr17N6tWryc3NrQ5aycnJ9OjRg759+3LyySfTu3dvsrKy6NGjBy3Ug0Zi3I4dewatNWvqtm/o3Bn69LFBlaysmqDVtm1wdcc87y1UrV5ds331Vd2glZJio1eHHQannGJffu/etk+/e0TqUACLYiUlJaxZs2aPsFX7SsPMzEyys7M5+eST6dOnD7179yYzM1PrCErM895OH65aBStX2rF+5Upr1xTWtq0FrVGj7LZPHzvet2kTXN1xoaiobsgK3w9faehcTdAaPdq++KwsG+VKTg6ubpEYoqN0lCgpKWHlypV8+eWX1duGDRuqR7VatWpFdnY2p556Kn379iU7O5s+ffrQqlWrgCsXabxQyM5a1Q5bq1ZZDgBrMJqVZSNaffva1qePNRfXmfNGKiy0L33lSvjyS9tyc2ueb9MGsrPhm9+0Lz4721Juy5ZBVSwSFxTAAnCgsNWxY0f69+/PySefTL9+/cjOzqZr166aoyVxwXubh718ec321Vc187JbtrRj/KmnQr9+tvXpozNYTSIctsJB68sv7QrEsM6doX9/G1Ls188CV6dOSrkizUABrJlVVlayZs0ali1bxhdffMGyZcv2Gbb69+9P//79ycjICLhqkabhvXUWWL4cVqyw2y+/rBnZSkuDww+HsWPtuN+vn53ZUm/eJhAK2WnDZcts++KLumGra1f70k8/3U4l9u9vVySKSEQogDWxHTt2sGzZsurAtXz58urld9q3b88RRxzBKaecwmGHHaawJXGnrMwC1uef2/F+xYqaOVspKTUjW0ccYcGrVy+FrSaTn29fejhwrVhhfyBgHWEHDLDTiP37W+Bq1y7YekUSnAJYI3jvWb16NZ9//nn16NbGqn9hJicn07dvX04//XQGDBjAgAED6N69u04jSlzZsQOWLrXAtXSpha/wqcSePW3O1uGHW+Dq21enEZtMRYWdt12ypCZ0bd1qz6WkWMAaM8ZC15FH2qlF/e4RiSoKYAchFAqxcuVKlixZwuLFi/n8888pLCwE7FTikUceyVlnncWAAQPo378/LTVJVeJIeO5WOHB9/nnNXO2UFAta555r6xofeaTOZjWp8nJLt4sXW+j6/POavhtdu9oXfv75Frj69VN7fpEYoAC2H2VlZSxfvrw6cH3xxRfVpxN79uzJyJEjGThwIAMHDqRLly4a3ZK44r0FrM8+g08/tdvwYtNt28JRR9kZraOPtrNaGt1qQiUlNqoVDlzLltWcTuzdG047DQYOtK1Tp2BrFZFDogBWSygUYvny5SxYsIDFixezbNkyyqvaaGdnZ3P66adXBy7N3ZJ4tGVLTdhatKhmab6OHeHYY2HQIDvm9+ypM1pNqrzcTiUuXGh/AF9+aacZnas5nThokKVdzd0SiQsJHcC896xfv54FCxawcOFCPvvsM0pKSnDO0b9/f8455xwGDhzI0UcfTVu10JY4lJ9vx/tFi2zbssX2t28Pxxxjc7iOOcauTFTgakLe2xWKCxfatnixjXAlJdmEuQsvtKR71FHQunXQ1YpIM0i4AJafn8+nn37KwoULWbhwIflVl2hlZmYyatQohgwZwuDBg2mjVtoSh0Ihmz70yScwf75lALBTisccAxdcAIMHW9NTBa4mtnVrTeD69NOa87lZWXDmmTB0qI1yKXCJJIS4D2ChUIglS5Ywb948FixYwJo1awBo27YtQ4cOrd66du0acKUizWPTpprAtWiRTS9KSbGzWVdfbcf9vn0VuJpcWZmNbM2bZ19++IqFjAw47jj74ocM0RwukQQVlwEsPz+f+fPnV4eu4uJiUlJSGDRoEKeddhpDhw6lX79+mjQvcam01OZwhUNX+LjfrZs1OD/+eBvlSksLts64tHWrBa65cy3tlpba1QnHHAPf+pZNpNPwoogQJwHMe8/y5cuZO3cuc+fOZdWqVQB07tyZU045hWHDhjFkyBDSdMSROJWfb8f8OXPsDFd5uR33Bw+Gc86x0JWZqeN+k6ustL4cc+da8KoaYadbN7tEdNgwC1+6RFRE6onZAFZeXs6iRYuYPXs2c+bMoaCgAOccRx11FFdccQXDhw+nT58+GuWSuOQ9rF1rgWvOHFviB6wl1JgxdtwfOFDH/WZRVgYLFtR8+Tt32jndgQNtWZ9hw3SZqIgcUEwFsKKiIubPn8+sWbOYN28excXFpKWlMWzYMEaMGMHxxx+vqxUlboUHW2bOtOP+5s22/4gj4PLL4Wtfs0WrddxvBrt22SjX7Nl2bre0FNLTLWx9/es2p0uT50XkIER9ANu1axezZs1i5syZfPrpp4RCIdq3b883vvENTjjhBAYPHkwL/TNf4lRFhfXh/OgjmDULCgqsyfnQoXDRRRa6OnYMuso4tX27pd2PPrLJ9JWVNmH+9NMtdA0aZCNfIiKHICp/e+zevZvZs2czY8YMFi5cSEVFBd27d2fs2LGccMIJDBgwgCSt4CtxKhSy4304dO3YYacShw+Hk06yQZdWrYKuMk7t2GGha8YMu5LBe1sx/KKLLHT1768hRhFpElETwCorK5k6dSozZsxgwYIFhEIhunXrxgUXXMA3vvEN+vbtq/lcEre8t9D1wQd2/N+1y65S/NrXLHQdd5yuWmw2O3ZY0p0xw65c9N7mcI0bByNH2tI/+t0jIk3Mee+DrgGAjIwMP3LkSLp27crIkSMZOXIk/fv3V+iSuOU9fPUVTJsGH35oy/6kpdlAy8iR1rFAZ9ebSUmJzeeaNs0m1FdWWrv/kSPhG9/QZDoROSDn3Hzv/bBD/vloCWDZ2dn+nXfe4YgjjlDokri2caONdH3wAaxfD8nJ1ibi1FNtxKtly6ArjFMVFTbC9f77NuJVUgJdusApp1joUjdaETkIjQ1gUXMKsnPnzgwYMCDoMkSaRWEhTJ8O770Hy5bZvkGD4Lzz7BSjLt5tJuFhxqlTbZixoMCuXjzlFEu8AwcqdIlIIKImgInEG+9tyb/33rMBl7Iym0501VV2/O/cOegK49iOHTbS9e671jAtJcWuXjjtNLvVuV0RCZgCmEgT27QJpkyxbetWG3A5/XTbdBFdM6qstPlckyfDxx/b5aQDBsBNN9ncLg0zikgUUQATaQLl5Xb14ttv29WMzlmvrquuskn1GnBpRps320jXlCmQlwft2sHZZ8MZZ9iQo4hIFFIAE2mEjRstdL33nq1I0727daUfNUqnGJtVKGTLAbz1lp3ndc4uG73uOhgxQg1SRSTq6beUyEGqqLAzXG+9ZWe8kpJslGvMGBgyRKcYm1V+PrzzjqXe/Hy7ivGyy2D0aLsvIhIjFMBEGmjbNjvuT55sx/7One3Yf8YZWg6oWYW71L75pl3NUFFhfTtuvtkm1GtVDBGJQQpgIgewbBlMnGiN0r23rvQ33WTH/uTkoKuLY8XF1j7ijTdg3Tpo0wbOPdeGGjMzg65ORKRRFMBE9iIUskn1EydaAGvd2o79Z59t87ykGW3dCpMm2anGoiK7dPSWW6xZqrrUikicUAATqWXXLjvuv/66nXLMzITvf9+mGGkB7Ga2YgW8+qoNNYK1jjj3XDjiCE2sE5G4owAmgl3N+N//2hmvsjJrIRGeYqRjfzOqrLSrGV99FT7/3IYazzsPxo7VpHoRiWsKYJLQvvwS/vMf+Ogj61xw2ml27M/ODrqyOFdaar27Jk609NtprglaAAAgAElEQVS1q7WQOOMMDTWKSEJQAJOE4z189hn83//BwoU26PLtb9vZroyMoKuLc4WF1r/j1VdtuaABA+DKK62Ph65oEJEEogAmCcN762Lw8ss23ahDBzv2jxljywVJM9q500a7Xn/dQtjxx8N3vmOLYYuIJCAFMIl7FRXwwQcwYQJs2GBXMd58s3Wr1xJBzWzbNnjlFWugVlYGJ5xgwat//6ArExEJlAKYxK2KCvjwQ3jxRcjNhb594bbb4MQTdbar2W3ebOd4p0yxifanngoXXQRZWUFXJiISFRTAJO5UVtYErw0bLHjdcYctEagrGptZXp4NNU6ebB3qzzgDLrwQunULujIRkaiiACZxo7ISpk+HF16w4JWdDb/+tc3vVvBqZgUFNrnurbdsst2ZZ8LFF0OnTkFXJiISlRTAJOZ5b707X3jBVqzJzoZf/cqmGyl4NbOdO62Px+uv2/IBo0fDJZdYWwkREdknBTCJaQsXwlNPwcqV0KcP3H67zfFS8GpmhYU2uf6116yn16mnwne/qzUaRUQaSAFMYtLKlRa8Fi60wZaf/cwygIJXMysvt8WxX3oJdu+25YIuvVST60VEDpICmMSUjRth/HibZN+2rTVP/9a3IDU16MrinPc2we6ZZ+wKx+OOsyZq/foFXZmISExSAJOYsH27Dbq89Za1kLj4Yru4Tg1UI2DxYnjiCete27cv/OEPtlimiIgcMgUwiWplZTbNaMIEu3/mmTbHu2PHoCtLAOvW2Xnejz+Gzp3hpz+187xJSUFXJiIS8xTAJCqFlw164gk74zViBFx9NfTsGXRlCWDHDjvPO3kypKXZqcZzz9WyASIiTUgBTKLO6tXw6KOwaBH07q0zXhFTUQFvvgnPPQclJXD22Tbc2K5d0JWJiMQdBTCJGjt32sDL229DmzZw4412ylHLBkXAokXwyCOwZo2l3Rtu0JWNIiLNSAFMAhcK2cDL889DcTGcc461lGrbNujKEsDWrXaed8YM6+ehNZtERCKiSQKYcy4ZmAds8N6f45zrCLwEZAOrgYu99wVN8VkSXz7/HB54ANautYGX66+3047SzMrKrJHqhAn2+LLL7LJSzfMSEYmIphoBuwVYCoQni9wOTPHe3+Ocu73q8S+b6LMkDuzaBU8+Ce++C126wJ13wte+poGXiJg7Fx5+2K5uOOkkuOYaLR0kIhJhjQ5gzrlewNnAH4GfVe0+Dzi16v7TwDQUwAS7unHqVHj8cVvN5sIL7XRjWlrQlSWA/Hy7umHGDJvfdffdMGRI0FWJiCSkphgB+ztwG1B7xk437/1GAO/9Ruec/nktrFsHDz5ofT2POgpuuskWzpZm5r1d2fD003bq8fLLLfmmaAqoiEhQGvUb2Dl3DrDFez/fOXfqIfz8DcANAL018SdulZZaF/v//hdat4Yf/xhOP12nGyNi7Vr4179g6VIYPBhuvhl69Ai6KhGRhNfYfwKfBJzrnPsWkAa0c86NBzY75zKrRr8ygS17+2Hv/SPAIwDDhg3zjaxFotCiRXD//TbdaPRoa6bavn3QVSWAsrKa1NuqFfzkJzBqlFKviEiUaFQA897/CvgVQNUI2K3e++855+4FrgTuqbp9rZF1SowpLrZJ9m+9BZmZ8Kc/wTHHBF1Vgli0yC4tzc210HXttWqmKiISZZprEsg9wATn3LXAWuA7zfQ5EoUWLIB//hPy8uD88+F734OWLYOuKgGUlFjqffNNS71aQkBEJGo1WQDz3k/DrnbEe78NGN1U7y2xobDQrm58913o1Qv+93/hyCODripBLF4M//iHnes97zybaK/UKyIStXQZlDSJefNsrnd+Plx0kbWWUE/PCCgthWeegUmToHt3+POfYeDAoKsSEZEDUACTRikstNZSU6ZYB/s77oDDDw+6qgSxdCn8/e821+ucc+DKK9VQTUQkRiiAySFbvBhycmzUa9w421JTg64qAZSVwXPP2VJCXbrAH/9oLSZERCRmKIDJQQuF7Pj/n//YXO9774Ujjgi6qgSxahX89a/W1fass6yvR+vWQVclIiIHSQFMDsq6dXb8X7UKzjwTrrtOZ70iwnt47TXrZt+uHdx1Fxx3XNBViYjIIVIAkwbx3np6Pf64XVx3550wYkTQVSWIggK47z7r7zFiBNxyC7Rte+CfExGRqKUAJge0fbt1s587F44/3pYS6tgx6KoSxLx5NtG+uNgWzzzrLHWzFxGJAwpgsl+1j//f/z6cfbaO/xFRVgZPPWXtJbKzrb1EVlbQVYmISBNRAJO9CoVg/HibaN+3L9x6q7WZkAhYt8662K5eDWPHwlVXqamaiEicUQCTPeTl2fF/6VIYM8Ym2uv4HwHew+TJ8MgjtoD2b34Dw4cHXZWIiDQDBTCpY/58+Nvf7AzYL34BJ58cdEUJorQUHnwQpk619Rt/+lNNtBMRiWMKYAJARQU8/zxMmGBTjm6/HXr2DLqqBLFhA9xzD6xZY2s4XXIJJCUFXZWIiDQjBTAhP9+aqS5eDGecYZPtdcoxQmbOtKscUlLgd79Tby8RkQShAJbgFi60xqolJfCzn8FppwVdUYIIhewqx9degwED4Je/tGWFREQkISiAJSjv4eWX4dlnoVcvdTmIqG3b4C9/sasczjkHrr3WRsBERCRh6Ld+AioutrNeM2faJPsf/UjLCUXMokV2iWlpqa5yEBFJYApgCSY3F+6+G9avt4GX885TY9WI8B4mTrS1nHr1gl/9SkOOIiIJTAEsgcydCzk5doHd3XfD4MFBV5QgysrggQesxcSJJ1qLCQ05iogkNAWwBOC9tZcYPx769YM77oCuXYOuKkFs2wZ//COsWAGXXQbjxmnIUUREFMDiXVkZ/OMf8OGHdoXjD3+oFhMR88UX8Kc/2aS7O++EESOCrkhERKKEAlgcy8+3U41ffglXXgnf/rYGXyJmyhT417+stcTdd2shTRERqUMBLE6tWGHH/aIiO+WowZcI8R6eecZ6fAwdCrfdBm3bBl2ViIhEGQWwODR9urWZ6NDBOtxnZwddUYIoKbGFNGfNslXMb7hB/b1ERGSvdHSII7Un2x91lI18tW8fdFUJIj8f/vAHWLkSrr8exo7V+V4REdknBbA4EQrBgw/Cu+/aZPsf/QhSU4OuKkGsWgW//z0UFsL//A8MHx50RSIiEuUUwOJAYSHcc4+t63jJJXDppRp8iZh582xZoTZtdL5XREQaTAEsxm3dCr/7HWzYAD/5CYweHXRFCeSdd2zYsW9f+M1voGPHoCsSEZEYoQAWw1auhLvusl5fd90FQ4YEXVGC8B6efx5efBGOPx5uv12d7UVE5KAogMWoBQusx2fbtmozFVGhkPX3mjIFvvlNuOkmXekoIiIHTUeOGPTBB3DffbaW81136cxXxBQVwZ//bJPttKyQiIg0ggJYjHntNXjsMRg0yFa3SU8PuqIEsX07/Pa3sHo13HILnH560BWJiEgMUwCLEd7D00/Df/4DJ54IP/+51nSMmC1bLO1u22aT7Y8/PuiKREQkximAxYBQCP75T5g6Fb71Lfj+9yEpKeiqEsTatdbbq6wM/vhHOPLIoCsSEZE4oAAW5crKrMfX3LmadhRxX3xhk+xatLA/hD59gq5IRETihAJYFCsutiscP/sMbrzRRr8kQj75xC4z7djRlhjq1i3oikREJI4ogEWpXbusweqXX8JPf2rLC0mEzJgBOTl2menvf2+rmouIiDQhBbAoVFBg0442bIBf/xpGjAi6ogQydSr8/e821+u3v9VlpiIi0iwUwKJM+IK7ggIbAVN3+wh6+2144AH70u+8U93tRUSk2SiARZGNG23Eq7jYph3pgrsICjdYGz7clhZSjw8REWlGCmBRIny6MRSyud/9+gVdUQKZMAGefRZOOgluvVVLC4mISLPTkSYKrFsHd9wBlZUWvtTtIEK8h/HjLYCddpp1uE9ODroqERFJAApgAVuzxsJXUpItM5iVFXRFCcJ7eOYZePllOPNMuPlmNVgTEZGIUT/1AH31lZ12TE5W+Iqo2uFrzBiFLxERiTgFsICsWmUjX+Em6z17Bl1Rgqgfvm68UeFLREQiTqcgA/DVVzVdDv70J+jePeiKEkTt8PWtb8EPfqDwJSIigdAIWIStWWPhq2VLha+IUvgSEZEoogAWQeGrHVNSFL4iyntrM6HwJSIiUUIBLEI2bLDw5ZyFr8zMoCtKIBMmwP/9H5x1lsKXiIhEBc0Bi4CNG2v6fP35z5pwH1GvvGK9vkaNgptuUvgSEZGooADWzLZssVYTZWU28qVWExH05pvwxBMwciT8+McKXyIiEjUUwJrR9u024b642MJXdnbQFSWQ996Df/8bRoyAn/9cHe5FRCSqKIA1k9274X/+B/LzbWFtre0YQR9+CPffD8ceC7fdprUdRUQk6mgSfjMoKYHf/Q7Wr7cRsKOOCrqiBDJ3LuTkwMCBNZ1uRUREoowCWBMrK7MRrxUrbPBl6NCgK0ogixfbsgKHHQa/+Y01WxMREYlCCmBNKBSC//1fWLQIbrkFTjgh6IoSyKpVlny7dLHhx1atgq5IRERknxTAmoj3Nu1ozhxrNTVqVNAVJZDcXBvxat0a7r4b2rULuiIREZH9UgBrIk8+Ce+/D9/7Hpx9dtDVJJBt2+xqB+8tfHXuHHRFIiIiB6TLw5rAK6/Yds45cPHFQVeTQHbtsvC1a5f1+VCHWxERiREaAWukqVNren1ef716fUZMaSncdRds2mQhrH//oCsSERFpMAWwRpg/H/7xDxg8GH72M0jStxkZFRVw772wfDnceiscc0zQFYmIiBwURYZDtGyZreuYnW3tplJTg64oQXgPDz1kVzvccAOceGLQFYmIiBw0BbBDsGGDnf3KyLCOB61bB11RApkwAd5+Gy66yCbdiYiIxCAFsIO0Ywf89rd2uvH3v7cQJhHy3nswfjycdhpccUXQ1YiIiBwyXQV5EEpLLXQVFNhFd5mZQVeUQObPh3/+05YW+PGPdbWDiIjENI2ANVBlJfz1r7bE0C9+AQMGBF1RAlm5smbC3a9/rcW1RUQk5imANdDjj8Ps2dZq4utfD7qaBJKXZ8OO7drZuV8tMSQiInFAQwkNMHGibeedB2PHBl1NAikutqsdiout7UTHjkFXJCIi0iQ0AnYAs2bBY4/ZwtrXXBN0NQmkosJWNl+7Fm6/Hfr0CboiERGRJqMAth8rVti8ryOOgJ//XI1WI8Z7ePRRmDcPbrwRjjsu6IpERESalCLFPmzbZms7d+hgK920bBl0RQlk0iR44w244AI466ygqxEREWlymgO2FyUl8Ic/QFGRTT1q3z7oihLIxx/bOd8TT4Srrw66GhERkWahEbB6vIf77oNVq+C226zzgUTI6tWWePv3t8U11etLRETiVKMCmHMuzTn3sXPuU+fcEufcXVX7Ozrn3nXOrai6jZl+8ePHw8yZcO21MHx40NUkkB07bNixdWu4806d8xURkbjW2BGwUmCU934IMBQ4yzn3deB2YIr3/nBgStXjqPf++7bU4JlnwrnnBl1NAgmFrNHq9u0WvtRuQkRE4lyjApg3u6seplZtHjgPeLpq/9PA+Y35nEhYuhTuvx8GD4Yf/EBnvyLGe3jwQViyBH7yEzj88KArEhERaXaNngPmnEt2zi0EtgDveu/nAN289xsBqm67NvZzmlNenq3t2KWLtZzSSjcRNGkSvPsujBsH3/hG0NWIiIhERKMDmPe+wns/FOgFfM05N6ihP+ucu8E5N885N2/r1q2NLeWQlJVZ+CopsXYTbdsGUkZi+uSTmi63l10WdDUiIiIR02RXQXrvtwPTgLOAzc65TICq2y37+JlHvPfDvPfDunTp0lSlNJj38K9/WcPVW2+FrKyIl5C4NmywTvd9+uiKRxERSTiNvQqyi3OuQ9X9VsDpwBfARODKqpddCbzWmM9pLhMn2sT7yy6DESOCriaBFBVZl9vkZBt2TEsLuiIREZGIauxsp0zgaedcMhbmJnjvX3fOzQImOOeuBdYC32nk5zS5hQvh8cet3+e4cUFXk0DCjdZyc63tRNeonh4oIiLSLBoVwLz3i4Bj97J/GzC6Me/dnDZuhL/8BXr3hp/+VGe/ImrCBJg9G667zi45FRERSUAJ1wm/pAT++Ee7f8cdOvsVUXPnwnPPwWmnqdGaiIgktIQKYN5br6+1a+GXv4TMzKArSiC5uZCTA337ws03a9hRREQSWkIFsEmTYPp0uPxyGDo06GoSSHGxTbpPSrJhRy0zJCIiCS5hAtiSJfDEE/D1r8NFFwVdTQLxHv7xD1i/3oYdNeleREQkMQJYfr5Nuu/WzVa70dmvCHrtNfjoI7j6ahgyJOhqREREokLcB7BQyMJXURH8+teQnh50RQlkyRJ48knr9XF+1C8HKiIiEjFxH8Ceego+/xx+/GNrui4RUlBgne67dbMvX8OOIiIi1eI6gH34oZ0BO/dcOPnkoKtJIBUVcO+9sHu3hh1FRET2Im4D2Pr18M9/wlFH2fQjiaDx4+Gzz+CmmyA7O+hqREREok5cBrDSUrjnHmjRwi68S2nsgkvScHPmwMsvw1lnweioXQxBREQkUAcMYM65bOfc4kgU01Qeftiarf7859CpU9DVJJBNm2ydx8MOg+uvD7oaERGRqBV3I2BTpsC778LFF8NxxwVdTQIJhWzSPcCvfmXDjyIiIrJXBxXAnHP9nHMLnHPDm6ugxlizBh58EI45Bi69NOhqEsxTT8GKFdZorVu3oKsRERGJag0OYM65AcB/gKu993Obr6RDU1Ji875at4Zbb7VVbyRC5s61y03POceWGhAREZH9amhM6QK8BnzPe7+wGes5JN7DAw/Ahg3wi19Ax45BV5RA8vJs3le/frrcVEREpIEaGsB2AOuAk5qxlkM2ZQpMm2anHQcPDrqaBFJRAX/9K5SXw223ad6XiIhIAzU0gJUB5wNXOOeianbVhg3w0EM27+vii4OuJsG8+KItN3TTTdCzZ9DViIiIxIwGd8jy3hc6584B3nXOFXrvX2vGuhqkvNwuvGvRwlpOaN5XBC1aBC+9ZL2+Tjst6GpERERiygEDmPd+NTCo6v52IGqugHz6aVi1Cu68U/2+ImrHDjv12LMn/OAHQVcjIiISc2J2zGj+fLvw7uyzYcSIoKtJIN7D3/5m6zz+8peQlhZ0RSIiIjEnJgNYQYFdeNenD1xzTdDVJJj//hc++cQ63WudRxERkUMScwHMewtfxcW68C7ili2DZ5+Fk06ytR5FRETkkMRcAHv1VViwwAZgevcOupoEUlhoVzx06gQ/+hE4F3RFIiIiMSumAtiKFTbx/sQT4cwzg64mwTzyiDVd/cUvID096GpERERiWswEsOJiuPdeyMiAH/5QAzARNWMGTJ0K48bBkUcGXY2IiEjMi5kA9tBDsGmT9ftq2zboahJIXp6t8zRggDrdioiINJGYCGAffFAzADNoUNDVJJDwFQ+hEPzsZ5DS4L69IiIish9RH8Dy8uDf/7YzX5dcEnQ1Cea116zj/fXXQ48eQVcjIiISN6I6gIUHYCoqbAAmOTnoihLI6tV2xcOIEfDNbwZdjYiISFyJ6gA2aZINwFx7LWRmBl1NAikrs6WG2rRRywkREZFmELUBbN06G4AZPlwtJyLumWdgzRr4yU+gffugqxEREYk7URnAQiFbbrBlSw3ARNzChTb365xz4Pjjg65GREQkLkVlAHvpJfjyS+v3lZERdDUJZNcum3SXlQVXXRV0NSIiInEr6gLYsmUwYQKMGmUd7yVCvId//Qt27rRmay1bBl2RiIhI3IqqAFZSYqceO3WCG24IupoEM20azJwJl10Ghx0WdDUiIiJxLaoC2JNPQm6uzf3WcoMRtG0bPPwwHHUUXHhh0NWIiIjEvagJYEVF8OabcN55MHhw0NUkkPCpx/JyS75JUfNXQkREJG5FzdF2yxab+33FFUFXkmCmTIF582zSvbrdi4iIRETUBLBQCG69FVq0CLqSBJKXB48+agtsnnNO0NWIiIgkjKgJYJ06Qb9+QVeRQLyH+++Hykq45RY1WxMREYmgqAlg6vcVYe+8AwsWwNVXQ/fuQVcjIiKSUKImgEkEbdkCjz8OQ4bAmDFBVyMiIpJwFMASjffwj3/Y/R//WKceRUREAqAAlmjeegsWLYLrroOuXYOuRkREJCEpgCWSTZvgiSfguOPgjDOCrkZERCRhKYAlivCpx5QU+NGPdOpRREQkQApgiWLSJFi8GK6/Hjp3DroaERGRhKYAlgg2b4ZnnoFhw2DUqKCrERERSXgKYPEuvNZjUhLcfLNOPYqIiEQBBbB4N3UqLFxoaz3q1KOIiEhUUACLZ9u3w2OPwdFHq+GqiIhIFFEAi2cPPwylpWq4KiIiEmUUwOLV7NkwYwZccgn07Bl0NSIiIlKLAlg8KiyEf/8b+vaFCy8MuhoRERGpRwEsHj35JBQU2KnHlJSgqxEREZF6FMDizWefwTvvwAUXQP/+QVcjIiIie6EAFk9KS+Gf/4TMTLj00qCrERERkX1QAIsnzz8PGzfCD38ILVsGXY2IiIjsgwJYvPjyS3jlFTjzTBg8OOhqREREZD8UwOJBKAT33w8ZGXD11UFXIyIiIgegABYPJk2Cr76CH/wA0tODrkZEREQOQAEs1m3ZAs89ByNGwAknBF2NiIiINIACWCzzHh56yJYZ+v73g65GREREGkgBLJbNmgVz51rLiS5dgq5GREREGkgBLFYVF8Mjj9hyQ+eeG3Q1IiIichAUwGLV+PGQnw833wzJyUFXIyIiIgdBASwWrVxpVz6OGQMDBgRdjYiIiBwkBbBYU1kJ//oXdOgAV1wRdDUiIiJyCBTAYs0bb1jX++uvV88vERGRGKUAFku2bYNnn4XjjoORI4OuRkRERA6RAlgseeQRqKiAG2+03l8iIiISkxTAYsXcuTBzJowbB927B12NiIiINEKjAphzLss5975zbqlzbolz7paq/R2dc+8651ZU3WY0TbkJqqTEOt5nZcGFFwZdjYiIiDRSY0fAQsDPvfdHAV8HbnbOHQ3cDkzx3h8OTKl6LIfqpZdszcebb4aUlKCrERERkUZqVADz3m/03n9SdX8XsBToCZwHPF31sqeB8xvzOQlt/Xp49VUYPRoGDgy6GhEREWkCTTYHzDmXDRwLzAG6ee83goU0oOs+fuYG59w859y8rVu3NlUp8cN7ePhhaNkSrr466GpERESkiTRJAHPOtQH+A/zEe7+zoT/nvX/Eez/Mez+sixaT3tNHH8HChXD55dC+fdDViIiISBNpdABzzqVi4es57/1/q3Zvds5lVj2fCWxp7OcknJISeOwx6NfPlhwSERGRuNHYqyAd8Diw1Hv/t1pPTQSurLp/JfBaYz4nIb34ojVevfFGSFK3EBERkXjS2EvqTgIuBz5zzi2s2vdr4B5ggnPuWmAt8J1Gfk5iWbfOJt5/85tw5JFBVyMiIiJNrFEBzHs/A9hXS/bRjXnvhOW99fxKS4Mrrzzw60VERCTm6NxWtJkxAxYtgiuu0MR7ERGROKUAFk2Ki23i/WGHwVlnBV2NiIiINBMFsGjywguQn6+J9yIiInFOR/losXYtTJwIZ5wBAwYEXY2IiIg0IwWwaBCeeN+6tSbei4iIJAAFsGgwfTp89plNvG/XLuhqREREpJkpgAWtuBgefxwOP9xOP4qIiEjcUwAL2oQJNvH++9/XxHsREZEEoSN+kDZutI73o0Zp4r2IiEgCUQAL0mOPQUqKJt6LiIgkGAWwoMyfDx9/DJdcAh07Bl2NiIiIRJACWBBCIXj0UejRA849N+hqREREJMIUwILw+uuwYQNcdx2kpgZdjYiIiESYAlikbd9uSw4NGwbDhwddjYiIiARAASzSnnkGysps9EtEREQSkgJYJK1YAe++a/O+evYMuhoREREJiAJYpHgPDz8MHTrAuHFBVyMiIiIBUgCLlPffh2XL4KqrbNFtERERSVgKYJFQXAxPPQVHHGFd70VERCShKYBFwoQJUFAAN9wAzgVdjYiIiARMAay55ebaeo+jR2u9RxEREQEUwJrfY49Zs1Wt9ygiIiJVFMCa0/z5MHcufPe7kJERdDUiIiISJRTAmkt4vceePWHs2KCrERERkSiiANZcJk2y9R6vvx5SUoKuRkRERKKIAlhzCK/3OHw4HH980NWIiIhIlFEAaw7PPWfrPV57bdCViIiISBRSAGtqq1fDO+/A2WdrvUcRERHZKwWwpuS9tZ1IT4dLLgm6GhEREYlSCmBNae5c+PRTuPRSaNs26GpEREQkSimANZVQCJ54Anr1gjFjgq5GREREopgCWFN5801rO3HNNWo7ISIiIvulANYUdu2C55+HoUNh2LCgqxEREZEopwDWFF54AYqK4LrrwLmgqxEREZEopwDWWOvXwxtvwFlnQZ8+QVcjIiIiMUABrLGeeALS0uCyy4KuRERERGKEAlhjLFhgrSfGjYP27YOuRkRERGKEAtihqqiwpqvdu8PYsUFXIyIiIjFEAexQTZ4Ma9fC1VdDamrQ1YiIiEgMUQA7FIWFtuD2oEFwwglBVyMiIiIxRgHsUEyYADt3qu2EiIiIHBIFsIO1cSNMnAijRsFhhwVdjYiIiMQgBbCD9dRTttTQFVcEXYmIiIjEKAWwg7F4McycCRddBB07Bl2NiIiIxCgFsIaqrIRHH4XOneGCC4KuRkRERGKYAlhDTZ0Kq1bBVVdBixZBVyMiIiIxTAGsIUpK4JlnYMAAOPnkoKsRERGRGKcA1hAvvwwFBXD99Wo7ISIiIo2mAHYgW7fCK6/YyNeAAUFXIyIiInFAAexAnnrKbq+6KsgqREREJI4ogO3PsmXw4Yd21WOXLkFXIyIiInFCAWxfvLe2Ex07Wt8vERERkVzyetcAAB3MSURBVCaiALYv06fbCNjll0NaWtDViIiISBxRANub0lJ48kno1w9Gjw66GhEREYkzCmB78+qrkJenthMiIiLSLBTA6svPt75fJ54IgwYFXY2IiIjEIQWw+p59FkIhtZ0QERGRZqMAVtvKlTBlCowdC5mZQVcjIiIicUoBLMx7eOwxaNsWxo0LuhoRERGJYwpgYbNmweLF8L3vQXp60NWIiIhIHFMAAygvt7YTvXvDGWcEXY2IiIjEOQUwgEmTYNMmuO46SE4OuhoRERGJcwpgO3bASy/BsGFw7LFBVyMiIiIJQAHsueegpASuvTboSkRERCRBJHYAW7MG3n4bzj4bevUKuhoRERFJEIkbwMJtJ9LT4bvfDboaERERSSCJG8DmzoWFC+HSS633l4iIiEiEJGYAC4Xg8cfttOOYMUFXIyIiIgkmMQPY669Dbq61nUhJCboaERERSTCJF8B27IAXX4Tjj7dNREREJMISL4A99xwUF6vthIiIiASmUQHMOfeEc26Lc25xrX0dnXPvOudWVN1mNL7MJrJ6dU3biaysoKsRERGRBNXYEbCngLPq7bsdmOK9PxyYUvU4eGo7ISIiIlGiUQHMe/8hkF9v93nA01X3nwbOb8xnNJmPP4ZPP1XbCREREQlcc8wB6+a93whQddu1GT7j4ITbTmRlqe2EiIiIBC7QSfjOuRucc/Occ/O2bt3afB/0+uuwcaNNvFfbCREREQlYcwSwzc65TICq2y37eqH3/hHv/TDv/bAuXbo0Qymo7YSIiIhEneYIYBOBK6vuXwm81gyf0XBqOyEiIiJRprFtKF4AZgEDnHPrnXPXAvcA33TOrQC+WfU4GGo7ISIiIlGoUROivPf76ucwujHv2yTUdkJERESiVPx2wlfbCREREYlS8RnAysvVdkJERESiVnwGMLWdEBERkSgWfwEs3HZi2DC1nRAREZGoFH8B7NlnobQUrrkm6EpERERE9iq+AtiKFTB5Mowdq7YTIiIiErXiJ4B5Dw8/DO3bq+2EiIiIRLX4CWBTp8KyZXDVVdC6ddDViIiIiOxTfASwwkJ48kkYMABGjQq6GhEREZH9io8A9sILsHMn/OAH4FzQ1YiIiIjsV+wHsLVrYdIkOPNM6N8/6GpEREREDii2u5SGJ963bg2XXx50NSIiEgHl5eWsX7+ekpKSoEuRBJCWlkavXr1ITU1t0veN7QA2cyYsWmSnHtu1C7oaERGJgPXr19O2bVuys7NxmnYizch7z7Zt21i/fj19+/Zt0veO3VOQpaW23mN2Npx1VtDViIhIhJSUlNCpUyeFL2l2zjk6derULKOtsRvAXn4Ztm610a/k5KCrERGRCFL4kkhprr9rsRnANm2C//wHTjkFBg4MuhoRERGRgxKbAeyxx2zU6+qrg65ERERE5KDFXgCbPx/mzIFx46BTp6CrERGRBNWmTZs6j5966il++MMfAnDiiSfu92dXr17NoEGDGvQ57733Hpcf5JX+27dv58EHHzyon9nXzx3ov6U5HeizD/W/MxrEVgArK4NHHoEePeC884KuRv6/vfuPiuq89z3+fjRcFfBYtTGt1ao5KwhhBMJPFSSmiRij4s9FwwoRf6A52t7ktEuWJk2ysvKj0dZ4PK5VkkKVa28jelKO3li9uS25tRcaNQWVSFEOMXcac8zSVBqO/PJKfO4fDBx+DDoqzAb5vNaa5cye59n7ux+f2fPlefbsLSIiXn3wwQc9tq7y8nIeeOCBm6pzK4mJtZaampou9XpyX27WjbatBMxfCgvh/HlYuxZ6+HocIiIiPaX96Ngrr7xCaGgos2bNIj09nS1btgDw1VdfsXr1asLDw0lJSaGxsdHruloTsCtXrrB8+XKee+45rLVt79fX1zN37lwiIyNxuVzs3buXjRs3cvbsWaKiosjOzgZg4cKFxMTEEB4eTm5uLtAyEhcWFsa6deuIjo5m1apVXeq17ktrWW8xd7eP7bndbkJDQ8nMzCQiIoKlS5fS0NAAwNatW3G5XLhcLrZt29alHbvbtrf97C/6z3XAzp+Hd96B5GSIinI6GhER6QPy8vL45JNPenSd9957L6tXr75hucbGRqLafR/V1NSQmpraoUxpaSmFhYWcOHGC5uZmoqOjiYmJAaC6upqCggLy8vJIS0ujsLCQjIyMLtspLy9nzJgxzJ49m6ysrC5l3nvvPcaOHcvBgwcBqK2tJSEhgYqKCk6ePNlWbufOnYwaNYrGxkbi4uJYsmQJAFVVVeTn55OTk4Pb7WbevHkd6rXnLebQ0NBu97GzqqoqduzYQWJiIitXriQnJ4eHHnqI/Px8jh07hrWWhIQEHnzwwS6jft62vWnTpi772V/0jxEwa+HNN1tGvVatcjoaERERhg0bxsmTJ9seL7/8cpcyJSUlLFiwgGHDhjF8+HDmz5/f9t6kSZPaEriYmBjcbneX+levXsXtdpOens7rr7/uNUGbMmUKRUVFbNiwgeLiYkaMGOE13u3btxMZGcnUqVM5d+4c1dXVAEyYMIGpU6f6tM/eYr7ePnY2fvx4EhMTAcjIyKCkpISSkhIWLVpEUFAQwcHBLF68mOLiYp+23Z/1jxGwkhI4eRKeegpGjXI6GhER6SN8GalyUvupws6GDBnS9nzw4MFepyArKyuJi4ujpqaGwd1c8zIkJISysjIOHTrEs88+S0pKCsuWLetQ5vDhwxQVFXHkyBECAwOZOXNm28VFg4KCfN4fbzFfbx8763xNLWOMz/V9aa/+pO+PgNXXQ15ey422H3vM6WhERER8lpSUxIEDB2hqaqKurq5tmtBX5eXlTJ8+nT179rBixQouXLjQpcz58+cJDAwkIyOD9evXc/z4cYYPH87ly5fbytTW1jJy5EgCAwM5c+YMR48e9bq9zvV6eh8//fRTjhw5AkBBQQFJSUkkJyezf/9+GhoaqK+vZ9++fcyYMcOnbd9KvH1F30/A3n4bvvwS1q2DQX0/XBERkVZxcXGkpqYSGRnJ4sWLiY2N7XaK0Jvy8nJcLhchISFs3ryZtLQ0rl692qHMqVOniI+PJyoqitdee43nn3+e0aNHk5iYiMvlIjs7m0cffZTm5mYiIiJ44YUXup1y7Fyvp/cxLCyMXbt2ERERQU1NDWvXriU6Oprly5cTHx9PQkICWVlZPv/q81bi7SvMzQwd9qbY2FhbWlraceHHH8MPfwhz57ZMP4qIyIB3+vRpwsLCnA7DZ3V1dQQHB9PQ0EBycjK5ublER0c7HVaP8mUfW0/wr6iocCjKW+etzxljyqy1sbe6zr57Dti1a5CTA1/7Gng56VBERKQ/WLNmDZWVlTQ1NZGZmXnHJV8wMPaxp/XdBOzgQaiuhuxsuIkTBEVERPqS3bt3Ox1Cr/NlHydOnNgvR796S988qeriRfjlLyE6Gnw8EU9ERESkv+h7CZi1LVOPAN/7HnT6yaqIiIhIf9f3ErA//KHlhtvLlsGYMU5HIyIiItLj+lYCVlvbcrPtyZNbfvkoIiIicgfqWwlYXh40NsLTT+uaXyIiInLH6jtZTn19y/RjWhp8+9tORyMiIiLSa/pOAvbFFzB+PCxd6nQkIiIiIr2q7yRgzc0tU48BAU5HIiIiItKr+k4CNmIEhIY6HYWIiIhPjDE8+eSTba+bm5u5++67mTdvns/reOmll9iyZUvb6+nTp/dojK2Kioo6xOqLL7/8kpzWy0LdZr3e2i9f3Gjbt7qft6vvJGBf/7rTEYiIiPgsKCiIiooKGhsbAfjd737Ht771rdta5wcffNAToXVRXl7u8w2uW91KYmKtpaampku93tovX9xo20rAdMFVERHpZ+bMmcPBgwcBKCgoID09ve29X/3qV8THxxMVFcVTTz3FV199BcBrr73G5MmTeeSRR6iqquqwvuDgYNxuNy6Xq23Zli1beOmll4CWG1qHhoaSlZWFy+XiiSeeoKioiMTERO677z4+/PBDr3G2JmBXrlxh+fLlPPfcc1hr296vr69n7ty5REZG4nK52Lt3Lxs3buTs2bNERUWRnZ0NwMKFC4mJiSE8PJzc3Ny2mMLCwli3bh3R0dGsWrWqS73g4OAOZVevXk14eDgpKSltCewrr7xCaGgos2bNIj09vcPIYKvW/c/MzCQiIoKlS5fS0NAAwNatW3G5XLhcLrZt29ahTa+3bW/76Q99916QIiIiN5CXB5980rPrvPdeWL3at7KPP/44L7/8MvPmzeOjjz5i5cqVFBcXc/r0afbu3csf//hHAgICWLduHW+//Tbh4eHs2bOHEydO0NzcTHR0NDExMTcV38cff8w777xDbm4ucXFx7N69m5KSEt59911+/OMfs3///i51ysvLGTNmDLNnzyYrK4uMjIwO77/33nuMHTu2LZmsra0lISGBiooKTp482VZu586djBo1isbGRuLi4liyZAkAVVVV5Ofnk5OTg9vtZt68eR3qtVddXU1BQQF5eXmkpaVRWFhIaGgohYWFPrVLVVUVO3bsIDExkZUrV5KTk8NDDz1Efn4+x44dw1pLQkICDz74YJdRP2/b3rRpU5f99AclYCIiIrcoIiICt9tNQUEBjz32WNvy999/n7KyMuLi4gBobGxkzJgx1NTUsGjRIgIDAwFITU296W1OmjSJKVOmABAeHs7DDz+MMYYpU6bgdru7lL969Sput5v09HR+/vOfM23atC5lpkyZwvr169mwYQPz5s1jxowZ/O1vf+tSbvv27ezbtw+Ac+fOUV1dzTe+8Q0mTJjA1KlTfY4/KioKgJiYGNxuN3/9619ZsGABw4YNA2D+/Pnd1h8/fjyJiYkAZGRksH37dgICAli0aBFBQUEALF68mOLi4i4JmLdtJyUl+RR3T1MCJiIi/ZavI1W9KTU1lfXr13P48GEuXboEtJwLlZmZyeuvv96h7LZt2zA3OOXmrrvu4tq1a22vm5qaOrw/ZMiQtueDBg1qez1o0CCam5u7rK+yspK4uDhqamoYPHiw122GhIRQVlbGoUOHePbZZ0lJSWHZsmUdyhw+fJiioiKOHDlCYGAgM2fObIutNfHxRfv4Bw8eTGNjY4fp0Bvp3H7GGJ/re9u2U/rOOWAiIiL90MqVK3nxxRfbRqUAHn74YX79619z8eJFAGpqavjLX/5CcnIy+/bto7GxkcuXL3PgwIEu67vnnnu4ePEily5d4sqVK/zmN7+5rfjKy8uZPn06e/bsYcWKFVy4cKFLmfPnzxMYGEhGRgbr16/n+PHjDB8+nMuXL7eVqa2tZeTIkQQGBnLmzBmOHj3qdXud6/kiKSmJAwcO0NTURF1dXdtUqDeffvopR44cAVrOu0tKSiI5OZn9+/fT0NBAfX09+/btY8aMGT5t+1bi7QkaARMREbkN48aN45lnnumw7P777+fVV18lJSWFa9euERAQwM9+9jOmTp3Kd7/7XaKiopgwYYLXJCEgIIAXX3yRhIQEJk2aROhtXqKpvLychIQEQkJC2Lx5M2lpaRQVFRHQ7rqbp06dIjs7m0GDBhEQEMCbb77J6NGjSUxMxOVyMWfOHF599VXeeustIiIimDx5crdTjp3r/fSnP71hjHFxcaSmphIZGcmECROIjY1lxIgRXsuGhYWxa9cunnrqKe677z7Wrl1LYGAgy5cvJz4+HoCsrCyff/V5K/H2BHMzw369KTY21paWljodhoiI9HGnT58mLCzM6TCkh9XV1REcHExDQwPJycnk5uYSHR3doUzrCf4VFRV+jc1bnzPGlFlrY291nRoBExEREcetWbOGyspKmpqayMzM7JJ83WmUgImIiIjjdu/efcMyEydO9PvoV2/RSfgiIiIifqYETERERMTPlICJiIiI+JkSMBERERE/UwImIiIi4mdKwERERET8TAmYiIiIiJ8pARMRERHxMyVgIiIityA4OLjX1l1UVMSTTz55U3W+/PJLcnJybnpb3upNnz79ptfTU2607Vvdz75GCZiIiEgfU15e7vPNpFvdSmJiraWmpqZLvQ8++OCm1tOTbrRtJWAiIiLSwdatW3G5XLhcLrZt2wbAT37yE7Zv3w7AD37wA77zne8A8P7775ORkeF1Pa0J2JUrV1i+fDnPPfcc1tq29+vr65k7dy6RkZG4XC727t3Lxo0bOXv2LFFRUWRnZwOwcOFCYmJiCA8PJzc3F2i5oXVYWBjr1q0jOjqaVatWdanXOrrXWnb16tWEh4eTkpJCY2MjAK+88gqhoaHMmjWL9PR0tmzZ0mEf3G43oaGhZGZmEhERwdKlS2loaLhuW/mybW/72R/pXpAiItJ/5eXBJ5/07DrvvRdWr77pamVlZeTn53Ps2DGstSQkJPDggw+SnJzMG2+8wdNPP01paSlXrlzh6tWrlJSUMGPGDK/rKi8vZ8yYMcyePZusrKwuidp7773H2LFjOXjwIAC1tbUkJCRQUVHByZMn28rt3LmTUaNG0djYSFxcHEuWLAGgqqqK/Px8cnJycLvdzJs3r0O99qqrqykoKCAvL4+0tDQKCwsJDQ2lsLCQEydO0NzcTHR0NDExMV3qVlVVsWPHDhITE1m5ciU5OTmsX7++27bqPOrnbdubNm3qsp/9kUbAREREekBJSQmLFi0iKCiI4OBgFi9eTHFxMTExMZSVlXH58mWGDBnCtGnTKC0tpbi42GsCdvXqVdxuN+np6bz++uteR8mmTJlCUVERGzZsoLi4mBEjRniNafv27URGRjJ16lTOnTtHdXU1ABMmTGDq1Kk+7dekSZOIiooCICYmBrfbTUlJCQsWLGDYsGEMHz6c+fPne607fvx4EhMTAcjIyKCkpOS6beXLtu8UGgETEZH+6xZGqnpL+ynC9gICApg4cSL5+flMnz6diIgIfv/733P27FnCwsK6lK+srCQuLo6amhoGDx7sdZ0hISGUlZVx6NAhnn32WVJSUli2bFmHMocPH6aoqIgjR44QGBjIzJkzaWpqAiAoKMjn/RoyZEjb88GDB9PY2NjtvnZmjPH62tf63rZ9p9AImIiISA9ITk5m//79NDQ0UF9fz759+9pGuJKTk9myZQvJycnMmDGDt956i6ioqC4JCrRMP06fPp09e/awYsUKLly40KXM+fPnCQwMJCMjg/Xr13P8+HGGDx/O5cuX28rU1tYycuRIAgMDOXPmDEePHvUad+d6vkhKSuLAgQM0NTVRV1fXNhXa2aeffsqRI0cAKCgoICkp6YZtdSO3Em9fpARMRETkFjQ0NDBu3Li2x+HDh1m+fDnx8fEkJCSQlZXVdk7TjBkz+Pzzz5k2bRr33HMPQ4cOve75Xy6Xi5CQEDZv3kxaWhpXr17tUObUqVPEx8cTFRXFa6+9xvPPP8/o0aNJTEzE5XKRnZ3No48+SnNzMxEREbzwwgvdTjl2rueLuLg4UlNTiYyMZPHixcTGxnqdBg0LC2PXrl1ERERQU1PD2rVrAYiOju62rW7kVuLti4yvw4C9LTY21paWljodhoiI9HGnT5/2OnUn/lVXV0dwcDANDQ0kJyeTm5tLdHR02/utJ/dXVFQ4GGXP8NbnjDFl1trYW12nzgETERGRm7ZmzRoqKytpamoiMzOzQ/IlN6YETERERG7a7t27r/v+xIkT74jRr96ic8BERERE/EwJmIiIiIifKQETERER8TMlYCIi0u/0lV/wy52vt/qaEjAREelXhg4dyqVLl5SESa+z1nLp0iWGDh3a4+vWryBFRKRfGTduHJ999hlffPGF06HIADB06FDGjRvX4+vttQTMGPMo8M/AYOAX1tpNvbUtEREZOAICApg0aZLTYYjcll6ZgjTGDAZ+BswB7gfSjTH398a2RERERPqb3joHLB742Fr7ibX2/wF7gAW9tC0RERGRfqW3ErBvAefavf7Ms0xERERkwOutc8CMl2Vdfq5ijFkDrPG8vGKM0T0Luvo68Feng+hj1CbeqV28U7t4p3bpSm3indrFu8m3U7m3ErDPgPHtXo8DzncuZK3NBXIBjDGlt3NX8TuV2qUrtYl3ahfv1C7eqV26Upt4p3bxzhhTejv1e2sK8k/AfcaYScaY/wI8DrzbS9sSERER6Vd6ZQTMWttsjPk+8L9ouQzFTmvtn3tjWyIiIiL9Ta9dB8xaewg4dBNVcnsrln5O7dKV2sQ7tYt3ahfv1C5dqU28U7t4d1vtYnQrBxERERH/0r0gRURERPzM8QTMGPOoMabKGPOxMWaj0/E4xRgz3hjze2PMaWPMn40xz3iWv2SM+XdjzEnP4zGnY/U3Y4zbGHPKs/+lnmWjjDG/M8ZUe/4d6XSc/mSMmdyuT5w0xvyHMeYfB1p/McbsNMZcbH8Jm+v1DWPMs55jTZUxZrYzUfe+btrlp8aYM8aYj4wx+4wxX/Msn2iMaWzXZ95yLvLe1U27dPuZGeD9ZW+7NnEbY056lg+I/nKd7+QeO744OgXpuWXRvwGzaLl0xZ+AdGttpWNBOcQY803gm9ba48aY4UAZsBBIA+qstVscDdBBxhg3EGut/Wu7ZT8Baqy1mzyJ+0hr7QanYnSS53P070ACsIIB1F+MMclAHfBLa63Ls8xr3/DcDq2Aljt1jAWKgBBr7VcOhd9rummXFOB/e34ktRnA0y4Tgd+0lruTddMuL+HlMzPQ+0un998Aaq21Lw+U/nKd7+Tl9NDxxekRMN2yyMNa+7m19rjn+WXgNLp7wPUsAHZ5nu+i5YMxUD0MnLXW/sXpQPzNWvt/gJpOi7vrGwuAPdbaK9ba/wt8TMsx6I7jrV2stb+11jZ7Xh6l5fqMA0o3/aU7A7q/tDLGGFoGAgr8GpTDrvOd3GPHF6cTMN2yyAvPXxgPAMc8i77vmTbYOdCm2jws8FtjTJlpuXsCwD3W2s+h5YMCjHEsOuc9TseD40DvL931DR1v/tNK4H+2ez3JGHPCGPMHY8wMp4JykLfPjPpLixnABWttdbtlA6q/dPpO7rHji9MJmE+3LBpIjDHBQCHwj9ba/wDeBP4eiAI+B95wMDynJFpro4E5wPc8w+UCmJYLHacC73gWqb90T8cbwBjzI6AZeNuz6HPg29baB4AfAruNMX/nVHwO6O4zo/7SIp2Of+ANqP7i5Tu526Jell23vzidgPl0y6KBwhgTQMt/9NvW2n8FsNZesNZ+Za29BuRxhw6BX4+19rzn34vAPlra4IJnjr51rv6icxE6ag5w3Fp7AdRfPLrrGwP+eGOMyQTmAU9YzwnAnimTS57nZcBZIMS5KP3rOp8Z9Rdj7gIWA3tblw2k/uLtO5kePL44nYDplkUennn2HcBpa+3Wdsu/2a7YImBA3bDcGBPkOQESY0wQkEJLG7wLZHqKZQL/w5kIHdfhr9OB3l88uusb7wKPG2OGGGMmAfcBHzoQnyOMMY8CG4BUa21Du+V3e37IgTHmXlra5RNnovS/63xmBnR/8XgEOGOt/ax1wUDpL919J9OTxxdrraMP4DFafgl5FviR0/E42A5JtAxXfgSc9DweA/47cMqz/F1afpXheLx+bJd7gXLP48+tfQQYDbwPVHv+HeV0rA60TSBwCRjRbtmA6i+0JJ+fA1dp+Qt01fX6BvAjz7GmCpjjdPx+bpePaTlHpfX48pan7BLPZ6scOA7Mdzp+P7dLt5+ZgdxfPMv/G/APncoOiP5yne/kHju+6Er4IiIiIn7m9BSkiIiIyICjBExERETEz5SAiYiIiPiZEjARERERP1MCJiIiIuJndzkdgIiIr4wxrT8BB/gG8BXwhed1g7V2uiOBiYjcJF2GQkT6JWPMS0CdtXaL07GIiNwsTUGKyB3BGFPn+Xem5ybB/2KM+TdjzCZjzBPGmA+NMaeMMX/vKXe3MabQGPMnzyPR2T0QkYFECZiI3IkigWeAKcCTQIi1Nh74BfBfPWX+Gfgna20cLVf3/oUTgYrIwKRzwETkTvQna+3nAMaYs8BvPctPAQ95nj8C3N9yyzcA/s4YM9xae9mvkYrIgKQETETuRFfaPb/W7vU1/vO4NwiYZq1t9GdgIiKgKUgRGbh+C3y/9YUxJsrBWERkgFECJiID1dNArDHmI2NMJfAPTgckIgOHLkMhIiIi4mcaARMRERHxMyVgIiIiIn6mBExERETEz5SAiYiIiPiZEjARERERP1MCJiIiIuJnSsBERERE/EwJmIiIiIif/X+9pF+V+1jIKAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M3kyiMsya2HG"
      },
      "source": [
        "## 5. THE GOLDEN RULE\n",
        "\n",
        "Since the Solow model operates with an exogenous savings rate there is no guarantee that the steady-state will maximize consumption per capita. The savings rate that yields the level of output that maximizes consumption is called the golden-rule, denoted with $g$.\n",
        "\n",
        "We can obtain $s^g$ in two steps. First, since consumption is the difference between output and investment, we can obtain $k^g$ by maximizing $c$ in terms of $k$.\n",
        "\n",
        "\\begin{align}\n",
        " c&= Ak^{\\alpha} - (\\delta + n)k^g                                            \\\\\n",
        " \\frac{\\partial c}{\\partial k} &= \\alpha A k^{\\alpha - 1} - (\\delta + n) = 0  \\\\\n",
        " k^g &= \\left( \\frac{\\alpha A}{\\delta + n} \\right)^{\\frac{1}{1-\\alpha}}\n",
        "\\end{align}\n",
        "\n",
        "Knowning $k^g$, we can now move to the second step and obtain $s^g$ from the equilibrium condition:\n",
        "\n",
        "\\begin{align}\n",
        " sA \\left(k^g \\right)^{\\alpha} &= (\\delta + n)k^g                                                                         \\\\\n",
        " s^g &= \\frac{\\left( \\delta+n \\right)k^g}{A \\cdot \\left(k^g \\right)^{\\alpha}} = \\frac{\\left( \\delta+n \\right)k^g}{y(k^g)}\n",
        "\\end{align}\n",
        "\n",
        "From this the golden-rule value for the other variables can be obtained as well:\n",
        "\n",
        "\\begin{align}\n",
        " y^g &= A \\cdot \\left(k^g \\right)^{\\alpha} \\\\\n",
        " i^g &= s^g \\cdot y^g                      \\\\\n",
        " c^g &= y^g - i^g                          \\\\\n",
        " d^g &= \\delta k^g \n",
        "\\end{align}\n",
        "\n",
        "### 5.1 THE COBB-DOUGLAS CASE\n",
        "\n",
        "Note that in the stead-state the level of per capita consumption remains stable (assuming no growth of technology); $c = f(k^*) - (\\delta +n)k^*$. Therefore: $\\frac{\\partial c}{\\partial k} = \\frac{\\partial f(k^*)}{\\partial k} - (\\delta + n) = 0$; then $\\frac{\\partial f(k^*)}{\\partial k} = (\\delta + n)$.\n",
        "\n",
        "Knowing this, we can re-write the $s^g$ condition in the following way:\n",
        "\\begin{align}\n",
        "    s^g &= \\frac{\\left( \\delta+n \\right)k^g}{y(k^g)}          \\\\[10pt]\n",
        "    s^g &= \\frac{\\left( \\delta+n \\right)k^g/k^g}{y(k^g)/k^g}  \\\\[10pt]\n",
        "    s^g &= \\frac{\\partial f(k^g)/\\partial k^g}{y(k^g)/k^g}\n",
        "\\end{align}\n",
        "\n",
        "This means that the golden-rule savings rate is equal to the ratio of the marginal product of labor with respect to the average product. In the case of the Cobb-Douglas function, this equals $\\alpha$ (the golden-rule savings rate can vary depending on the production function being used).\n",
        "\n",
        "\\begin{align}\n",
        "    s^g &= \\frac{\\partial f(k^g)/\\partial k^g}{y(k^g)/k^g}  \\\\[10pt]\n",
        "    s^g &= \\frac{\\alpha A k^{\\alpha-1}}{A k^{\\alpha-1}}     \\\\[10pt]\n",
        "    s^g &= \\alpha\n",
        "\\end{align}\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "wSZ7cPkza2HG",
        "outputId": "383bfd51-83c8-4ade-d9b8-ada62ebd0f1c"
      },
      "source": [
        "\"1|IMPORT PACKAGES\"\n",
        "import numpy as np               # Package for scientific computing with Python\n",
        "import matplotlib.pyplot as plt  # Matplotlib is a 2D plotting library\n",
        "\n",
        "\"2|DEFINE PARAMETERS AND ARRAYS|\"\n",
        "# Parameters\n",
        "K_size = 200                     # Model domain\n",
        "A = 1                            # Total Factor Productivity\n",
        "alpha = 0.50                     # Output elasticity of capital\n",
        "delta = 0.03                     # Depreciation rate\n",
        "s = 0.35                         # Savings rate\n",
        "n = 0.02                         # Population growth rate\n",
        "# Arrays\n",
        "k = np.arange(K_size)            # Create array of k\n",
        "\n",
        "\"3|CALCULATE GOLDEN-RULE VALUES\"\n",
        "def output(k):   # Cobb-Douglas Production Function (per capita)\n",
        "    y = A * (k)**(alpha)    \n",
        "    return y\n",
        "\n",
        "k_gold = ((alpha*A)/(delta+n))**(1/(1-alpha))\n",
        "y_gold = output(k_gold)\n",
        "s_gold = ((delta+n)*k_gold)/y_gold\n",
        "i_gold = s_gold * y_gold\n",
        "c_gold = y_gold - i_gold\n",
        "d_gold = delta*k_gold\n",
        "\n",
        "\"4|PLOT GOLDEN-RULE CONSUMPTION\"\n",
        "#Plot consumption as function of savings\n",
        "step = 0.05\n",
        "size = int(1/step)+1\n",
        "savings = np.arange(0, 1.01, step)\n",
        "\n",
        "k_s = (savings / (n+delta)*A)**(1/(1-alpha))\n",
        "y_s = output(k_s)\n",
        "c_s = (1-savings)*y_s\n",
        "\n",
        "v = [0, 1, 0, c_gold]\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.plot(savings, c_s, \"k-\", label=\"Output\", alpha = 0.7)\n",
        "ax.set(title=\"CONSUMPTION\", xlabel=r'$k$')\n",
        "plt.axvline(x=s_gold, ls=\":\", color='k', alpha=0.6)\n",
        "plt.xlabel('k')\n",
        "plt.axis(v)\n",
        "plt.show()\n",
        "\n",
        "# Plot Solow Model with golden-rule capital\n",
        "y = output(k)              # Production function\n",
        "i = s_gold * y             # Investment\n",
        "c = (1 - s_gold)*y         # Consumption\n",
        "d_and_i = (delta + n)*k    # Break-even\n",
        "\n",
        "v = [0, K_size, 0, y[K_size-1]]\n",
        "fig, ax = plt.subplots(figsize=(10, 8))\n",
        "ax.plot(k, y      , \"k-\", label=\"Output\"    , alpha = 0.7)\n",
        "ax.plot(k, i      , \"b-\", label=\"Investment\", alpha = 0.7)\n",
        "ax.plot(k, d_and_i, \"r-\", label=\"Break-even\", alpha = 0.7)\n",
        "ax.set(title=\"Consumption\", xlabel=r'$k$')\n",
        "plt.legend(loc=2)\n",
        "plt.axvline(x = k_gold, ls = \":\", color = 'k', alpha = 0.6)\n",
        "plt.xlabel('k')\n",
        "plt.text(170, 13.5, r'$y(k)$'         , color = 'k')\n",
        "plt.text(170,  9.5, r'$(\\delta + n)k$', color = 'r')\n",
        "plt.text(170,  7.0, r'$s \\cdot y(k)$' , color = 'b')\n",
        "plt.axis(v)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "etAYaG4na2HG"
      },
      "source": [
        "## 6. GROWTH ACCOUNTING"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eJl5E0fia2HG"
      },
      "source": [
        "Growth accounting allows to separate the drivers of growth of output and obtain the change in TFP as the residual between the observed frowth ouf output and the observed growth of inputs. This difference is the **Solow residual**.\n",
        "\n",
        "Proceed the following way. Start by total differentiating output. Then divide the total differential by output (this yields the percent change). Then do some algebra to obtain elasticities and \"solve for\" the growth of TFP. \n",
        "\n",
        "\\begin{align}\n",
        "    Y            &= A \\cdot F(K; L)                                                                                             \\\\[10pt]\n",
        "    dY           &= \\frac{\\partial Y}{\\partial A} dA + \\frac{\\partial Y}{\\partial K} dK + \\frac{\\partial Y}{\\partial N} dN      \\\\[10pt]\n",
        "    \\frac{dY}{Y} &= \\frac{\\partial Y}{\\partial A} \\frac{dA}{Y} + \\frac{\\partial Y}{\\partial K} \\frac{dK}{Y} + \\frac{\\partial Y}{\\partial N}               \\frac{dN}{Y}                                                                                                                    \\\\[10pt]\n",
        "    \\frac{dY}{Y} &= \\left(\\frac{\\partial Y}{\\partial A}\\frac{A}{Y}\\right)\\frac{\\partial A}{A} + \\left(\\frac{\\partial Y}{\\partial K}\\frac{K}{Y}\\right)\\frac{\\partial K}{K} + \\left(\\frac{\\partial Y}{\\partial N}\\frac{N}{Y}\\right)\\frac{\\partial N}{N}                      \\\\[10pt]\n",
        "           g_{Y} &= \\varepsilon_{A} g_{A} + \\varepsilon_{K} g_{K} + \\varepsilon_{N} g_{N}                                       \\\\[10pt]\n",
        "           g_{A} &= g_{Y} - \\left(\\varepsilon_{K} g_{K} + \\varepsilon_{N} g_{N} \\right)\n",
        " \\end{align}\n",
        "\n",
        "The last line shows that growth of TFP can be calculated as the difference, or residual, of observed growth rates and input-output elasticity of factors of production.\n",
        "\n",
        "Note that: $\\frac{\\partial Y}{\\partial A} \\cdot \\frac{A}{Y} = F(K; N) \\cdot \\frac{A}{Y} = 1$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E6hcM-u432Gd"
      },
      "source": [
        "## Reproducibility info"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4NLvTa4L32Gd",
        "outputId": "dfbd0adf-1eeb-413c-b353-e7ee1245209d"
      },
      "source": [
        "import watermark\n",
        "\n",
        "# More details about the packages of this session\n",
        "%load_ext watermark\n",
        "\n",
        "# python, ipython, packages, and machine characteristics\n",
        "%watermark -v -m -p numpy,sympy,matplotlib -g\n",
        "\n",
        "# check the import versions\n",
        "%watermark --iversions\n",
        "\n",
        "# date\n",
        "print (\" \")\n",
        "%watermark -u -n -t -z"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Python implementation: CPython\n",
            "Python version       : 3.7.9\n",
            "IPython version      : 7.19.0\n",
            "\n",
            "numpy     : 1.19.4\n",
            "sympy     : 1.7.1\n",
            "matplotlib: 2.2.5\n",
            "\n",
            "Compiler    : Clang 11.0.0 \n",
            "OS          : Darwin\n",
            "Release     : 19.6.0\n",
            "Machine     : x86_64\n",
            "Processor   : i386\n",
            "CPU cores   : 12\n",
            "Architecture: 64bit\n",
            "\n",
            "Git hash: 5393c9757a072b0ddcd48359fd99b5717e1c4a07\n",
            "\n",
            "numpy     : 1.19.4\n",
            "watermark : 2.1.0\n",
            "matplotlib: 2.2.5\n",
            "\n",
            " \n",
            "Last updated: Tue Dec 29 2020 13:55:11JST\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AO0hpZnZ32Gd",
        "outputId": "645d2400-22d5-4067-e1bb-c0835907c640"
      },
      "source": [
        "# List of used packages to be added to the `requirements.txt` file (ref: https://stackoverflow.com/questions/40428931/package-for-listing-version-of-packages-used-in-a-jupyter-notebook)\n",
        "import pkg_resources\n",
        "import types\n",
        "def get_imports():\n",
        "    for name, val in globals().items():\n",
        "        if isinstance(val, types.ModuleType):\n",
        "            # Split ensures you get root package, \n",
        "            # not just imported function\n",
        "            name = val.__name__.split(\".\")[0]\n",
        "\n",
        "        elif isinstance(val, type):\n",
        "            name = val.__module__.split(\".\")[0]\n",
        "\n",
        "        # Some packages are weird and have different\n",
        "        # imported names vs. system/pip names. Unfortunately,\n",
        "        # there is no systematic way to get pip names from\n",
        "        # a package's imported name. You'll have to add\n",
        "        # exceptions to this list manually!\n",
        "        poorly_named_packages = {\n",
        "            \"PIL\": \"Pillow\",\n",
        "            \"sklearn\": \"scikit-learn\"\n",
        "        }\n",
        "        if name in poorly_named_packages.keys():\n",
        "            name = poorly_named_packages[name]\n",
        "\n",
        "        yield name\n",
        "imports = list(set(get_imports()))\n",
        "\n",
        "# The only way I found to get the version of the root package\n",
        "# from only the name of the package is to cross-check the names \n",
        "# of installed packages vs. imported packages\n",
        "requirements = []\n",
        "for m in pkg_resources.working_set:\n",
        "    if m.project_name in imports and m.project_name!=\"pip\":\n",
        "        requirements.append((m.project_name, m.version))\n",
        "\n",
        "for r in requirements:\n",
        "    print(\"{}=={}\".format(*r))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "watermark==2.1.0\n",
            "sympy==1.7.1\n",
            "numpy==1.19.4\n",
            "matplotlib==2.2.5\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}