{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Information and Consumption Smoothing\n", "\n", "This notebook describes two consumers who have exactly the same nonfinancial income process and who both conform to the linear quadratic permanent\n", "income of consumption smoothing model described in the quantecon lecture https://python.quantecon.org/perm_income_cons.html\n", "\n", "The consumers differ only in having different information about their future nonfinancial incomes\n", "\n", "One consumer each period receives **news** in the form of a shock that changes today's income and also contains exact information about an altered present value of future nonfinancial income.\n", "\n", "The other, less well informed, consumer each period receives a shock consisting of the part of today's nonfinancial income that could not be forecasts from the all past values of nonfinancial income. \n", "\n", "Even though they receive exactly the same nonfinancial incomes each period, our two consumers respond to time $t$ shocks differently.\n", "\n", "The do this because, while they receive exactly the same histories of nonfinancial income, they receive different **shocks** or **news** about their **future** nonfinancial incomes.\n", "\n", "We compare behaviors of our two consumers as a way to learn about \n", "\n", "* operating characteristics of the linear-quadratic permanent income model, and\n", "\n", "* how the Kalman filter introduced in this lecture https://python.quantecon.org/kalman.html and/or the theory of optimal forecasting introduced in this lecture https://python.quantecon.org/classical_filtering.html embody lessons that can be applied to the **news** and **noise** literature\n", "\n", "* various ways of representing and computing optimal decision rules in the linear-quadratic permanent income model\n", "\n", "* a **Ricardian equivalence** outcome describing effects on optimal consumption of a tax cut at time $t$ accompanied by a foreseen permanent increases in taxes just sufficient to finance the interest payments used to service risk-free government bonds issued to finance the tax cut\n", "\n", "* a simple application of alternative ways to factor a covariance generating function along lines described in this lecture https://python.quantecon.org/classical_filtering.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Two representations of the **same** nonfinancial income process\n", "\n", "\n", "\n", "Where $\\beta \\in (0,1)$, we study consequences of endowing a consumer with one of the two alternative representations for the change in the consumer's nonfinancial income $y_{t+1} - y_t$.\n", "\n", "We'll call the **original representation**.\n", "\n", "It is \n", "\n", "$$ y_{t+1} - y_t = \\epsilon_{t+1} - \\beta^{-1} \\epsilon_t \\quad (1) $$\n", "\n", "where $\\{\\epsilon_t\\}$ is an i.i.d. normally distributed scalar process with means of zero\n", "and variances $\\sigma_\\epsilon^2 $ \n", "\n", "This representation of the process is used by a consumer who at time $t$ knows both $y_t$ and the original shock $\\epsilon_t$ and can use\n", "both of them to forecast future $y_{t+j}$'s\n", "\n", "The second representation (of the **same** $\\{y_t\\}$ process) is \n", "\n", "\n", "$$ y_{t+1} - y_t = a_{t+1} - \\beta a_t \\quad (2) $$\n", " \n", "where $\\{a_t\\}$ is another i.i.d. normally distributed scalar process, with means of zero\n", "and now variances $\\sigma_a^2$. \n", "\n", "The two i.i.d. shock variances are related by \n", "\n", "$$ \\sigma_a^2 = \\beta^{-2} \\sigma_\\epsilon^2 > \\sigma_\\epsilon^2 $$\n", "\n", "so that the variance of the innovation exceeds the variance of the original shock by a multiplicative factor $\\beta^{-2}$. \n", "\n", "The second representation is the **innovations representation** from Kalman filtering theory.\n", "\n", "To see how this works, note that equating the two representations (1) and (2) for $y_{t+1} - y_t$\n", "implies $\\epsilon_{t+1} - \\beta^{-1} \\epsilon_t = a_{t+1} - \\beta a_t$, which in turn implies\n", "\n", "$$ a_{t+1} = \\beta a_t + \\epsilon_{t+1} - \\beta^{-1} \\epsilon_t . $$\n", "\n", "Solving this difference equation backwards for $a_{t+1}$ gives, after a few lines of algebra,\n", "\n", "$$ a_{t+1} = \\epsilon_{t+1} + (\\beta - \\beta^{-1}) \\sum_{j=0}^\\infty \\beta^j \\epsilon_{t-j} \\quad (3) $$\n", "\n", "which we can also write as \n", "\n", "$$ a_{t+1} = \\sum_{j=0}^\\infty \\epsilon_{t+1 -j} \\equiv h(L) \\epsilon_{t+1} $$\n", "\n", "where $L$ is the one-period lag operator, $I$ is the identity operator, and \n", "\n", "$$ h(L) = \\frac{ I -\\beta^{-1} L}{ I - \\beta L} $$\n", "\n", "Let $c_j \\equiv E z_t z_{t-j}$ be the $j$th autocovariance of the $\\{y_t - y_{t-1}\\}$ process.\n", "\n", "\n", "Using calculations in the quantecon lecture https://python.quantecon.org/classical_filtering.html, where $z \\in C$ is a complex variable, the covariance generating function $g (z) = \\sum_{j=\\infty}^\\infty c_j z^j $ of the $\\{y_t -_y_{t-1}\\}$ process equals\n", "\n", "$$ g(z) = \\sigma_\\epsilon^2 h(z) h(z^{-1}) = \\beta^{-2} \\sigma_\\epsilon^2 > \\sigma_\\epsilon^2 $$\n", "\n", "which verifies that $\\{a_t\\}$ is a **serially uncorrelated** process with variance \n", "\n", "\n", "$$ \\sigma_a^2 = \\beta^{-1} \\sigma_\\epsilon^2 .$$\n", "\n", "To verify these claims, just notice that $g(z) = \\beta^{-2} \\sigma_\\epsilon^2$ implies that the coefficient \n", "$g_0 = \\beta^{-2} \\sigma_\\epsilon^2$ and that $g_j = 0 $ for $j \\neq 0$. \n", "\n", "Alternatively, if you are uncomfortable with covariance generating functions, note that we can directly calculate $\\sigma_a^2$ from\n", "formula (3) according to\n", "\n", "$$\n", "\\sigma_a^2 = \\sigma_\\epsilon^2 + [ 1 + (\\beta - \\beta^{-1})^2 \\sum_{j=0}^\\infty \\beta^{2j} ] = \\beta^{-1} \\sigma_\\epsilon^2 .\n", "$$\n", "\n", "\n", "\n", "\n", "## Application of Kalman filter\n", "\n", "We can also obtain representation (2) from representation (1) by using the **Kalman filter**.\n", "\n", "Thus, from equations associated with the **Kalman filter**, it can be verified that the steady-state Kalman gain $K = \\beta^2$ and the steady state conditional covariance $\\Sigma = E [(\\epsilon_t - \\hat \\epsilon_t)^2 | y_{t-1}, y_{t-2}, \\ldots ] = (1 - \\beta^2) \\sigma_\\epsilon^2$. \n", "\n", "In a little more detail, let $z_t = y_t - y_{t-1} $ and form the state-space representation\n", "\n", "\\begin{align} \\epsilon_{t+1} & = 0 \\epsilon_t + \\epsilon_{t+1} \\cr\n", " z_{t+1} & = - \\beta^{-1} \\epsilon_t + \\epsilon_{t+1} \\end{align}\n", "\n", "and assume that $\\sigma_\\epsilon = 1$ for convenience\n", "\n", "Compute the steady-state Kalman filter for this system and let $K$ be the steady-state gain and $a_{t+1}$ the one-step ahead\n", "innovation\n", "\n", "The innovations representation is \n", "\n", "\\begin{align} \\hat \\epsilon_{t+1} & = 0 \\hat \\epsilon_t + K a_{t+1} \\cr\n", " z_{t+1} & = - \\beta^{-1} a_t + a_{t+1} \\end{align} \n", " \n", "By applying formulas for the steady-state Kalman filter, by hand we computed that $K = \\beta^2, \\sigma_a^2 = \\beta^{-2} \\sigma_\\epsilon^2 = \\beta^{-2},$ and $\\Sigma = (1-\\beta^2) \\sigma_\\epsilon$ \n", "\n", "We can also obtain these formulas via the classical filtering theory described in this lecture https://python.quantecon.org/classical_filtering.html \n", "\n", "## News shocks and less informative shocks\n", "\n", "Representation (1) is cast in terms of a **news shock** $\\epsilon_{t+1}$ that represents a shock \n", "to nonfinancial income coming from taxes, transfers, and other random sources of income changes known to a well-informed person having all sorts of information about the income process. \n", "\n", "Representation (2) for the **same** income process is driven by shocks $a_t$ that contain less information than the news shock $\\epsilon_t$\n", "\n", "Representation (2) is called the **innovations** representation for the $\\{y_t - y_{t-1}\\}$ process. \n", "\n", "It is cast in terms of what time series statisticians call the **innovation** or **fundamental** shock that emerges from applying the theory of optimally predicting nonfinancial income based solely on the information contained solely in **past** levels of growth in \n", "nonfinancial income. \n", "\n", "**Fundamental for the $\\{y_t\\}$ process** means that the shock $a_t$ can be expressed as a square-summable linear combination\n", "of $y_t, y_{t-1}, \\ldots$. \n", "\n", "The shock $\\epsilon_t$ is **not fundamental** and has more information about the future of the $\\{y_t - y_{t-1}\\}$ process than is contained in $a_t$. \n", "\n", "Representation (3) reveals the important fact that the **original shock** $\\epsilon_t$ contains more information about future $y$'s than is contained in the semi-infinite history $y^t = [y_t, y_{t-1}, \\ldots ]$ of current and past $y$'s. \n", "\n", "Staring at representation (3) for $a_{t+1}$ shows that it consists both of **new news** $\\epsilon_{t+1}$ as well as a long moving average\n", "$ (\\beta - \\beta^{-1}) \\sum_{j=0}^\\infty \\beta^j \\epsilon_{t-j} $ of **old news**.\n", "\n", "\n", "The **better informed** representation (1) asserts that a shock $\\epsilon_{t}$ results in an impulse response to nonfinancial income of $\\epsilon_t$ times the sequence \n", "\n", "$$ 1, 1- \\beta^{-1}, 1- \\beta^{-1}, \\ldots $$\n", "\n", "so that a shock that **increases** nonfinancial income $y_t$ by $\\epsilon_t$ at time $t$ is followed by \n", "an **increase** in future $y$ of $\\epsilon_t$ times $1 - \\beta^{-1} < 0$ in **all** subsequent periods. \n", "\n", "Because $1 - \\beta^{-1} < 0$, this means that a positive shock of $\\epsilon_t$ today raises income at time $t$ by $\\epsilon_t$ \n", "and then **decreases all** future incomes by $(\\beta^{-1} -1)\\epsilon_t$.\n", "\n", "This pattern precisely describes the following mental experiment:\n", "\n", "* The consumer receives a government transfer of $\\epsilon_t$ at time $t$.\n", "\n", "* The government finances the transfer by issuing a one-period bond on which it pays a gross one-period risk-free interest rate equal to $\\beta^{-1}$\n", "\n", "* In each future period, the government **rolls over** the one-period bond and so continues to borrow $\\epsilon_t$ forever\n", "\n", "* The government imposes a lump sum tax on the consumer in order to pay just the current interest on the original bond and its successors created by the roll-over operation\n", "\n", "* In all future periods $t+1, t+2, \\ldots$, the government levies a lump-sum tax on the consumer of $\\beta^{-1} -1$ that is just enough to pay the interest on the bond. \n", "\n", "The **present value** of the impulse response or moving average coefficients equals\n", "$d_\\epsilon(L) = \\frac{0}{1 -\\beta } =0 $, a fact that we'll see again below.\n", "\n", "\n", "Representation (2), i.e., the innovation representation, asserts that a shock $a_{t}$ results in an impulse response\n", "to nonfinancial income of $a_t$ times\n", "\n", "$$ 1, 1 -\\beta, 1 - \\beta, \\ldots $$\n", "\n", "so that a shock that increases income $y_t$ by $a_t$ at time $t$ can be expected to be followed by an\n", "**increase** in $y_{t+j} $ of $a_t$ times $1 - \\beta > 0$ in all future periods $j=1, 2, \\ldots $.\n", "\n", "\n", "The present value of the impulse response or moving average coefficients for representation (2) is \n", "$d_a(L) = \\frac{1 -\\beta^2}{1 -\\beta } = (1 + \\beta)$, another fact that will be important below.\n", "\n", "\n", "\n", "\n", "## Representation of $\\epsilon_t$ in terms of future $y$'s\n", "\n", "\n", "Notice that reprentation (1), namely, $y_{t+1} - y_t = - \\beta^{-1} \\epsilon_t + \\epsilon_{t+1} $\n", "implies the linear difference equation\n", "\n", "$$ \\epsilon_t = \\beta \\epsilon_{t+1} - \\beta (y_{t+1} - y_t ). $$\n", "\n", "Solving forward we eventually obtain\n", "\n", "$$ \\epsilon_t = \\beta ( y_t - (1-\\beta) \\sum_{j=0}^\\infty \\beta^j y_{t+j+ 1} ) $$\n", "\n", "This equation shows that $\\epsilon_t $ equals $\\beta$ times the one-step-backwards error\n", "in optimally **backcasting** $y_t$ based on the **future** $y^t_+ \\equiv y_{t+1}, y_{t+2}, \\ldots ] $ \n", "via the optimal backcasting formula\n", "\n", "$$ E [ y_t | y^t_+] = (1-\\beta) \\sum_{j=0}^\\infty \\beta^j y_{t+j+ 1} $$\n", "\n", "Thus, $\\epsilon_t$ contains **exact** information about an important linear combination of **future** nonfinancial income\n", "\n", "\n", "## Representation in terms of $a_t$ shocks\n", "\n", "\n", "Next notice that representation (2), namely, $y_{t+1} - y_t = - \\beta a_t + a_{t+1} $\n", "iimplies the linear difference equation\n", "\n", "$$ a_{t+1} = \\beta a_t + (y_{t+1} - y_t) $$\n", "\n", "Solving this equation backwards establishes that\n", "the one-step-prediction error $a_{t+1} $ is\n", "\n", "$$ a_{t+1} = y_{t+1} - (1-\\beta) \\sum_{j=0}^\\infty \\beta^j y_{t-j} $$\n", "\n", "and where the information set is $y^t = [y_t, y_{t-1}, \\ldots ]$, the one step-ahead optimal prediction is \n", "\n", "$$ E [ y_{t+1} | y^t ] = (1-\\beta) \\sum_{j=0}^\\infty \\beta^j y_{t-j} $$\n", "\n", "\n", "\n", "## Permanent income consumption-smoothing model\n", "\n", "\n", "When we computed optimal consumption-saving policies for the two representations using formulas obtained with the difference equation approach described in the quantecon lecture https://python.quantecon.org/perm_income_cons.html,\n", "we obtain: \n", "\n", "**for a consumer having the information assumed in the news representation (1):**\n", "\n", "\\begin{align} \n", "c_{t+1} - c_t & = 0 \\cr\n", "b_{t+1} - b_t & = - \\beta^{-1} \\epsilon_t \n", "\\end{align}\n", "\n", "**for a consumer having the more limited information associated with the innovations representation:**\n", "\n", "\\begin{align}\n", "c_{t+1} - c_t & = (1-\\beta^2) a_{t+1} \\cr\n", "b_{t+1} - b_t & = - \\beta a_t \n", "\\end{align}\n", "\n", "\n", "\n", "These formulas agree with outcomes from the Python programs to be reported below using state-space representations and dynamic programmings\n", "\n", "Evidently the two consumers behave differently though they receive exactly the same histories of nonfinancial income.\n", "\n", "The consumer with information associated with representation (1) responds to each shock $\\epsilon_{t+1}$ by leaving his consumption unaltered\n", "and **saving** all of $a_{t+1}$ in anticipation of the permanently increased taxes that he will bear to pay for the addition $a_{t+1}$ to his\n", "time $t+1$ nonfinancial income.\n", "\n", "The consumer with information associated with representation (2) responds to a shock $a_{t+1}$ by increasing his consumption by what \n", "he perceives to be the **permanent** part of the increase in consumption and by increasing his **saving** by what he perceives to be the temporary part. \n", "\n", "Do you think it is appropriate to regard the first consumer as someone whose behavior sharply illustrates the behavior assumed in a classic Ricardian equivalence experiment?\n", "\n", "\n", "\n", "\n", "\n", "#### State space representations\n", "\n", "We can cast our two representations in terms of the following two state space systems\n", "\n", "\n", "\n", "\\begin{align} \\begin{bmatrix} y_{t+1} \\cr \\epsilon_{t+1} \\end{bmatrix} &= \n", " \\begin{bmatrix} 1 & - \\beta^{-1} \\cr 0 & 0 \\end{bmatrix} \\begin{bmatrix} y_t \\cr \\epsilon_t \\end{bmatrix}\n", " + \\begin{bmatrix} \\sigma_\\epsilon \\cr \\sigma_\\epsilon \\end{bmatrix} \n", " v_{t+1} \\cr\n", " y_t & = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\begin{bmatrix} y_t \\cr \\epsilon_t \\end{bmatrix} \\end{align}\n", " \n", "and\n", "\n", "\n", "\n", "\\begin{align} \\begin{bmatrix} y_{t+1} \\cr a_{t+1} \\end{bmatrix} &= \n", " \\begin{bmatrix} 1 & - \\beta \\cr 0 & 0 \\end{bmatrix} \\begin{bmatrix} y_t \\cr a_t \\end{bmatrix}\n", " + \\begin{bmatrix} \\sigma_a \\cr \\sigma_a \\end{bmatrix} \n", " u_{t+1} \\cr\n", " y_t & = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\begin{bmatrix} y_t \\cr a_t \\end{bmatrix} \\end{align}\n", " \n", "where $\\{v_t\\}$ and $\\{u_t\\}$ are both i.i.d. sequences of univariate standardized normal random variables. \n", " \n", "These two alternative income processes are ready to be used in the framework presented in the section \"Comparison with the Difference Equation Approach\" in the quantecon lecture: https://python.quantecon.org/perm_income_cons.html\n", " \n", "All the code that we shall use below is presented in that lecture. \n", "\n", "\n", " \n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computations\n", "\n", "We shall use Python to form **both** of the above two state-space representations, using the following parameter values\n", "$\\sigma_\\epsilon = 1, \\sigma_a = \\beta^{-1} \\sigma_\\epsilon = \\beta^{-1}$ where $\\beta$ is the **same** value\n", "as the discount factor in the household's problem in the LQ savings problem in the lecture https://python.quantecon.org/perm_income_cons.html\n", "\n", "For these two representations, we use the code in the https://python.quantecon.org/perm_income_cons.html\n", "lecture to \n", "\n", "* compute optimal decision rules for $c_t, b_t$ for the two types of consumers associated with our two representations of nonfinancial income\n", "\n", "* use the value function objects $P, d$ returned by the code to compute optimal values for the two representations when evaluated at the following initial conditions $x_0 = \\begin{bmatrix} 10 \\cr 0 \\end{bmatrix} $ for each representation. \n", "\n", "* create instances of the [LinearStateSpace](https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/lss.py) class for the two representations of the $\\{y_t\\}$ process and use them to obtain impulse response functions of $c_t$ and $b_t$ to the respective shocks $\\epsilon_t$ and $a_t$ for the two representations. \n", "\n", "* run simulations of $\\{y_t, c_t, b_t\\}$ of length $T$ under both of the representations (later I'll give some more details about how we'll run some special versions of these) \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "We want to solve the LQ problem:\n", "\n", "$$\n", "\\min\\ \\sum_{t=0}^{\\infty}\\beta^{t}\\left(c_{t}-\\gamma\\right)^{2}\n", "$$\n", "\n", "subject to the sequence of constraints \n", "\n", "$$\n", "\\quad c_{t}+b_{t}=\\frac{1}{1+r}b_{t+1}+y_{t}, \\quad t \\geq 0\n", "$$\n", "\n", "where $y_t$ follows one of the representations defined above. \n", "\n", "Define the control as $u_t \\equiv c_t - \\gamma$. \n", "\n", "(For simplicity we can assume $\\gamma=0$ below because $\\gamma$ has no effect on the impulse response functions that interest us.)\n", "\n", "The state transition equations under our two representations for the nonfinancial income process $\\{y_t\\}$ can be written as\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "y_{t+1}\\\\\n", "\\epsilon_{t+1}\\\\\n", "b_{t+1}\n", "\\end{array}\\right]=\\underset{\\equiv A_{1}}{\\underbrace{\\left[\\begin{array}{ccc}\n", "1 & -\\beta^{-1} & 0\\\\\n", "0 & 0 & 0\\\\\n", "-\\left(1+r\\right) & 0 & 1+r\n", "\\end{array}\\right]}}\\left[\\begin{array}{c}\n", "y_{t}\\\\\n", "\\epsilon_{t}\\\\\n", "b_{t}\n", "\\end{array}\\right]+\\underset{\\equiv B_{1}}{\\underbrace{\\left[\\begin{array}{c}\n", "0\\\\\n", "0\\\\\n", "1+r\n", "\\end{array}\\right]}}\\left[\\begin{array}{c}\n", "c_{t}\\end{array}\\right]+\\underset{\\equiv C_{1}}{\\underbrace{\\left[\\begin{array}{c}\n", "\\sigma_{\\epsilon}\\\\\n", "\\sigma_{\\epsilon}\\\\\n", "0\n", "\\end{array}\\right]}}\\nu_{t+1},\n", "$$\n", "\n", "and\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "y_{t+1}\\\\\n", "a_{t+1}\\\\\n", "b_{t+1}\n", "\\end{array}\\right]=\\underset{\\equiv A_{2}}{\\underbrace{\\left[\\begin{array}{ccc}\n", "1 & -\\beta & 0\\\\\n", "0 & 0 & 0\\\\\n", "-\\left(1+r\\right) & 0 & 1+r\n", "\\end{array}\\right]}}\\left[\\begin{array}{c}\n", "y_{t}\\\\\n", "a_{t}\\\\\n", "b_{t}\n", "\\end{array}\\right]+\\underset{\\equiv B_{2}}{\\underbrace{\\left[\\begin{array}{c}\n", "0\\\\\n", "0\\\\\n", "1+r\n", "\\end{array}\\right]}}\\left[\\begin{array}{c}\n", "c_{t}\\end{array}\\right]+\\underset{\\equiv C_{2}}{\\underbrace{\\left[\\begin{array}{c}\n", "\\sigma_{a}\\\\\n", "\\sigma_{a}\\\\\n", "0\n", "\\end{array}\\right]}}u_{t+1}.\n", "$$\n", "\n", "As usual, we start by importing packages." ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import quantecon as qe\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [], "source": [ "# Set parameters\n", "β, σϵ = 0.95, 1\n", "σa = σϵ / β\n", "\n", "R = 1 / β\n", "\n", "# payoff matrices are the same for two representations\n", "RLQ = np.array([[0, 0, 0],\n", " [0, 0, 0],\n", " [0, 0, 1e-12]]) # put penalty on debt\n", "QLQ = np.array([1.])" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [], "source": [ "# original representation state transition matrices\n", "ALQ1 = np.array([[1, -R, 0],\n", " [0, 0, 0],\n", " [-R, 0, R]])\n", "BLQ1 = np.array([[0, 0, R]]).T\n", "CLQ1 = np.array([[σϵ, σϵ, 0]]).T\n", "\n", "# construct and solve the LQ problem\n", "LQ1 = qe.LQ(QLQ, RLQ, ALQ1, BLQ1, C=CLQ1, beta=β)\n", "P1, F1, d1 = LQ1.stationary_values()" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , -1. , -0.05]])" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the optimal decision rule for c\n", "-F1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evidently optimal consumption and debt decision rules for the consumer having news representation (1) are\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}^{*} &= y_{t}-\\epsilon_{t}-\\left(1-\\beta\\right)b_{t}, \\\\\n", "b_{t+1}^{*} &=\\beta^{-1}c_{t}^{*}+\\beta^{-1}b_{t}-\\beta^{-1}y_{t} \\\\\n", "\t& =\\beta^{-1}y_{t}-\\beta^{-1}\\epsilon_{t}-\\left(\\beta^{-1}-1\\right)b_{t}+\\beta^{-1}b_{t}-\\beta^{-1}y_{t} \\\\\n", "\t& =b_{t}-\\beta^{-1}\\epsilon_{t}.\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [], "source": [ "# innovations representation\n", "ALQ2 = np.array([[1, -β, 0],\n", " [0, 0, 0],\n", " [-R, 0, R]])\n", "BLQ2 = np.array([[0, 0, R]]).T\n", "CLQ2 = np.array([[σa, σa, 0]]).T\n", "\n", "LQ2 = qe.LQ(QLQ, RLQ, ALQ2, BLQ2, C=CLQ2, beta=β)\n", "P2, F2, d2 = LQ2.stationary_values()" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , -0.9025, -0.05 ]])" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "-F2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a consumer having access only to the information associated with the innovations representation (2), the optimal decision rules are\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}^{*} &= y_{t}-\\beta^{2}a_{t}-\\left(1-\\beta\\right)b_{t}, \\\\\n", "b_{t+1}^{*}\t&= \\beta^{-1}c_{t}^{*}+\\beta^{-1}b_{t}-\\beta^{-1}y_{t} \\\\\n", "\t&=\\beta^{-1}y_{t}-\\beta a_{t}-\\left(\\beta^{-1}-1\\right)b_{t}+\\beta^{-1}b_{t}-\\beta^{-1}y_{t} \\\\\n", "\t&=b_{t}-\\beta a_{t}.\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct two Linear State Space models given the optimal policies.\n", "\n", "Take the original representation case as an example,\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "y_{t+1}\\\\\n", "\\epsilon_{t+1}\\\\\n", "b_{t+1}\n", "\\end{array}\\right]=\\left(A_{1}-B_{1}F_{1}\\right)\\left[\\begin{array}{c}\n", "y_{t}\\\\\n", "\\epsilon_{t}\\\\\n", "b_{t}\n", "\\end{array}\\right]+C_{1}\\nu_{t+1}\n", "$$\n", "\n", "$$\n", "\\left[\\begin{array}{c}\n", "c_{t}\\\\\n", "b_{t}\n", "\\end{array}\\right]=\\left[\\begin{array}{c}\n", "-F_{1}\\\\\n", "S_{b}\n", "\\end{array}\\right]\\left[\\begin{array}{c}\n", "y_{t}\\\\\n", "\\epsilon_{t}\\\\\n", "b_{t}\n", "\\end{array}\\right]\n", "$$\n", "\n", "To have the Linear State Space model of the innovations representation case, we can simply replace the corresponding matrices." ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [], "source": [ "# construct two Linear State Space models\n", "Sb = np.array([0, 0, 1])\n", "\n", "ABF1 = ALQ1 - BLQ1 @ F1\n", "G1 = np.vstack([-F1, Sb])\n", "LSS1 = qe.LinearStateSpace(ABF1, CLQ1, G1)\n", "\n", "ABF2 = ALQ2 - BLQ2 @ F2\n", "G2 = np.vstack([-F2, Sb])\n", "LSS2 = qe.LinearStateSpace(ABF2, CLQ2, G2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following we compute the impulse response functions of $c_t$ and $b_t$." ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [], "source": [ "J = 5 # number of coefficients that we want\n", "\n", "x_res1, y_res1 = LSS1.impulse_response(j=J)\n", "b_res1 = np.array([x_res1[i][2, 0] for i in range(J)])\n", "c_res1 = np.array([y_res1[i][0, 0] for i in range(J)])\n", "\n", "x_res2, y_res2 = LSS2.impulse_response(j=J)\n", "b_res2 = np.array([x_res2[i][2, 0] for i in range(J)])\n", "c_res2 = np.array([y_res2[i][0, 0] for i in range(J)])" ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1.99997796e-11, 1.89473992e-11, 1.78947621e-11, 1.68421319e-11,\n", " 1.57894947e-11]),\n", " array([ 0. , -1.05263158, -1.05263158, -1.05263158, -1.05263158]))" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_res1 / σϵ, b_res1 / σϵ" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title(\"original representation\")\n", "plt.plot(range(J), c_res1 / σϵ, label=\"c impulse response function\")\n", "plt.plot(range(J), b_res1 / σϵ, label=\"b impulse response function\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above two impulse response functions show that when the consumer has the information assumed in the original representation, his response to receiving a positive shock of $\\epsilon_t$ is to leave his consumption unchanged and to\n", "save the entire amount of his extra income and then forever roll over the extra bonds that he holds\n", "\n", "To see this notice, that starting from next period on, his debt permanently **decreases** by $\\beta^{-1}$ \n" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.0975, 0.0975, 0.0975, 0.0975, 0.0975]),\n", " array([ 0. , -0.95, -0.95, -0.95, -0.95]))" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c_res2 / σa, b_res2 / σa" ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 222, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title(\"innovations representation\")\n", "plt.plot(range(J), c_res2 / σa, label=\"c impulse response function\")\n", "plt.plot(range(J), b_res2 / σa, label=\"b impulse response function\")\n", "plt.plot([0, J-1], [0, 0], '--', color='k')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above impulse responses show that when the consumer has only the information that is assumed to be available under the innovations representation for $\\{y_t\\}$, he responds to a positive $a_t$ by permanently increasing his consumption. \n", "\n", "He accomplishes this by consuming a fraction $(1 - \\beta^2)$ of the increment $a_t$ to his nonfinancial income and saving the rest in order to lower $b_{t+1}$ to finance the permanent increment in his consumption.\n", "\n", "Now let's simulate some paths of consumption and debt for our two types of consumers\n" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [], "source": [ "# set time length for simulation\n", "T = 100" ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 224, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x1, y1 = LSS1.simulate(ts_length=T)\n", "plt.plot(range(T), y1[0, :], label=\"c\")\n", "plt.plot(range(T), x1[2, :], label=\"b\")\n", "plt.plot(range(T), x1[0, :], label=\"y\")\n", "plt.title(\"original representation\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 225, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x2, y2 = LSS2.simulate(ts_length=T)\n", "plt.plot(range(T), y2[0, :], label=\"c\")\n", "plt.plot(range(T), x2[2, :], label=\"b\")\n", "plt.plot(range(T), x2[0, :], label=\"y\")\n", "plt.title(\"innovations representation\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulating the income process and two associated shock processes\n", "\n", "\n", "\n", "We now describe how we form a **single** $\\{y_t\\}_{t=0}^T $ realization that we will use to simulate the two different decision rules associated with our two types of consumer.\n", "\n", "We accomplish this in the following steps.\n", "\n", "1. We form a $y_t, \\epsilon_t$ realization by drawing a long\n", "simulation of $\\{\\epsilon_t\\}_{t=0}^T$ where $T$ is a big integer $\\epsilon_t =\n", "\\sigma_\\epsilon v_t$, $v_t$ is a standard normal scalar,\n", "$y_0 =100$,\n", "and\n", "\n", "$$ y_{t+1} - y_t =-\\beta^{-1} \\epsilon_t + \\epsilon_{t+1} . $$\n", "\n", "2. We take the **same** $\\{y_t\\}$ realization generated in step 1 and form an innovation process $\\{a_t\\}$ from the formulas\n", "\n", "\\begin{align} a_0 & = 0 \\cr \n", "a_t & = \\sum_{j=0}^{t-1} \\beta^j (y_{t-j} - y_{t-j-1}) + \\beta^t a_0, \\quad t \\geq 1 \\end{align}\n", "\n", "3. We throw away the first $S$ observations and form the sample $\\{y_t, \\epsilon_t, a_t\\}_{S+1}^T$ as the realization that we'll use in the following steps.\n", "\n", "4. We use the step 3 realization to **evaluate** and **simulate** the decision rules for $c_t, b_t$ that Python has computed for us above. \n", "\n", "The above steps implement the experiment of comparing decisions made by two consumers having **identical** incomes at each date but at each date having **different** information about their future incomes. \n", "\n", "\n", "\n", "### Values functions\n", "\n", "\n", "After doing this, we compute the discounted expected values obtained for the two consumers by using the pairs\n", "$P, d$ that we have computed for the value functions.\n", "\n", "We compute the value functions $x_t' P x_t + d$ (I might have a sign off here!) for the two $P,d$ pairs at the **same** dates along the income simulation. But we choose the states for two hypothetical consumer in the following peculiar way.\n", "\n", "We give each consumer the same income $y_t$ and the pertinent shock $a_t$ or $\\epsilon_t$, depending on whether it\n", "is the \"innovation representation\" or the \"orginal representation\" consumer.\n", "\n", "But we give **both** of these hypothetical consumers the $b_t$ of the \"innovation representation\" consumer. We then record the discounted present values for these two.\n", "\n", "Thus, the **state** vectors $x_t$ are different for the two consumers **only** because one sees $a_t$ while the other (better informed) consumer sees $\\epsilon_t$ -- they both have the same $b_t$, namely, that of the \"innovations representation\" consumer. \n", "\n", " " ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [], "source": [ "S, T = 10, 100\n", "\n", "ν_seq = np.random.normal(size=T+1)\n", "ϵ_seq = σϵ * ν_seq\n", "\n", "y_seq = np.empty(T+1)\n", "y_seq[0] = 100 # initial state\n", "for i in range(T):\n", " y_seq[i+1] = y_seq[i] + ϵ_seq[i+1] - ϵ_seq[i] / β" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [], "source": [ "# calculate innovations\n", "a_seq = np.zeros(T+1)\n", "for i in range(1, T+1):\n", " a_seq[i] += β ** i * a_seq[0]\n", " for j in range(i):\n", " a_seq[i] += β ** j * (y_seq[i-j] - y_seq[i-j-1])" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(T+1), ϵ_seq, label=\"ϵ\")\n", "plt.plot(range(T+1), a_seq, label=\"a\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we confirm that the constructed innovations generate the same income sequence." ] }, { "cell_type": "code", "execution_count": 229, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ya_seq = np.empty(T+1)\n", "ya_seq[0] = 100 # initial state\n", "for i in range(T):\n", " ya_seq[i+1] = ya_seq[i] + a_seq[i+1] - β * a_seq[i]\n", " \n", "np.max(np.abs(ya_seq - y_seq)) < 1e-10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Calculating innovations in another way\n", "\n", "Here we use formula (3) above to compute $a_{t+1}$ as a function of the history $\\epsilon_{t+1}, \\epsilon_t, \\epsilon_{t-1}, \\ldots$\n", "\n", "Thus, we compute\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{aligned}\n", "a_{t+1}\t&=\\beta a_{t}+\\epsilon_{t+1}-\\beta^{-1}\\epsilon_{t} \\\\\n", "\t&=\\beta\\left(\\beta a_{t-1}+\\epsilon_{t}-\\beta^{-1}\\epsilon_{t-1}\\right)+\\epsilon_{t+1}-\\beta^{-1}\\epsilon_{t} \\\\\n", "\t&=\\beta^{2}a_{t-1}+\\beta\\left(\\epsilon_{t}-\\beta^{-1}\\epsilon_{t-1}\\right)+\\epsilon_{t+1}-\\beta^{-1}\\epsilon_{t} \\\\\n", "\t&=\\cdots \\\\\n", "\t&=\\beta^{t+1}a_{0}+\\sum_{j=0}^{t}\\beta^{j}\\left(\\epsilon_{t+1-j}-\\beta^{-1}\\epsilon_{t-j}\\right) \\\\\n", "\t&=\\beta^{t+1}a_{0}+\\epsilon_{t+1}+\\left(\\beta-\\beta^{-1}\\right)\\sum_{j=0}^{t-1}\\beta^{j}\\epsilon_{t-j}-\\beta^{t-1}\\epsilon_{0}.\n", "\\end{aligned}\n", "$$\n", "\n", "We then verify that we recover the same $\\{a_t\\}$ sequence computed earlier." ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [], "source": [ "a_seq2 = np.zeros(T+1)\n", "for i in range(T):\n", " a_seq2[i+1] += β ** (i + 1) * a_seq2[0] + ϵ_seq[i+1] - β ** (i - 1) * ϵ_seq[0]\n", " for j in range(i):\n", " a_seq2[i+1] += (β - 1 / β) * β ** j * ϵ_seq[i-j]" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.max(np.abs(a_seq2 - a_seq)) < 1e-12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's take two consumers with exactly the **same** $\\{y_t\\}$ sequence and construct paths of $c_t$ and $b_t$ for our two types of consumers\n", "who are distinguished not by their histories of current and past $y_t$'s but rather by whether or note they see the valuable **news** $a_t$." ] }, { "cell_type": "code", "execution_count": 232, "metadata": {}, "outputs": [], "source": [ "# set the initial state\n", "c1 = np.empty(T-S)\n", "b1 = np.empty(T-S)\n", "c2 = np.empty(T-S)\n", "b2 = np.empty(T-S)\n", "\n", "# initial debt\n", "b1[0] = 0\n", "b2[0] = 0\n", "\n", "for i in range(T-S-1):\n", "\n", " # orginal representation\n", " c1[i] = y_seq[S+i+1] - ϵ_seq[S+i+1] - (1 - β) * b1[i]\n", " b1[i+1] = b1[i] - ϵ_seq[S+i+1] / β\n", " \n", " # innovations representation\n", " c2[i] = y_seq[S+i+1] - β ** 2 * a_seq[S+i+1] - (1 - β) * b2[i]\n", " b2[i+1] = b2[i] - β * a_seq[S+i+1]\n", "\n", "c1[T-S-1] = y_seq[T] - ϵ_seq[T] - (1 - β) * b1[T-S-1]\n", "c2[T-S-1] = y_seq[T] - β ** 2 * a_seq[T] - (1 - β) * b2[T-S-1]" ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(97.5581182952526, 102.68900055363287)" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ax.plot(range(S+1, T+1), c1, label=\"c1\")\n", "ax.plot(range(S+1, T+1), c2, label=\"c2\")\n", "ax.legend()\n", "ax.set_title(\"consumptions\");\n", "\n", "ax1_ = ax.twinx()\n", "ax1_.plot(range(S+1, T+1), y_seq[S+1:], color='g', label=\"income\", alpha=0.4)\n", "ax1_.set_ylabel(\"income\", color='g')\n", "span = (max(y_seq[S+1:]) - min(y_seq[S+1:])) / 2\n", "center = (max(y_seq[S+1:]) + min(y_seq[S+1:])) / 2\n", "ax1_.set_ylim(center-span*1.1, center+span*1.1)" ] }, { "cell_type": "code", "execution_count": 234, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(97.5581182952526, 102.68900055363287)" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ax.plot(range(S+1, T+1), b1, label=\"b1\")\n", "ax.plot(range(S+1, T+1), b2, label=\"b2\")\n", "ax.legend()\n", "ax.set_title(\"debts\")\n", "\n", "ax1_ = ax.twinx()\n", "ax1_.plot(range(S+1, T+1), y_seq[S+1:], color='g', label=\"income\", alpha=0.4)\n", "ax1_.set_ylabel(\"income\", color='g')\n", "span = (max(y_seq[S+1:]) - min(y_seq[S+1:])) / 2\n", "center = (max(y_seq[S+1:]) + min(y_seq[S+1:])) / 2\n", "ax1_.set_ylim(center-span*1.1, center+span*1.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let us compute the discounted expected values." ] }, { "cell_type": "code", "execution_count": 235, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 20. , -20. , -1. ],\n", " [-20. , 20. , 1. ],\n", " [ -1. , 1. , 0.05]])" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P1" ] }, { "cell_type": "code", "execution_count": 236, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 20. , -18.05 , -1. ],\n", " [-18.05 , 16.290125, 0.9025 ],\n", " [ -1. , 0.9025 , 0.05 ]])" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P2" ] }, { "cell_type": "code", "execution_count": 237, "metadata": {}, "outputs": [], "source": [ "# construct state vectors\n", "x1 = np.empty((3, T-S))\n", "x1[0, :] = y_seq[S+1:]\n", "x1[1, :] = ϵ_seq[S+1:]\n", "# use debt of \"innovation representation\" consumer\n", "x1[2, :] = b2[:]\n", "\n", "x2 = np.empty((3, T-S))\n", "x2[0, :] = y_seq[S+1:]\n", "x2[1, :] = a_seq[S+1:]\n", "x2[2, :] = b2[:]\n", "\n", "# compute discounted present values\n", "ev1 = np.diagonal(x1.T @ P1 @ x1) + d1\n", "ev2 = np.diagonal(x2.T @ P2 @ x2) + d2" ] }, { "cell_type": "code", "execution_count": 238, "metadata": {}, "outputs": [ { "data": { "image/png": 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a2uSae4zNDRG510gSUo9AR6UWXFmHrWZjT/cTwKaQZbxVkmWsALnHkXuMzQzh0d4gScg9IneNWvDkBCApSNPY031QbIrIXfQv7bVKv9SwWiL3za25x9jc8LgZmEmSPWUZDRaorMNLFJClNXhr3Mp4rWJTkLvoX9rL02KpYRvNqKPXBb1UKM1NwzKN3jvGiLGCEDa+ppTqGbknqAWqJEESeciEolYtrcQQNxw2Bbl7XI5Zad3bCZL7CjxYqOeh8XeX4vF/+PNl/6wYMfqB6ERmKSnIiI7EPdeFRhxA0SElCwCAWin2dB8Em4Pcuf/1SksjInKv0t5T0aXAwuwkxjENdf6VZf+sGDH6gs3I3ZHTXSN30+AeNGoSaoZZEMTkPhg2CbmzC0umK0vunsnJnXS/oJcKU689DwDQrdgDO8Yag2PAowSu0n1B1eLkThQdapqRuxF7ug+ETUHuQnPvlYK11HA5uTekzIpE7pVjrEFy2o49sGOsMTgGTKigktJVlhGRO1GTSGSHAABWNSb3QbApyF3kua905E5tdqE25MyKRO72zKsAgJwX+3HEWFsgrgmbqKCSCgXR94LNrYElNYFUboRtq8XByiDYFOQOTu7KCpM7uJ+GpWZX5MGiLLBuPwVajtPHYqwpENeEhd7kLmQZSUshnWctC2Pb38GwKcid8myZlY/ca3CoBFdOQqbLT7aZ+hEAgEI8lOdjg64YawfENWERDZAUKF3uBeEeKWsJZHJMc6eNOBVyEGwScheR+8pq7sRuwIAOT1JXZNYwah9FneoAgNLM0WX/vLWCV57+GZ79zJWob5B86I0465JcCzbRQOXFyTKyloKsKKjQJIgRR+6DYFOQO1aL3J0GDKKDSmrXRaSlQL1awggWcFBnfSpr85PL+nlrCbMvPYyzrV/g8LOPrPZQThjz08dQ/vROPPGv0T1G1zoOv/QUqOe1bJM8Cw7RQCQVGnE73hdwuZSp6MyHvkoykK3YGXIQbApyF7KMgpWVZWSnDpPooJICtUu0shSYfO0FAEB5dC8AwFg4vqyft5Yg/r6V159f5ZGcOA488G0UUIV5eH02jH/t+cex81tX4flH/rVlu+yZcHjkDgBuRGcy1xTkngIA1OUMFDt2hhwEm4LcRYs7daXJ3TVgkQSorEFeZnKfn3gJAJA65RIAgF2eWtbPW0ugvI2iO/XiKo/kxKEfuAcAoFZeX+WRDIb519l1WJ890rJd4d2VIDGvQtFjoR3CGljVkwAAQ85Aj21/B8LmIHdemaqusCwjuwZsSQckddk/25p+GQCw89yrAABedfMsqIo1Fb18cMmO+eRf/Rp+fuefLtnxFoPywizOajwBAEga63PmZZXYuN1GKyErnglX0kB45G5HkLtnCXJPs+MpOSTXCLk/dd+38cx/vWrdrIlsCnIXLe66LeQsB1S3AVtK8kWk5b0gyPwhlJBGcXQr5pGFVN885C7aJ440Di3ZIU+uPQl9+pdLdrzF4KUH/wkacfE6GUPRXp8zL7fC1nqo2U7uFlxJA4QsE0Xu3D1SS7DI3dFya8bT3XzhxzjHfAqV0vooqtoU5C4id424K/rUVT0DjpxgkXuXRaSlQKp6GFPKNgBAWSpANbtfgDPHj+DYa+tfxgDgk/tW7/iSOGJapoE8apDdlW2oLr3wL5hGEYfH344Rb2bdRIhBSDUWVFCzlZAV2PBk3Y/cHSec3CmXZbQEi9xdLYfMAJ7u1PPwyBdvwnMP/+++fzcKWu0YAKA8tz5mVZuC3IONMmx75W5YlZpw5QSIrPHPXj5XyiHrdZSTJwEAqkoBCat7Vd+hb/0+ql//zWUbz4pCLJgTD8cOvXDCh1uYYTex4q6cdXKjVsGZ1Ufw6shbIBV3QSMu5iYnVuzzlwpKYwYAQKxWclc9C54UIPeIe4HyyF3nkTtNFJAhjcj9o+A4Ni6evQvWv/9tX7/XDRmTzUpqC+tjVrVJyL25kGpbK0fuumfAVVKArPDPXh6ysC0TY940rNwuAICpDSHtdCf3pDGNEXd9XKS9IGQ3AJh77ZkTPl55hi1mKt7KXSvPP3QXUsRE+o3vgT68EwAwe3T9uXsmLebgKNlt5A4bntIkd9eOSG5wBLmzbBmSzAMAqlwKcWwL++/5Ss9ZjbjX3lDfv2QyypDLZiVGaX1InpuE3JuRu7OS5A4TnpIEeOTuRF3QJ4jJwwegEA/yyMkAADsxjHwPfxnNrSFPK31HRGsRxLNhUEYaxvETl5pqczxypyt3rXjP3o0FZHDGxe9AbmwPAKA69dqKff5SIeMwIpXtVilFdFfyyd2J+G4dAyZVQSRGTbLwdC+zh8aT93wF+x77BF7af1/XcdgWu6414uDFh7472MkEYBp1DIMVydmVmRM+3kpgk5B7MHJfual2gpqso4zIEFimz56bYISWGT8NAOClRlBAtessJenVIBGKhdn1X+xEXAsVksE0ilDmDpzw8awS+060FYrcLdPA6eWf4kDhCqiajuHtpwAA7Ln1R+4FHlQoTiu569QGlROQFBbouBHyKHFMmETzX6sZ5gxZ557uykv/AgAwejhFOoHjS8//oJ9TCMXM0WYmlluNyX3NQFoFWcZzXSSJBaqmQMQFHbGIdKJoTLI0yNFdZwEApMwoAKA0E73wk6SszLsyu/5tCohnw4GCKW0nctUTT4d0y4zcVboys5oXfn4PcqhDPfc9AIBcfgg1mgDK6yvX3TTqyIGRuurW/e3U86ATG1C0QOQePouVXAMWVP+1lhGe7vNsXaLGirucRveqVUHuVZrEmZWHYdRPLONm4XjzQUvr66N5yKYg96As49orE7kbvDk2UZuRu2MtD1nQuYNoUA0j40yrVXNbAHRf1c9wcq+tk5X/bpA8Gw5RUc3uwbhz5MSzknjGh46VCQRqr/wMAHDmZe8GABBJwrQ8Cr22vh6889PN8WoBcjd51SkUPRC5h98LzGBM918ns4zc7docnn/oLiQJL1hrdM99F/fa84UrkCImnn/orj7PphWNmSa5y8b6sCDeFOQebJSxUhqziBSIng5E7stDFnrlNUzK475OmSiMA4gmbtOos0gKgFHaALKM58AlCujwacijhrnpEyNFkfGhr1DkTqwaGlRDIpn2t5W1cWTWWSFThZvV1WgCCa9J7iI9lSgJSAoLdDw3PHKXXQN2QJZJ5pjtr1Obh/vc931jvPY8+naIyJ2ccg1KSMN59vuDnJIPe55V3B4lY1DNmNzXDIKyjLNCmrtP7loKkp8hsDzkXjQmMJ/Y4b/ODDFyN0vh5FArNy9Op7z+yV2iLHJPbWWmaZMHTyxjRuNtChOwlrU2QYC4rTozADRSW/3sjPWC+jwj9+PKNiRow9/ut85TE5Dk7hKlcI8UyBZYww6vOoMzSj/Fc/krAXTm0bdD3GuynsJL+StwRumhE6qBkMqvYwEZzKtboNvrw310c5A7DcoyKzPVtrksI2upnjrjiYB6Hsbc4zCzO/1t+ZHtAACnEp7q2Kg2M2noBrApkDwbLlEwsudcAEB14rkTOl7aZuQuEQprBYIB4hiw0EruXnYbhlE6Ya14JWEtsEChlNyBVIDchY0vUROQeeROI+4FxTPgSE1ZJpXOwaEShiZ+jBxqkM95D+pU78ijb4e4z4miQz3neuRQw4sP/3Dgc9PrxzErj8JUC0g568OCeNOQu0sJgGitb6lhCnJPZCCp7GJ1luHBMnP8MJLEAhk62d+WKwzDpnIkcTcqzYtTbqyPlf9ukD0bLlExftKpMKgKb/qlEzpezm1+P0a9/+rIfiG16cwAoBTZw3r66NL55Sw3HG49YGZ3I0VMuA4LqmyuuUtqApLKHmKeG34fysJgjINIEiokjdOdl9CgGs588/Wok2RHHn07/Mhd0XDmm69DneqoPz247p61JlHRxmDrRWS8teF10ws9yZ0Q8lVCyBQh5JnAtiFCyI8JIQf4/0W+/UxCyM8JISYh5BPLOfB+IFMHdTB/aG+ZdO922AYjBUVP+VNRbxki9+nDrCIzOXaqv41IEhZILpK4zUDkrvWwKVgPkKgNT1IgyTKOytuRLL868LE810WRljCPLADAMpaf3JnO3EruqdHdAIDSscHPZaVBatOsuUaGSSk13jzF5nKIrOq+ROk54T5PqmfClVq/ixrJAABeyFyEZDoLgyQ78ujbIYI4SdGRSGXwfPZSnDb7bwNnyw270zBT4/CSQ8jTyorIdSeKxUTuXwPwjrZtfwzgPkrpaQDu468BYA7AxwB8fqkGuBSQqQODMHJfKVnGMTm5J9KQRbSyDJ9dnzoEAMhvPaVle1kuRC782HV2080ji6S1/sldpg5cwkhjPrUbw8bg+eHl+WkoxMOszDKOVoTcPRO21CrLFLbuBgDUZw4v++cvFdTGDBakIiSdPRiF/Of4Ta+TzXshSpahFly5ldwbMiN357RfBQAYUqojj74dIogTn6fs/QCGUMYv/+0fO/adOX4EM8ePdGz3P79WQQFV0Ox2kNQQVOKiUl77i6o9yZ1S+gAYaQdxPYA7+c93AngP33eKUvoYsMLG6T0gUwcmJ3e6QpG7a7Bpo57MNDMEliFy97jRkh7ItACAulJEKoK47Tq76aaU7ci660M/7AaZ2vAkXihWOAVbvUmYRr3Hb4WjNM1yy8sJZsJmDXicfiB7ZovODAAj21iVqjsfTTprDQlzFlWlCCnJyN3gkbsvkWgBzT1CltEo86AJwpAzcKiE0694HwDAklMtefRhELKPzCXRs6+4AVMYgvzU11v2cx0HtS+/A8fuuDHyWDNH2exJLu6AnGazkso6SCEeVHMfo5QeAwD+/5Z+D0AIuZkQsp8Qsn96evBFvW5PXAGZOjAlZkS0XIVE7XB5tKIlM/4F5i3DZ4uHlWhuIGDqQ8i44dGFZ7ACkErqJL+icD1DoQ4obwKhjJ0BmVAcOzjYomqV37RWhmUf2StA7moIueuJFGZQgFxZP+ZhGWcODW0YKid3s86uM791npaErPBUxohUSJVa8JREy7ba7rdj//hvID88BgCw5VRLHn0YhHeNuPcUVcMrO96Dc+qP4fiRl/39nvzR/8QubwJF61jksUrHDwEAUiO7oPHUzOrc2s8yW7UFVUrplyml+yil+0ZHRwc6xv7v34aR287B668+23U/GS4sTu50hRZUPYtdfHoiA1npvoh0Iogidyc5goIXnrJFeXWfXTgZKWKu+8bSLHJn33Fh59kABjcQMxb4TV5gC5r2Csgyqmd16MwAMKdsQaKx9iNEgbw3Dzs5ApWbfVk1HrnzjCNFT0JWReQeTu4696AJ4pIP/L+45Lf/3n/tKGnoXqP9V1tAfVmmeaxdb/0/IROKg/d+hY3LcTD65N8BAIa8aHlSSGOFrbuR4AWCRnntJyIMSu6ThJCtAMD/XxV7wfE3XA4AmHjsX7rup1AbtszJfYVkGWoxUtDT2RWJ3DW9NdqhqWGkiRGaSkfNCiyqQC6y6HShi03BegCL3BlpbD35HACAeXww61/RnjAxshtAcwa2nBDW0O2o6uPIW2s/QgSYrUcBVXipUWipHNvGq0j91nlaEgrXwGnEvaCFRO7tcNW0b58RBXGvKWrTymDbnjPxS/0C7H7tu/BcF0/+769ilzeBl5TTkSImqhE6urvAZk8j2/YgXeBrMeW1n0I8KLl/H8BN/OebANy9NMPpDztOPQevkzFor93fdT8ZLhxB7ssQPYdBNB1IJNP+BRaV23tC4BexprXeEHKGXYTCmzwIySqjRlLQ82yfysz68jBphwLH19zT2QJmkYdcHkzOoNUpuJQgs4VF7o7VPUJcCmjUhCd3Ru5WZhtG3el1kZkhrAek7BYk0ixyF/4vnh+5p6Cq0bIM9TwkiA30IHdPzbTk0YdBPDyCkTsAWG/8LWzFNJ554HsYfeLvcEg6CaVzPsTOYTJ88VquvI5Z5KEnUsgOswJBt7b2/WUWkwr5vwD8HMAZhJAJQsh/AvBZAG8nhBwA8Hb+GoSQcULIBICPA/gzvn9u+YYPTAxditNrT3StPlPgMF91REcMSw67DovKUDXdv8CipqK9QD0P+3/w9+Hn6JqwqAxJlls2a3mmT1ZmO8ldtquokRSSha0AgGJj/0kAACAASURBVMbC+ogOo6DCBqRmhDYvj0CvDzYbkRszmCd5aEmWoSHkteWEChs0jNDyO5AiJkpza993X3jga/lxJDKM3D2DRe6idZ6qJ/zsFXid90LTg6Y7uVMtgxQxu3q6iyBOaSP3c675AOaRxfi//wF2eUcwe+HvIznMZrDl6fAgJ1E/jjmZSce5/BAcKq0L87DFZMt8gFK6lVKqUkp3UEr/J6V0llL6Vkrpafz/Ob7vcb5PjlJa4D93t287QehnXos0MXCgi7+zQl14KssmGZRg+4Vk1/30S38qOuCs4aUn7se+x/8Qz4WYHxHHhB1w0RNIFhi51+c7SU6xqzCktB+FWOvcX0alDqjcTCWs6luQtQabNqvGLCpSIUDuyx+567RTZwYAbYh11po9uvZz3YUHfrI4jnSWebB73CKA8gYcmh6QZULuQ7PRrGTtBqKzv02ty1qRCOLUthmtnkjhxbFfwxbM4TXpJJx/7YeQ4RXdjflwcs9Zk6jq7H4ikoQSyUJaB+Zh675C9dSL3wmbyig/E90rUYUDqvAFxxXS3InTgAF2w3abii4GNb6gI9IrWz7HNWGRTnLPDrNUPjOEuDWnClNOozjKLmq3uvYjw25Q4ILKze/ATI5hyBtswStlzaGqFqHzHp7LHblTz2MeNmqy473MFpYOWZk8tKxjiMLxwwdQml/c92gusCAiO7wdiWSaVYQLcy+xLpRI+vcC3M4iJtv3oOn8LoIgfh59l0QAV5C71vHW1mt+GwZVMXfxH0BWFBS3sIeoE+HFNOxOw0qN+6+rUg5qTO7Lj0yuiJf0N2DL1EOR+yhwQRUdDpX8P/pyQ3IMv6Tcn4oO+NkWN2TyQuyKiWuFRu6FUSa5eCH+MrpXg6VkkEhlUKVJkNraX/mPAvU8aMTxu10BgJfdigKqA/myZN15mPow9CST8WAvb+RuWQYkQkGUTkIb2sYsJczZ1Wna4d7xa3jhm//P4vbl11lxyzYQSUKNJH3/l+aifxKyosCjJFyWMUSxU/fIXU6wyL07ubOHR3vkDgC7zjgf5E8O44Jr2bJhrjgKk6qglU5yr5TmkCUN0Nx2f1tNzkO3134K8bondwAob78Kp7ivYuZ454KI6ziQCAVkDTYUkBUid9ltwJTYhaVqJ6i5V9iUN6zCVfIsOCGReyqTR4Nqvjd5EEmvBkdlN8iClIdirH39MAqOWKQORO5KgWmos8f7J8WCtwAnOYIEl2WEpLBcMLgUAbVTlhka3QaLKvBKK5/rbtSr2E4nkaksztuG1KZQpzpSXG9vIAlJWAQ4Bmwq+5KMAzk0cvcrWbXukbuSZMt4Zq2LLCM0d6Xz3gCaPVoBJrXMkQKUemcgNMe9fRQukQGAqRWQctZ++vCGIPfR81lZ8sGHO9tp+a3tJAU2UUIjhuWA4jZgc829ORUd7LOVGpNWwohG8lotUoNYIHnIRmf+borW4XFyr8pF6Ob6JXfx9yWByD3Bb8SFPsm9Xi0hRUzQ1AgkWYZFFSBktjRz9LUl6+jVdEzsJDRJljEljUCrrnzTjkle6JO3FyfZKY0ZzEsF/zWzCOC2147Z0l3JgdzS+lLA4t+F3EOWUTm5W/XusoxFFb/HQS+UlWEkjM5AqMQlsfToLn+brRWQjaghWUvYEOR+8jmXYAYFkFd/0vGezYuWiKzChrpikbvqmXD4Ipkky1wSGozc/YsuZL1AdCEKQ0UpQm8zBqOehwytw9PZDdLQikjba18/jIJohByUZXJj7EZszPZXur8wzWZIco4tnhlEB3FaZRnbMqH//cV44p//pufxnnnwbjz703u67mM1uuvMJXUM6VVo2lE6yls3ejOLSsVMmDOoyEP+a1NKQnH4ubkmrEAA4hAllNxdni0j693JXUvzPPp6dK4GcS02Q1gk6towsnZnkGPM8gKm8d3NcSaHkBvQPMyoV/HMgyuTOb4hyF2SZRzMX4RTyo92pEf5Fr+yCmcFZRnVa8CWm1M/B/LAn521mSYeVoAVJcsAQEMtImW3krvRqEEhHsDJ3U4MI7cMFgQ///LH8PCXbl7y47bDj9yVJnkMb2Xk7sz3J2eUZ1m2hMj/N6FBaiP3WnmeabBzvTNY1H//DJR/+4uu+4gKWDlCimjoI8g4K2/u1phm56cTe1GdrTL2HBr6sP/aClgEEMeADcV/z4EMeCELqoLce8gyCU7urhFtvUs8m83UFwkrOYpCSJWquzABjxKMcCM3ACCpIWjERbXS/33z9L9+FefcdyOmjx7q+3f7xYYgdwAgp7wVRZTxytM/bdnuOCJy1+AQpaUr03JC80x4gapDG0roBb0YFD0eUYSQu+xZcKVwWcbUhzuMwWoVFqVLCX6DJEdQoOWuOcODoDD9GE6d+tclPWYY/HZqgcg9kyuiQpNAJdovJAzGPJO/UkVuGkY0SG6rLNPgOq8SIne1Q/fqyDvdF6t9KUJLhb7valkkexTsLAfo3CH/57lFpGLmvQVYiRH/tS2noXNylzyrNXJHROQuKln18O9CIJlm8k83codnhyYaRO6eGUcB1Q7DOblyFDOk6K+bAYDkm4f1n2XmltksrF5e/gf2hiH3ky95NzxKMPOL1m4rjiVufhUOUUMvquWATg24gQyIqKloLxj1KvK8ozwJ0dwV3qgiDG5yBEVaapk+iotK5rolyYxCId6SF8qonokRLIQuci8l/I47cut3MCePQOuzkMkqiXQ+lmlkEx2S2/pANWpMCtCs3lKWRg0M03m/aUUYHJ/cwzNEqJpGukepfRgmXn4GjdrgTSW06oTf4KYy1X3twrEt5GkFXqrpEeWoaeh83JJrwQmQuwu5pWm9v51H7koPWSaZZYu2tFvk7tpwsPjIXc6xVMf5qdZc92TjGOaVVu8rLcvIvTrff30IabBgy2osf4etDUPuQ1u2Y450lp27TlNzd4gKyVsZWSYBs5lbj+hopRfmJpvnEybrKDQ6cifZLdCIg/J8c6FI2LAqKXaDKNwIqTyztIt2Km8uffT5R5f0uO3wH95q63dQVkeRNvt7YIl8/8Ioi9xtSYfcFrmLDI3UIlLhktSAStwOwgjCEY0sIqJVqmeRIHZf/T+p5yH/jbfhqX/8z4v+nXZkjaM4qLBUTGuu+wN6YfoYJEIhZZvmsJ6a8Wccsme2LPq7RAkld2FfrSW6R+6pdA4eJaBdWu0xuXLx5K4X2QO9NNW6TpO3p1BLjLVsS+QZ2Rul/gvlRPHTShjSbRhyB9g0mrRFWg63/iSKCpeoKybLJKgJT2lepC4UkAEWVMtTzRur/dwAZormRZC7mmcX7FzAM0N0YdL41DbBbQqqS+xPrVI21trhJ5f0uO1w+JqKrLR+B0ZyDEWnv5tP4p2EEtwb35YSULzW71yYYS3GBz9BGSHPT0ZHvi4vkoqSIgiXz+p96LsVvi6gLAxe2TriTGIu/wYYVAUWui9Ml3zrgSYJemoG6QC5B1vnuRHyqKgG7iXLEElCHYmufVSlLjPaMKSGWB57fa4Z5Di2hTF3ClbmpJZ90wVG7lalf3JXLd6dKqQgcamxocjdJhqktuhWdGSRFA0uUSDT5Sd3x7ZYYU1AR3WIAkL719xrs82or10iAFjk7snh5C48M6ozzejf4dNCnZN7hleyGhHVeYNC45G7NtPdjvlEEWyEHISTHscQXegqibRDMWaxIBWbx5B0qF5rxCzMsAq03DVbwnUcJAn7DqrT0ZGvT+4R0ao0ALlXF5jOnzQGk9pqlQUUUYab34VpaRRqrfvahW89wL2KAAB6GhpxYJlGx7pQ1L0gUn31HpE7ANZHtQu5E8/pK3Iv8CpVa6FJ7q+/8gx0YkMeP7tl39wQk3Ccav8pxLrDPe7NOHLvC2Gyi4jsJFmDR1RIAy5q9oMGr4wMprexaKV/ScheYOQ+h1zo76tdIvfcCCN3Y675gBAt9pJZRmI5ri875aXV3HUeuY/UDizpcdvhBRohByHlt0MhHuamFp8xwzoJNXO1XUmH2n498chdJ3ZXb5NGvakHWxGeJUAwWk2Hvq9y+9xGdfHkXudyQd4a7G86dfhFAIA2sgclbQvSRndtWVgPiEABaFoE1CsLUNr86r2IyJ3ymoJesgwAGFISshO9FiHR/iL34ug2JvWUm0HOzKu/YO/tOb9l32xhBC4lA5mHJQW5x7JMf3CIBrntZvQ1d0WFK2lQ6PJr7iZfLCHtkfsADxZaOQaLKpiXh8PJHa2mWUEMjQvPjGbk5fHIU5g75YfG2IVaXVp/ah0WHCrhJPf1ZW0G4vgzs7ZORkPswTbPu+gsBmlnHg2tmc7nyglfXhIQZlgAUOrig29UmznYXqk3uWuJ8EVEJcn+TmZt8eRulBnpDHuzA+Vii6bcmbGT0UhuxZDTndzdCnu/sKVZoi8lOLlXS1Db1oVcKJDCZrF9RO5mjz6qkmfD6yNyV1QNcyQPqdY8V/voL+FSgh2nt5K7JMsokyykRv8ZL2mPO2WugNvohiJ3V9Igt2mkom+pJGtwJRXyANJIvzB51CZpzWgsKlrpBaU+hVlShEO0yMg9zFEQYBYEFZqEVG2SEOUt9tI5FrnLioIFkgNpLJ2/jOs40IiLQ8oeSITiyAuPL9mx2yE88uW2BdXMKPNjr04vvpAp7y3ATjTJ3ZN1aO3kHsjQqM5FyxVGIHJXatEPAd8xMREeueu8nF/0vV0MzAojnRQxUS71T0AGz3EfOel0uJltGKbz3Styq1NoUA1pPlYAUDi5m7UFti4UuEY9KYLcbQMWVTrsq8NgSd1b7bGm6YsndwAoyUPQjOZ9oM+9gNflbf4aTBBlKRfZgL4bspT77Vhx5N4XHEmD0kagnm/ar4FKK6O5izSnYAaES9TwC7oHksYUSsoIP7dOctcQTe4AMCcPQ200p+fELKNOdd/nAwDKUgHaEpK7wc9/tvhGAMDCwSeW7NjtcCOaMhTHWSGTNbc4cndsC0W0pvNRJQkdbaQW0HkbpWjZwwxUTya7yBrUb3AeHq3qbV2NFgOn1iT0uWOL84ZpwcJh1KmOodFtkAo7IBOKmWOHIneXjXmUSL6l1N/3f+GRe1A69IgMmXbWVRDXgBFhpdEOS0lD87qQu2fDlRYvywBATR1G2mreB6ONVzGTOiV037qcg271V8Rk1Kv+OgxdZkM6YIORuyvpHbKLJzR3RYUnaVB6EOwL++/Dq888ckLjsBq86jCgo7pEHmjWkLVnUddH+ayk9dx8R0Ql+oaoKsNImc0LVuKNOoKoqUUkl9CCwOTnT4dPRRlp4Pgvl+zY7QjrlQkAxZGtsKgCWl5cIZOwHpAyQXJPQG+7nkgg4urWas3iZFyhSb/COAzENuBRAj0it1usjbhdSu3b4dWb5F7pkqkTBb1yBFPyFhBJQmKEPSQXushbslv3TfIERKs9q15mAUigAYcXEegQx4CFxZG7q6SQ6Ebu1IbXh+YOAEZiFHmXfXf1agnbvOMwh84K31ctINmneVhlIXAdxLJMf6CS2knuPP1QVjRO7t0jd/2H/zcK//Q+zBzvz5ckCJHmpHBrUgADL+YWvVnYydHQB5flm2ZFR+6NxChyTnPhR7YqaEit5G5qQ8g4S0fulrBu1VI4op2CQmmwfqaLQVTkLskyZqQhqLXF5e+XeMcqNZDOR9UkEsRu0a0lu4Yy2PfndVmnsPns5Zh6EobdLgtvjgETaqTBVYqvjVCzj543RjOiNOb6d5TMmUdR0tniaH5sNwCgNh39kJBds8O8Tk83ZxxaWzMST1JCAx2pzYOmG9xAHn3omGiz9eJi4aa3+BlWEy89BYlQJLafHbqvrRWQ8frrQ1RdaF4vUpfF4KXChiJ3V9ahtpG3sP6UVR1UVqGgO8EWvVkMoYyJOz8ycO9KUXWoBnRUbwBJqFGrIIc6vOx46IPJNERbsugbwkmNYdib889FdWowpFYN0U4MI7+E/jIWzwSQ1CQqhTNxkn2wr5TEfkDt8HZqAFBSRhedDliaeB5A03qAHZRFm8GSdMWpYl4agklVoIsPvsO1+XJqJzKkgUqE9k2cBswuhCYKdhBSjfnwf/8IHv7mrR3bZbOEeWThUQK3y2JuFEbdSRhptiA9vJ0VMtld5C3ZM2G3Re4i1dYzROTemi0TRe5RDqftoGq6ax9Vhdp+0/TFQsqOQyEe5meOoXToKQDAyCl7Q/d1k0PI92ke1ig1rxdix+TeF6ik+ZWRAmJBVVZUQFJZv80IiA7ur5MxnN94GI9+t7fzXxhEDquWbF1Q7VeWEcVHSn4bPLnz3ITRUnuOdwuy49CJjfICix5FF6YgaHoEWdKA0ViaRR7RUUfWk5C2nocUMfH6q8/0fRzqeT1vHt+3O6TjTj2xBXl7cVlA+pNfxSSGccoFV/nbRLaTGfheFKcBU0phgeRC7ZQFRKqbXTwVADB37FDofsQ1u0oRkiyjhgRgdZL7zpl/R+bIv3VsV8wSylKBVWxX+/PXKc1NI4c6aIEtSGdyRZSRhtSl4bjqGnCk1mtQ+Lq7jQWoxG3pi0ojIndWydrlWg5AVO6KVOeOY8HtO3JXC80qVXfyOTSohm27w2UZkhyCTmzUa4uP3s1KYAbtLm+fAGCjkbusd5C3v6CqaKCSCrULwS7MsBth4qyP4Jf6BTj3mc/hyIFf9D2OJrlnm2OTVMg9Zg3tEKXQiaHt7NzaInffEbFL5xqFX7CiSjLh1WArmZZ95CyTIsT5nyhsnt4naSkMn3IhAGD6wP6+j/PwV34Xz332qq770MDft2McqfFFpQMeePIBnG09jYOn3thqEMXrFIyAD4jq1mBLSVTkAjQzmtxFyqQ2diYAoDwVHvkuRoqok1RowU7WqyAdYoOgOWXU5exAjcKnj7Acd310j79tVhrt6tOjUBOO3HoN+nJSjRFa0NiNEgUyOhdUZdds8aDpBr+PaiVc9x4kchezttrsUaQXXsSEshOyEp5xI2eYv0x5bvH+MjZf6C4jDdmNF1T7ApU1aO3Sh9DcVRVU0aF2IdgS736u5rdi7MY7YBMFje98JFRSeOQ7n8Xz/+Wy8HHwxRI9GLkPkIbZmGXRUmZkB6ikQUNbQY0p7G6jo50Uz/eu8HNjXZiyLfto3L+8skT+MkEzrJPO2AuLyrBef7rv4wxN78c261DXfajfKzPkAZfbhiSx/FlLFMo/+RtUaBJnv/tjLdtFRyArIMvobh2WkkZdLXRdhBapboWTWORnRMgasmv0jFYbUgqK3UruruMgSxrIhshpSacMU8mhqm9Brs9G4ZXjrwAAsuOn+tvK+hhyZjS5tzugAoCmJ2BRBXKDf/eBACTqXlACPRB6QfL7qIbLiQocUKm/VMjsKKsLMRaOYqt5EAvZ0yL3VTIsZbY6v/hCMY+T+6w0AiUm9/5AlQR0hC+oqmoCkDWoxI20t63zvOVUYQxbtu/Bi+f+AU53XsLLTz3QsW/+5btxivVi+Dg4uSdSzQiZLfb2R+42L4UeGtsJqiQ6Zh0Or+iTQvRmgeyoqFJlD4oUrcPTWiN3PccuVKO8NOmQTXe/FDQ9gSPKTqTmnuvrGNTzsNU5giytdo+8/S73nRGfWmQ369yxaI+VowdfwPnl+/Hs1huQzQ+1vCfI3Q6SO23AVVKwtCIybpc2b5zct+5h5O4shMsasmvClroTmimloTqt5C4yL8LsmlNuBbaWg5UaR7HPRuHmNEudHD3pdH+bkdqKITf6IaFRE67c+XCtkSRUPrshbbJM2NpXNxO8dsh8VmxEtNpTuhT3RWGYF/15x5/FCBbgjoZLMgCQ5J7/jYXFkzttzMOhEmpqEWosy/QJRYdMaKsO5waKXLgtrB3SixQAzBKbYoky6lOv+A0AwPwz97bsV6+WcIr1IjTihEb1gtyTqaAsE35Bd0XlOEyqIlccBZW1jgeXw2WZ9urMIIbGeJVq+Tg810UaBihv1CGQyLAptNWlJ2U/aJphsZnLXOYMbDNe7usYs1OvIwfWWKRbmX+3yD3N7RcqEZIIABz+4efhQcKed3U2ghYe60EHvyRtwFXTcBLDyHdptUasmt9TtIQ0pAhvednr1KvbwRpftK6HVHjmhUK81hQ7sEIZVy/4jcL7sf4lC4dRRgr5oUBKaHY7iqhEHkeD1ZLqKNAgSSS5bNTS9DriXlA9E64ULTEGIfLoo8hdpQ7QpyyTSGVQRgpj0z8HAKR3nBu5b6rIyN2qLP7hKRkLKJMMbDnV4Vm0HNhQ5C7kiWB2QzNbRvN1v6hqu/Yy6qEt2/GqtBuZY60NQF55/D62SIRWPdYfh12HQdWWSjsq9c7UaYdSn8SsNMTS5EIeXILc5S6aezpbQJUmQSrHUKuWIBHq+34IJHnk7jaWJmOmvaTe3XI2RjHfV3rp5KvN3PjqQpc8cf7wDmuELFqjRUkipdlJnDf1fTxVeBvGdnQWqyj84eSYzSl0ijZA1QxoaghpYkQuQhOnjgbvoTsnjUJrhEd4ime1OCaGwVYy0NtyuhvlptQUXCtxbAsZ0gBNFPxG4d0KkNqRqE1gWm61uBXNoadffyX0d3RqtdhbC5gkhbTDyT3w8KWyBiWkiKmbCV47VB65R7Xa62bL0Q3z0hD2eGx9autpF0bu55uHVRYfuSvmAqpSFq6chEZjcu8PPHqwA97XlHdZV1XNJ387yhu7OgWDqi1l1FMjF+NU49mWm7j64v3+z2bIzU2cBow2HZXJMv11O0oa0ygpjHjDHlwuf0hJWvfIb04egtaYQl10YUrmW95P55gc4TWWJnL3zbB4Kqg+ytLp5vuolqy+3pRxaqVozZy6dmQj5OHxnTwdMHwt4fkf/DekiImRX+mM2oFm0wiHL5A7tsXy3rUMpDSLbEuz4Vq0bNdgcHKvaKPIRHjLs2i1+9/PUTNItpG7ESD32nxzDBW+vkCSRd8VtDy5+IYpefMoyvq2lm1JXshUCmk4Tj0PKWK2ZMMImHIKecquqWDTazaL7bwXNGp1aPdREJW7wqUzCNdxWCvJAci9yu+3eWR9mSYM+aEtqFMdWFj8d6vZJTSkLDwl6RvrLSc2FLkLArQCkRb8abvu/7GdCFlGNmYxTwotRJE44xokiI2Xn2g23y5ONRtQmCGRu+Q0YKD1IqWy2nUxNwxZZwYNnbcu4zePZTTPzeUkqnSJ3AGgogwjaU6jwclddGESSGfyPJe6v6KMKIimCzond+EzYpuLz+2l0y/5Pze6VIISz2rpzxmEquksHbASTu6p4w/jFflk7Dn74vDf5+MXMlONm4ERPQ2VNzmpRJG704BFeLZNcguKbvjsQ10EoXlaBqm2bkxWwG5WyIkAUOUasJIuIu83Cl8cAVHPwxZ3Cma2ldSKW9nD2Zg51PE7Jr/XaMg1aMkp5CB6xAZlmfBZrAarq5VGEAkegDkhtgy+7Cr3J8sA8O+3o9ruyMIygHnKH5e3IlFZPLknnTIMNQdPSfpe/8uJDUXuQtdricx5VagsK34T5ShZRjdnUVGKLdtO2fcrcKiEyvOM3GuVBZxiv4SjhGtuRueqt+Q0YLVHYyEXNPW8roZMQ+4crCSbIvuzDqt5bi5fUI1q0SbQSGxBzpmFwTML1FSh5X1JllElSaCfKsguENatwi9FeJU7fdicpsqvskIhAHY1OuWQuN0bIc/LI9Ab4elqulNFXSmEvgc0xy1mIiIzQ9KzSBbEglr4sRW3DlPislRmK4ZoKfRvHbUY2bpTFmkYLQunbq2ZqWMFPG7qfJajZoYxzJs624tsFD43fZRF4TzHXWBk2254lIQuCpsN3gRb7fTGcQLNalo0d1mFTGjHQjCTdxYXuSfSjNy9kOIuIV2SLsV9UXBS7O9azZ3eY0+glNiOgrn4IrGUV4Gt5kHVFBIIz89fSmwscuck5wQjRNeCRWUQSYLE/9iCFNuRtudQV1szJrL5IbyinobicbbIIvT2I8OXAwhvlyW7BizSdpHKGmRCWxZgH7/nK6h+5lQY9c7ov1ZZYNppluWpNx9czXMTjUjUHj0nneQohr05WH4XpnzHPnWkIYcUygwEHrknkiwrR+EGak4fkfuI+RoOaiwVza52sUbwuvfK7JYOmPBqsNVM6HtA01dckLvJC1akZBbpInvomhHmYaprwJbZ30XOb4dEKGZD+slGLUa2DjQLidCWghmv0fxOvEClrMELZfTsEFKZPCtAWmSjcJHjnuAymj9GPcFnQJ1E5ttbq53XoBOop1ACAQiROhMbqOdBhx0q74RBWFZ7Zgi5+32T+yd38JoPjIXbDgRhZndi3D2+6ObyGVqFoxcANQmVuN2dNpcAG4vc/ei2GU0HG+UKcnescHLPuQuwApavAnNjl+JU+0VUy/OovXQ/bCpDPe0adqwQclfdRkc5NmQ2huAFbU+/jCLKOHbo+c7PnGSLgEpekDs7NycwKxGNKnrJMsiOI0FsNGaYZprMFDt2aUhpKPbSRO5wGi3WraJSd7Ee1ka9inFvGgtDzFUySGTtkDwbTpcu993SAZNevYWA2iEeTkJmEk6PSiKLvGhyEuEvo3sNOJzchbf8QoiJl057SxFE7+zGRBoLqFOdkXetOQYxy0nmmLwwKy2uUfjc1OtQf/QJWFTB+Blv6nxf2YJkvfMhIUzyRNpoEJ7arPNQgq3z+L0QTA6wLAMSoaHyThj0RAoOlYAQ61xB7oPIMkqR/a3ybQ06wkCG9iBBbMxO9k4UcGyLVf4miyDcCrx+Ag3MF4MNRe4yv8BayDvQbktEv2Ely57rokhLcAOWrwLZM6+BQjy8sv9fMTT1KF7RzvCn5bbZKcsongG7bapNfL2/+dnCYXBhojNfXlQ0JorbW8YefHAJR0RF735DKAW2QEZnmI6dyHZKEYachuYsTV9HyWm1btUESYaQ+5P/3zfx8qf3tiwUH331WUiEQt25Dw6VQLtk8RDP7tpOzUsOIUdrodFVhtbgtaWFBiGK0ERqq0gVVZM5IHi62wAAIABJREFUZAsjbGwR/jIaz4cHmt7y9ZlWEmDRau/IXeR0izUTAJDMEqokjRLJQwlUyrq8UCZTYORe0UaR7lHINHP0NZRvuxbbnSN44S1fxvhJp3bsU9XHkbM7Zym2KRxQO2UZGqinUPVWWQZo9jcGmj5JZJGRO5GkyFZ7ti2K+/qP3M+55jexf99f4Yy9b+m5b3KMfU/Th3sb4wUXuoWthRWyXreU2FjkLsg7GLl7NhywCLIpy3ROh0pzU1CIB5LuJPdTL3wrTKrCfOZfcIr9Eua3XORHIm4IYWlh+brigg5MxYjNbgxzqjMHvMGLjnK8CCnswSXIPbQ6M4Akf0AkSyyVLZXtjNwtJQPdXRpvmXbr1kQXcjcOP45T3Vdw4LEf+9vmDzMfmuKuc1EhaUhGNLn36nJPEnlIhKLa1oPUdRykiAmqZSN+M9ARiDfUEJ7qejoHSZZRItlmBWYbEtSAy3XoIeEt36Z927YFmdCW6s0wiFZ7RqAaU7UWUJNyqCoF6FZAouEPwlyRXce9GoUfP3wAxleuxag7jVeu/TrOu/o/hO5nZbZh1J3uKCjz7a21ED/6QMptUDokPrk37wVhNhcm70ShjiQkOyRyD7TW7BeJZBr73nVz18VUgaEdZwAAqsc6W0m21wQ0F7qHfCvwYEOX5cDGInceHXhBAg1ospIqyL0zci/z0nslP9bxXiKVwcv6G3D+7A+hEA+ZM66BJsg9pNGtSg24bXm/fuTuND9b2H6S+c4UQdEar8CJIezBRRepuee2sAfEqHkYHiUtqZ4CtppF0luiyN01YQVSQUWlLg0hd8Ilj+ozP/K3WcdfhEcJtp18NmokA8WKlouI173jjszTPmul1gi7WmaESBLRkTuRJBhU9cfo8sU7nRenVaQ81AjzsCQ1QHnkXhgeY4vDbd7yIr22F6GJBXArQAa6U0FDycJQi0gHbBBIYx41mvA9ctzMVgzThUh999i3fw95bwFH3v0tnH3Zr0YPIjOGFDE7CspEDYAccg1KejByD5A/19xdpxm5i8SEbj5J7TCkJOQQco9qmr7U2HLSqXApgTfbev8efO4xKJ/bhQNPPehvE9efmhnyZznWEhn1RWFDkbvQnoMLpsRz4PLIXeF/bC9kQbUyx8g9URgPPXZ566XQiAuLyjhl79VQeTTqWp2yjE47vTZISOSucHJPVUPSqcrH0KAacrwkPuzBJchd6yHLFMeYLDDuTaGGRGgbM1ftTLcbFO1mWCICJiHdZwj/DrZON28Edf5lHJdGkUhlUJezULusBche90bICreebbRF7nXeik5Odj7ogjCJBsIjd0HuSX7MmlJAIsS4y3NdPitgERqRJMxIQx3t9hYbrQr7XCcgTyWdCkwlBysxjGygUlY2S6iQJqn6i7kRunDROIyXMxfizH1v7ToGYdTVHm06bdXIQYg+quz9QOSuiMi9GeiIxAQ5RLuPgimloITMNsU9JoUUti0lND2BSWkUSrl1LWXq6XuhEhdzL/6sOVZel6DnhiHz77Kf7lqDoCe5E0K+SgiZIoQ8E9g2RAj5MSHkAP+/yLcTQsjfEUJeJoQ8TQgJN0NeJogLyLWDsowDh9/8ImXQdTojd0N0cB/aGnrs4jlvBwC8op2BVCbvZ1KEtcvSYcJrj9yFJBT4bOEMN2R1ZiHo1SOYkUb86WHYg0v4qmg9ZJlMrogaTUAiFDUS3qvT03PI0PrAHvZByJ7R4u5HJAkNqgEhHtaSw76DXd4EXn+VLSwX6ocwo7MZi6FkkXCiyZ11uY+O3EXUa1RaI2xB9u05/+0woYPwMVLu9JjMsgeCqRWRdjvJvcEJkAR66JaUUaTaCpkWG60muT1EsBoz7ZVha3l4yeEWfxnFLqMmN0lVH2Y561GdlIa8WT/dthtEP2CzjdzFzFUN6QGrBL5bPdAAXOKBTvBaFmtXUh+RuyWnoIU0vRCRezfPpaXCnLYN2Xqr3EaOM5M8OtuUW21el5DOj0Dh31XQs2g5sJjI/WsA3tG27Y8B3EcpPQ3Affw1ALwTwGn8380A/sfSDHNxEFM/GtDyJM+GS1ikKrr1iIg3CKfMbrz8yPaO9wDglDdegUkMo7TrVwB0LrYFkaAmaFverx+tBCJvjZP7mDfdMW0erb+C6VRzYUs8uFpmHY4Ji8qLaig8J7EZgCGFaKMAoOegEndJPN2VEDMsg+ggbuf3LjsNVCk7t4nH7obnutjmTKCe400i1DySbrRcJHvd26npWXbeVq2VhE3+Wk1H57kDgEV0SGLcgty5LGMnhpEL8ZcRemuQ3BuJLci1ecuLaDUs0yQIYZ/rBYrM2GJwHiQzCoV4KM+zYyfsEowAuWf5Ym4tpFF4vVrizWDCA5ogFD5TNdq05GY1cud1pQYsr/UQzT0oy4g0WSVkYTYKjpLusGVgx422gV5q1NMnYdRpLZIbKbPq6lS5Kdc4vC4hU9jiJxg4ITn6S4me5E4pfQBAu7B4PYA7+c93AnhPYPvXKcPDAAqEkN5XzhJBrMgHCZAEuqALcg+L3Gl1Cg6VkB/aEn5sTcfQnz6Piz5wCwD4HdHbI3fbMqERF2ibast+5N68oEX3doV4mDzcXJSpVRZY/8bhpiudonWSe69GD0GUVe78KIen/km+Nh1dMLRYKJ7ZYYZlQvej9JZ9XQNH1ZMwQbYicegnmHr9VaSICTLKikgcLYcM7ULutHsjZJH2adda0ykt/lpLdZdlbKI3GytYVTYD4g9TLzmMAqod2VciZTKoOdupMYy2ecuLmgW5hyzje6NzcjeNOpN9kgUoWW6DwNeMkm4FltqMmP1CppACpNljhwAASiE8oAkiSkoQ5K4nO68rUU9h0tY2gkILd1t8krh234cs4yjp0D6qoofDSkTubn4XhlD213CMehU7XSazDptNuZXydN5sYRhqQki6qx+5h2GMUnoMAPj/ghG3AwiGCBN8WwcIITcTQvYTQvZPT/fnOR0FjUcHwchc8mx4nNxFKzYaki0j16exQHJdo2BV0/33VU2HTWU/k0KgwQuSSFv2gFhQDWbqaNTAcbCbcy6QDjnx4hOsf+OO85r7JgS5BxaLXRP2IpsAGzr7HEsOl2VkLl/UKl0KhhYJJaTq0pKiyJ3VBEyMXI7T60/i+IuPAQAy298AAPASha62v716Zabz7KHW7ptj87TGRHao43da9pM0yB6f5ts11ElAXuANGxZmW6tUTX4NKEHCy2+HTmyU5prSjGMsLlrV9ARb2OUFO8IFUkoWkeAJALV5Noa0V4GtNR9YueIok8RC2u2Vphj5CA+abhBrTKI/sIDIgNJDInfh/2K2XaNCCw8GOoLo+oncPTWNJDqvKU9kyyyz5g4A2iibXU++xu7fwy/sh0I8HJR2Ydyb8lN8SWMeZaSgqBp0nmDghSRjLCWWekGVhGyjYTtSSr9MKd1HKd03OtqZfjgI/FzaQHQrUcdfcBPv05DIXTNmUZI7UwS7wYTWsUhoCXJvk2WkEM09QQ0c59JLY7IZuYv+jVtObbrSiXRH6gQj92hflXbYKUYCURWZUdr0INBCzLAskghtLaZ6Bhw5idTZ70SSWCBP3AEAGDuZ2a2SZAEK8TpSGQV6dbnP5IUpWlsqJDecSoXk/AdhSwkonNxlpwYjQO4KJ/fKXNtCKY/c5WC2CC9Gmw/YD9t+pklvQquTJAhv2FHj5C6ni0gVWQKAwf1lsrQKT2+eE5EkzErDUEMKmQzeDCa3ZWfHe+0QXcXsttxsMXMNNqYREP4v7bNLobl7gXvB5Sm+ao/kgCCY504IuTvRfXWXGrlt7P4tHWX37/zLzHdqcue7IBOK4wfZOpJiLqBK2HfYLTV4KTEouU8KuYX/L8KRCQBB16EdAJamvc8i4EfubmDRkjq+5q7wVMjg+wIpew41tXsU1w6mI7cSlskjG0lrJ3exiNT87BRtwMjuQoNqoHNNfY5OPosaTWDrrqa/hYjc0TIrsRYduYuyajeC3EVGRrs2PQjCzLAcSYcS4mGtUQOunMDpF78DDarhjY1HUUYKw9x2WUqyB26wc3wQSo/IXdV01KnuR70CQr9O57o/0B1J9723Fafm+8UAgM4bNgRdGYFmdBtss6hx+STYJFks/CuLkCLqJAWZF+wIu18tM+xbz9rlKRj1KnOtTLY+sErqKFIhjcJFMxgh3XSDxtcZRPtAAeKbxHU+oPyFYPSO3H3tPiTrJgpEy0IjbksBHNC05ZBXgNy37GLSqTXNFk/JsV9gARkMnXctAGD2MNPfVbuEmsTJPc3+pyHVtUuJQcn9+wBu4j/fBODuwPYbedbMJQBKQr5ZCSiq1iGVSJ7TlGW06Mg968zD1DutB7rBIlqH1CCqztqjMXGhiYbdnusiAQtUy+C4vBV6wF0uU3oRR9Q9LRJRuORkLbrnpJJnVaqeFp4dovPCpqVo2KHDgtdWaWhLemj3Gd0z4SopJJJpvJS6AABwTDnJ12j///a+NViW66xuff3ueZ5zz31IuvdK15KF/JCQZcvyA2yDbUgwBhslFHGFxMXDroALbANJAUURSEhVCFRi/0glRaxQJJWIJDZUIJVyykUoSCjbYOG4kJFtGSHreXVf5zUz/e6dH3vv7p6e7pnueZ1z5vb6I525c2Z6+vSs/va317eWLnrmoxLbX5WFM7Myh9SC4uU+l3eAkCljgSpFiFQLuqjc9ciBp6Z/1zJ/GVnd6pm2jC3aQ9mQZJlYVbQZmYertKGFnAykf4zV20H/NCf3eHBtrF2ThWOdRb9gkEk5fAGHzE58WqbBFi2WKNeWQejCYUbh0I+cpwgn2jL8mo2z5C5W27pVvecOsTIa5XJU08p99Ruq/e3T2EMHtPs0AODUwRN41vwm3HoXX3l6L4mp8OAArsavNdO0uQtrgdJumagihXwUwGcB3ENEzxHRjwD45wC+g4ieBPAd4mcA+J8AngLwdQD/DsCPr+SopyCABsoQoIqU3A2jWC3D4hjbbA9Rga/M1PfKbrYJJBN7uQokXYry93adAQ/O0FvYs85j2302OZYL/lPY743nN2q6wb00xm5cwcQXpwzWKWFBYBaTmS3IfRmBHSbzJkbqQ9WGVuBhbcJNZKPuJa61Pmin4cx6h6+mnMNicudxatPPwUjpQAvGK3fFO8CQ7JmTiLFqQhfHbUQjhBly70p/mVwaTzrslN5IW31euYcZq165LDcqkLuXSWNK/WN2oBsmT3oaXU1WN1p7nNyD7gWcia9PbPzqo5dwQz09870BwCypNouyCyRUTcOImQhyBYis3OPMCjrZmC2QVJZB6uidQTG5TwuxWSauarfCHj4Lzx3h9vBpDE7di27/FK5hC+oNXtG3ogP4Or/ZkaLAgQkqkAYvE1XUMu9jjN3KGNMZYxcYY48wxq4zxt7BGLtb/PeGeC5jjH2IMXYXY+w+xlj9yPsF4ZExJrlTMsv2ZEw/Gg/RHg72YVEAdIqVMmXwyYSak/dJrw3NGm9/pJU7v/ASuZzZgde9I3GXu/LCX6OPYaErnQ997MbFK/dq5N4T4b/5FCaJZQV2lPmlxKoFI54kd4t5SYrPxTe8l4drnHlF8u92l99wy2x/eRDy9HPgKm3oeXIPBqWa/4njZvxvZsUjhFr6O/1TvHKPc/4ycqPMyqwKekKFFY3SzyENyYwKhBZk7CGikVReCKWMsgXNvZG2a7rjRYp6+i7oFOGlZ8fH5NveFRzo1ci91eY3qrz0N281kceI7ImkKakcY5nKXRYtRo3KXSvJUWVJru7q2zIAcGBfwCnveTzzlcdgUATjIh/vuWJcRHf4NICMI6SAS+n8xKqwUROqAO/vZcldY2kKuqppvPrN9dz3rnAlgdqdPcyRRaiY0HKVe9lQh6qPL0WlXlgxO6CdO2FRgKsvPo3LX3sMANC9Y9KVzqfxz6bG1QOFb3vZq/D5nffi/Ou/p/DfZWAHcxcj98QvJUfukWrBzAUUxFEEm/xkJuC2S/fga9/zKXzze38qeU6rL8m9WMWjs9lxap7WhZnTymvBAC7NrphjzU6yay2Rn5q8d1I1j5M7E71xq5NW7u1OHwFTwUbp52A1yJ3L/vi1xRJy58Q8VLdg+bvwxWa4lSP37m3cA+X6N8bdR7fCa3Ctate8qmlcsZMz6uL21uUk6pI9IYuV5J6t3JMMgBqVuy6GpCZaidH6NlQBwO/ejnPxVdz4GrcFv+UVDwEABp1LuCV4DiyO+Ua3lZK7RxbUo67cTxoC0qHkNlSzaooAGihH7oPrfGPJLPCVmfpeaqqkkJAWwEZOPZDfzJVaaNVqo3ULb8Fce+arGD3Hs0PP3/PgxPv5MMaOXYv9qaP3+fd/w0/8Fi7efX/hv8vADmXBwI4yvxSm2TDh5Z47KRt9xYPvQCvjfdMR1WmZ7a+O9OZdhkDvTAxCGeGgVPOfP25LtGVazBmzsQWAA+pDy/nLFAWkk6LggDpQvLTtlShNKlSr3B5CTLS6ezhAC6rGP7drbKMd7ibpTLIFJHFGbPqNLqfpVlEYYoftIuwU220UwSFrotpUIncymCb7O0q7gNxlWyZbuTvwmZp8piqQhmp+LkeVyVzdNVXu6s6d0CmC/dSncYA2brvEz3d86i5u6f3Mk9yUMLMXwofjVpvGtIHkbkDJEK7Kxr/8AWkTlftIpOm0SqwHyhAp5kQfOfJkHzXXltHG2zK+GAbRrC5OXeBtiNHlJ6Ff+0tcxhn0tyeXyyHp6bQkAI0FiCrGklXBCG0oCwZ2+FLXO0HuFiw2ft7TSc7yCrrT3Sq1/WVxzKMLZ1TuodGDnfPNMaMhAq1ClahbMChEGPjCL2b87zrUeNWcBflDOMyYIKqB0oWeIXepfCpSmuQRGx20xWdQ/X0MMv4x0l8mHskpyPFrZ+fsBQyZBdx4Knls98rz0CiG0hvPS50GDxaUXLWpRS7CKZW7//Z/AuOdPz/2WFFbRvEHGFZYSWVhiiGp/KSnJHd9DRuqANC6hYerv8r5Ip4x7072caxb+Pf6hS//MQBAaadqPF+xoEVNW6YWQjLGK3dEYz3ZADooHu+5B/tcytY/M3tSL4uiPrKs2vKVu6qLYxAXnpz0M+wuzl28CwFTEV77K+wMnsRl+67C9+M3rkzlzoKpMsC64IEdSyL3nLyP6S2YFIwlUclw8eyYfh6kKDikTqHtbxSFUIjNJPfY6KLLxjcC7XiAQJ+ulAFSf/E9kZVK5ji5O/oWWuH4sVEwhJNP4gLgqD0YwX7meQ5vdVSwl4XZhUEhPHcEw9/HSEmPXfrLsNF1xIzQ7Y9LeklR8KJ2Hvbh08ljuyI4xNiufs27igU15+VSNI2cxau/5bsnTMny3wWA74E4dcldhmTnx/iT3OT1bKievshJXKMYg+10r+zU7byCD7/Bte96htwDxZpo6S4bG0nuaoYA88v2sKAtEw+4lG3rdM3KXbVg5Cp3JiobaXMrkUzHivfOyuU03cBLyllYe0/iQvQcnO17Sj6bniN3H3HFnnsVLCOwI/FLySkVZCXvZZKr5Opl1hDPoMT2N/HjmeXbbfVhUjDmm9NiTqnmfwziuA+vc0Uv5Sp37i8zTu5KOIJbQO6u1oMVpkREoQuvopRVpjEND3ZhhoeJrA4AqH0GKjEYB9/AIbUKp6wP7AvY8VILgsFVLr2VQSJV4Cv2RLWpxR7CWRmwOWg5cQHA90CcMt+jEsj23USOauQjYlSrxbMIztz2MvhMzNJcfCB5/NZLr0TIFJy6wYcSzcxeSKjaMOKmcq+FSNHHyF3NqSlC0qDkKndldA176NTeXWeaBSMXdMt8mR+a77lLchc6dzEMIquPG+YF3DN8DDpF0M/fV/h+Ya5y11mwVHJfRmBH4peSt18QP2fzYqVsVJuxieaoHejB5Eavn2RlTl+9KGKoZyB8c1gco82GpZr/sd8Vxz0QlbtqjVf7cessttnBmMxQDR14NNlHD4w+2lF6k6LIhYdq15x0r3QGexP+MVqP99i3Rt8Ya9dk4fVfhnPxleSG6IsBpu1zd1R6fwAIFBt6NF6584Dvet8b2XNnmcrdCAfwKuyBZJF47uRzVGtMbi8DqqbhJYXv1537poeSx3XDxIvKLbgU8JAcu5+2yyLVSiS2q8IGkrsJjWWr2wjIVu656hcAdOca9pV61gPA+GZbgoDnh+YHKHRD/CyqFTkMIuVyTuciT54HcObOYqfkUNGh5Vcl84QAl2AZgR3SLyVvACVJ0suMrwfJwNd0cs9XvMl7+dXi1KRn+0hIBT3P4eZu1uy2jHRs9ETrTstZBFPvVijEcONK6t2iRSP4+SQuAJHJfXKS167hDSQ/gzvYRzs+RJjxj5H+MreGz2OkFt+wEjmkMKiL919AyBRsn63elglUO5nWldALfIRmIQnLzhRZZjQs9T0qg2Fa8JkG5DxaKArWSu4AcMM8jwGzcf7Oe8cev27dzq81pOIAAIi0FsyCie1lYgPJfZwAtRwBhjTZc7f96xhos6f08mC6zaV8GVMrJRzBKdhgSip38d55uRw7xS1ufabh/MuLK/dIMcdbTiyYGa5cB5HRWziwQ/ql5A2gqCB9JvSksmg6yQZ6D62ogNxl4s6MG5wuhnpkTJ2s4JUpKUwS8qYUHooBoZz7obHFW3n7Gc8YI3IQqJOVO7O30SEnqZ45uVf7+xmZqL0eGyAy02JETsq2yBuz+80ikUM+K7xOhpdxnbZrtS4izYaZayUYzJ/ILpgFPVGOpfsvVjxEWKVNlsOQbChBzhKhxnDfsqB+y0/gift/bqIl5vbSgbxuZqM7LlCPLRsbR+58opATIItjftfMLNsj0ifaMp1wF65RbzoVQKLl9jIh2RSMCpfayc59JMl9XC5nneUGRM9od5SOTUeKMbYqMbBcco+N7sKBHWXuftLW1s/03KVstCjoIYvQ6KFdYPsb+vxczKrcpW+OJ3TgzkAGdUy3+wVS3xc25OSetwhun+bDYcNraT9bjx0E6mT/WGlxQpbe62rkTvjel8EQn8HdfQEGhUDGP0ZOygKAbxR/pjN3cJdN5zKv3C3nJexr9a75SGtNzCpYzAOr3XOX34Wsz9Ko2h5IDk4Rua+5LQMA977lPXj9wx+eeJxOc5mzw4yxfTim2bBZU7nXQqyY0Bgn0FBKrTJtmYg0qGyc3PtsD6FdbVIvi2STMNNHViMXXsFmGikK970R5J6Xy22LsN3dzmTyvESsGMln4zeuEFhmIIHVXziwQ5J73i8lTZ9JXzsWo+zmjMqd2/4OJ246SeU+4xxYPRnYwfv2rrA11iqQu9zsVcWgkpTfSfRFPq23l/rjmbGDSJskd1WoJQa7Iiw5rl65S4fF4DpXuSgZct/aSbXqYQm575w9jyGzQDd4/7cbXMXQrDeRHWstWBgnpKJp5FnQpBVvnFbuHTaqtAeSh0d2ElcpwSv39ZJ7GTrnuWLmMLcXwvQWLAqSBK1VYPPIXTWgQ5C73OTKLNtj0qFmKnfXGfI0mlZ9ck/6yBlXumlDHdkBqrxc7pZLr8B19MEuvaX0/WLVSFYlyWphiSHAsk2xSGCH9AjJ+6VItz85BwCkY/p52WgeZba/0qdHmUHuiW+O0IF7Ytp1VgoTkK4qdE9Mf7bHb0Snzl5AzAhxJvzaYm5hq8Lo8EpZOkNypUm1v590WKQDvkKQnjsAr4T3IGxkreLPlMoh+c2harxeFsxoo8Xc5CYb+B70gmCaWcgXOp474oVKhT2QPHzFSuIqk9ePQ0RrrtzLcO4Sl0YOldxejeAOZ7SY9HgaNo7cmWrCEOQeCHLPqikixRir3Peu8oqrrvUAkG62ZfvIWuQgKKjcASAkNalWuFwuYx9rtbD1C0/h9e/5UOn7MdVMfE58T24mLo/cVdFyWCSwIyX3nFpI/BxmyF3KRu329C91me1vmIQyTD8HHRnYIawV5ERjvgovglyBtHxh1tUZJ0/dMLFLPajDNLDDZu7EJCsAWD1eQEhXR73A974MUhliDTm5G51xLfu+IsjfLr9h7dsXccp7rla8Xhakt6FRDF9sZJdNI1dBCBUkvgtDkWJUZQ8kj0C1oefInUdrHg9y37nlIgbMhqONX+NF6rFlY+PIHaqREGCiphgjdx0qS5eDUr+s9+otUYEMuWdaDfqUaiyElmzmauFoon2jatrUgRammsmqRG5cLpPclxHYUeaXIqvzKKNskPsOVkFE29hxldj+JkHIMyr3Vrsnplw5uYcjvgKwZ6QwAekKpBNxAmp3Jm8Ie+oOTIe3Wlgcw4YHFJB7e4tfYzIsmfveVyT3dg8xI/Q9rtqRNwqJocr/dnm73yz8/iXcEr+Eq89yp8Iq8XpjkIQkJou9BcldqmVGC5A714uPt4oUtv4N1TKQouCvWvfhsDs+mEhJ4PjqyP143N6WCc2CgRAsjtMwgAy5M2W85z4SQQv2dnWPDQkp4QvGyN2FqxdXhFlyVyMHvlLvS8Erd0Hu/vIr92TjscSkqxKkAZQ93pYxitJnghFcpsOaodgwROJR3vZXBp8oM8bMSVEwoFbim1M1qANIb1L9+AAODNgFxzrQd9D2eavFdYawiYEVTN12trkULhrym2dRqMm0z3BINs5EVwACWv1xcneNU0AAaJ3yTVL19MuhPR/jpS//Ee5AtXi9LGQmrDM8QH/nXGYaud7wEcDnTWTl7sqw8lZ9xVpURO7HqHIHgPt+5tMgGg+pk3s5ft4ff4nYvMpds6AQQxD4yYabkiF3vimZVu7+Aa+4OnOQuyYu6iBTjRqxW6r7zV7QXC5XbyOKabzlxOIY4QraMjKwIxgt4OkeuogZjaXdA6nbX5bclWBU6gWehdUrtv1NEncqbCqPqA1VTLmyOci9Q85YfmoWnn0WWxG/8YyEt7hSoN3v9rYRMUrCkk1Ur9wBYIQW2sT/7nn/mMDiqxCzU74a6Qk5pPLMn/CfK8TrZaFYstrklXvUxE9nAAAgAElEQVQyp1Aj1FoigpoUOp44Z/qMsPLC1ylQ8KhxUNlQbx1QVHViRS7blL7TkHt1iC+6546SnmxWTZFVnABANOAVV6+m9QAA6EmrIe35mcxFVKBxBoAI6XSsEY0K5XJToRpQiSEMA4SiQl5mwnu68biA7W/owsOkX4qUgWX9wCl04WL2Da5dYvtbJ05tpHSgCWsF8g7hMKPSRLLVSknaKSH3qH0O22wfYeAny+wivxxFVbkzpPDJMTNe9lXgivH8kCno5m5MzObnyO6XCwNOC3fI2w/+HEC1eL0sNLHhKcndL5lGrgK+iuWFjj8UN7uCltcsxPqkgkdhAeIZTqFHjWTVv4AybRY2jtxJeJoEnpOkoGd77kzVoSGt3NnwOnymTnxZqkAX1WmUISwT5V/YKFu5M7dQLjcN8rP5npPsJ8zaTKyDJLBjAU93Cp1Cv5TE+TCTJKWGo6l2sRKySs3b/kaBaHFVqNw9tQ1DmKIp/kFlB0LDsHgkGjCWn5qF0rsVKjHsXn0Bnrgx5sNaJAbUhebtZUJNqv/9XIUTwiG1J26e1OPFicxULcLOWT5FeRY3KsfrZZHIWUW1KTfHZ00YFyGitHIPRVi5LC7qgOkt2Mwbk8ny3OTjU7kXQQ7uhXnrhCVi88hdfFl8z0l07jLWi/+gJ5uSAKA617BH/WrOfDkUyfss5iMu2WCKSIMiVg3WHOQOsYT33ZTclxkllgZ2zO/pXpbMo6gqz9rM5EbyoIcKlXunzzdER+PkLuMSq4Qy+FoXlvB0V2s4EJKiwBWfxy8xtjK2uG3u3pVnE3sFtYTcR2oXerCPMAwKQ02mfwb+/sMC/5j73vVBfOltn8Dp28q9YkhRcFnjx1o1Xi+LPCElQ2jmHG2ZjMeTTP/KK5GqgPQ2dIoSBQ8AqEt2S10FpMQ2dFdnHrZx5C7dCEPPTVznsuPpTNGhZ3ruhr+LgVJ/lx4AzJbcJOR/oCgMYVIA6MUkwC9o/t4t5oAVKCqmQX62wHcRivecp99Z+vo1Azs+959/BV/8te8ef43Ig1/idJiPFtMjB0GBB0seie1vLuQ6zcqcTe6h3kVLJBnpwQBuDR8TuRLxS9po7dN8Y3J4/XkEI+n2WSzvdLUe7PBgLhmhjPgbFVgMtDp93P/t3z/zNfZtPlFbNV4vCzlsFuYqd62CH30eUaYtw4SrY5U9kAnkFDzAZIbDcYQ8l5HX9NwrQ/pvB75TKJVjmskDHgRsfxcjvX7FAKSbbVL+lyQLzajc4yiCBb9QUTENclUSeCPEwp9EXXLaTNXAjue+/jge+OrH8OrBZ8eXxJFbOnXpwYSSIXctdgs9WIrAbX+LszKrJO5EZg8tiKGpcACvDrkLO4mylVbvjJhSvfF84i1ulMg7A6OPVnQwl4ww1Phrutp8xQgA+H3udVI1Xi8LQxYzQkCQTiPXtw3g3wVB7t4hPKZXCi3JQ25cZ4eBNBYu1S11FZDS4Hwm7TKxceSuGrJydxIp5FhbRjWgU5SM/bajfXjGbL1zEaTcTw7juMlmWvFFGpMOJQ7hOgMoxEAlFX4ZFCNdlURiQ1VbciDBqEJgB4tjXP/UR2FSAIMiHB6k7RI19kr9UgIyxsh9mrIoD277m49Tq07uzOyhwxx+Y42H8LXq05CBqNzDkuSmnXO8Go4PLydun2ar+PWlM2RZqMk0xAZ/zUCfn9zV01xvXSdeT8IWQ1+y2mTJwNp8bRkS5M73QOZbgUpyz+rFeW7y8W7LpAKDZkO1MiS5R76bhFGPDbmIzdVAVPU9to/QmpPcTRsxI5Ag2jRZqKQtIzT2SbycWa/ikZunge8kSpFlk7urdmYGdnzpD34b9zt/iidV7oNzeONy8m/Tknl8xYKaSa4ypiiLJo6rwPY3Sbmv0JYhqw+FGAaHe7DjYS2TKrnpGxvFv6MbJm6gB2VwORnSskqmX2NrGz0MkwzdfKjJNDBTtEXM+VaaQEYOWSNeT0JaL0hCimsEfOcRkwZVtGXUYIAR1X8NANDEd0gGvwCAhuPfc5eGgSxoeu6VITcYQ99J0tWzlbvsvwe+B99z5/aVATKbbUIBkiYLFV+oMfHpWNkfVGqSu+yvh76LOJCbicsl91mBHc7wEOf+5BfxtHI7Bm/4KIDq5B7kciNN5iGqKAUstP2tUblLB8jh/jXuQGhUr9xlRui0PZJddQemezWxci6r3Ek4Qw6uCduLGjJCEuQem/UlgxKX7nszvtD7Dlx86D21f9c0bUSMANFKSCaMW/XbMnGmLaMFg0TmWRd5BQ/Abb5xzMld1TR4TAetsHI/3rsOc0CT8sTASzbcsmqKtG/twhns4wwApT2H3a+AR0aySSg9ZsrInU/HhknVptaseLI3rkQpYi6X3EO9A9v969J//9Kj/xhvxFV8+Z2Poi16pO5+6vmixx6GpeRuQs/kRlrMA6vYmiq0/RV+4FWyMjUxfTvav45zcIE65C4/j1n+O0P9NNreVTiicm+V+OVowhnSvcH93+tsiMvxfHmDmAdWq4MHf+qTc/0uKQpGsEAB/4xMrFhn2UcUIVI0aKIoqrsHkoX01w8yk546W26Izarg5AQGy8bGVu5x4CQxXmqu5w5wu9gDEZ2md89gXngwQeIilTYEeS9ziVjRoSJMKnytpgueKog89r2E3JcdAjwtsCMKQ9z/7H/EY51vw6vf/C60t/imnH+QIfcpyTyhakMX04Tcg8WtPMQTW9sTtr+y514l5V6Oth9efYaHatfwMZEZodNWWq51Bv3oBhAM4TG91JNfF/YAkbAILrtWiiCj9pQFyH1RuGRBEXtMCB34TJ0rq5SRlng8mfEQvlb/BgEApiD3KEvuCMFmRC8eB+QFBsvGxpG7LggwCjzEkey5Zyv3tC3j7HEnP7NfXzkgEZABVVSjMlmoLBOUkQaNhQgEues1Kx7dkKsSNyX3OTTG0zAtsGOwfx02+QhuexAA0Nvh5y0eXkueY0wxw4pVC4boufu+y3XeFdsShba/kQ+fTY52F8EUJmHeNeGHXoPcZUboNHKP2ueww3ah+AOMpmj3peEXDbhhXR1ylxF/enu+PaJlwCMrISQKnEr2EUWISYPKuKjBnjOFCQAMcU7kXkeSc3ACKndPsRpyrwNJdnHggokNVU1P7+JyczUKXLiJr8z85O4rJhRB7vICM0qkYbFwpJT9wVnxcnnIzdMoSNsy5hxKhakQgR1FPtMD4UOutji5dLpb8JkGliF3PqFbTG6RaiU+IHLfoapiSG1N2v5S5COs2Fm0hbNkvPeceL3qfWu5ElHt8huCnFK1h8/Bm2Kp0BI5msZIrBpryP/O3nU/LuMMzr78dZV/Z9nwFBuaCMlWouKBtSpgigYFcuZjhHhOcjdz8syigJ7jCp+spDBcBY7/GagJSe4scBNlTHbIRXqxhL6LULQTujv1ZWESAVnQEnLnF32ZekBaH8Se3HSrJ2nTTSm99ABB7saS2zJJYMfBLlo5r4/hHidxGRRBioI96kF1UkMvgwWlrRamWTDAWymuM0AfxQZbRZApRlnb3zqJO9KfRh/wIGu9QgqThHRu1KeQuy6mVHe8Z+FOGczqCnLv+Pza02v03G+94x7gl75e+fmrgJ/ZFFdCF/68lbsodFgco80cxOZ88s6WzCAWG5Nh4EPH7Fzd44BAsSa86JeJDazcBQGGXtJzz/Y/ZYsmDHxgeI17ZJ+av3IPVROasByVjodmmXpA4eQu+4NWiaKiDLLlFAcuEPrw2XT/93kgK9rRwaSnuycsd61uugE9UHrQfd4qYXEMm/zSkXqm2bAYvylJ8ymlYltGuh06B+kqAXH1lPtOn/9+2+XtEKPGqLtciehTVCHtHe6Nfkt8ZaqVswxJ3gr555iVQnXcEKgtGNnKfU5y5y1KHumoUwTMSe5yM1cqd3wx3LfU+MkVIVCthDtWgY0jd1MQIAvclNy1LLnLtowHcq5jnzpzbQhJhIoFXfSR5QVWNp0orQ+kXM7q1LugDbkqCT1Q5IHXKMuF3Hh0CjzdPREykXUeHOlbsH0RXyfcMVmJPDObGzlLWZRHYvs7TI+LoqByW0Y3TIyYie2At+Jkm6YK5EqkTLsOAP2zfJBJJYZgCrmrmoYDtHGKCWfIOaYyjxLZcIw6Ad95MEWDhiBJ/VLmiNgDuGXGiJkg8Z1KA3qOP7kXedEvExtH7pIAEflJRqOardx1Se4+dO8GDpT5NcMAEKtmkmsql4ZlMjjelomSm4A9Z+WOwAVFHoIVON/JwA5/MOnpHgk/9XbGS9wzttGOuC2A54ipy5KRevm46wwS6VrZ5nMeRba/SuzXCkIeUgtnmFx91BgE0meT+ykxpQoAwQxDuEPq8M1kAOYJq9wjzYYh9k3qBHznwRQNKiI4gtzVGm2yPLKeRVVD048DItVKzuUqsHHkrqgqfKYCoZtK5TJDLpqetjZMfzeJJ5sXkWqld9/AQcDUUp9wUnQYFIL8IRxm1F4xJJV75IMiv3JLog6mBXZIy91uhtxDcxs9JrJJhRSUStoy2dzIxFGwoi9Jke2vEteLUxspKalKe+MqIItH3LWm/I5hWtiFUG7MmLodqemK7aRV7rHWgi0ISY/dRCZaF0zRobEQjlA/aXMEdUi4ZEEJeWER+pNmgccVPGjEm/3EObFx5A4APgxQ6KVDLpkNVbm5GoU+2uEeXGMxzXCs2ckmIYVOYg9bBKm9VfwDOBWsbvPQdAMhU4DQhRL7K6ncpwV2kLOHETPHCClunUYfQz7xKwhbKdkklJW75wySmQC9auUubX+d9KZDcVAr5V76oceM0GpXb4m96rv+AR7/9kfQ25o+7LarcPKfZeXsCOMvj02Gmhx3ML0NKyF3v3LA9wRUAxoi+CJiz2jPX2T5ZEHNV+4VZh+OGtk9qFXgZF1ZFeGTDoo8IA4QMxqrkCW5s9BDL95HYC5G7kyzYIq2jBI68KYtU0U1oXn7cOcgdwDwoYNCT7Qkln8Bd0T7oyiwQ/H2cZjzEpfTvfs3riRmWGXkriS5kU4iXTMqtqYS2183JXclDhDVGDP3hFnYgGwoqlr593pbO/jmb/tbM583MMTqYoa8MxAZu0WhJscdzGjDJh9RGE4dWJv5OooGDVGyQjQXIfeMgkc6wVYJcDlqML3FB/kKZkqWgYXInYg+TESPE9GXiegj4rH7ieizRPQXRPT7RDS/hd2cCKCDIh+IwonWRVK5+y767BCxPb/1AMDJ3YKwFp5B7qTyYzHCA3hzuuDJG5cSB4lb4TLR7vR5zmdBYIfu72GojJOxJsKrB7svIXCnx67JxwN3kMwEmDUGuYbUhuanx6WyelmZgdBSj7CaVohrnQUw3YMGSI2/vDk14kcJ2VpzRocwmIe4RtjIGFQdOkUIRvMHdUgEip1ICiW5n4S2DOktqMTGgkaWibnJnYjuBfABAA8BuB/Au4nobgCfAPCzjLH7APwugH+4jAOtg4AMKLEPin2EGK/QpM9MePASVGKg9nymYQl0GxrFCHxvZrKQvOCs8HCqXG4afBigyIcS+yuJEiNFwZBahYEdZnAAJ2eVa/Y5oQ1vvJTGrpWQe2Ly5A4Tm+Qyg60i8BSj9LgUFtVKuQ8NXmc4ymo2MaM2Pxezpm5jS2xan8DKXWbDuqNDPrA2Z+Uuh4ziodiknyeoQyBQbehi3ysKpVngCTi3BUEjy8QilfsrAXyOMTZijIUA/gjA9wG4B8Afi+d8BsDs9eySEZIOJfK4VI7GyT1RnBwIb48FfGWArAJkOFsaJnrurfgQwZxfCvnZtNhHuCLnuyFahYEddnQIXx/f+GoJfxnv4EpC7mWWCDKWMHSHibLIruEo6GpdWGGmcq/ZlpF+6HVSmOpAETmmVGINLEG22LSeU2lylJAWDO7gAOaUSMmZEIUOG3Fyb9XMc80i0myYsazcBbmfgJ67nPFwndWkMS1C7o8DeCsR7RBRC8C7AFwUj3+veM73i8cmQEQfJKIvENEXrl69WvSUuRGQwX3DWTihg5YDTboY/5aV57zIbhLy2Ljyi13KszpsgKAksm0W5KpEjX1EK0qbGao9GP6kzr0dH04ERXTFAFhweA2RCG8oi12Tj4feKFEWGTVcLQO9BztKvwgqCxDXWb1Y/Mbkr4jcjS1O7rO0+3LadhVttVVDrr7c4T4sCoCKxm95yBal6t6Aw4xShVkVRKqd2FokOQdLDI5fFdKgkWNWuTPGngDwq+DV+acBfAlACOCHAXyIiB4D0AWElGTy93+DMfYgY+zBM2cWq57zCBUDauwXDrlIf5aWK4ZZFiR3eff1ndFMaZgiKvceRvXDsQUkuWssWFmU2FA/hZY/OaHaZQPE1vjyuXeKn794eC2NXSsxw5Kyx8gbgoLRVGVREUKjP2b7WzcrUxHkHurzDczMgr1zQbzP9Mpd7/JWYJnv/XGGdDJ1hM8Q5q3cxYpL8/YwrBhWXgamt5J9L0nuSoUAl6OGLALkQN+ysdCGKmPsEcbYaxljbwVwA8CTjLGvMMa+kzH2OgCPAvirZRxoHUSC3JU4mOjJGqJC6Ivx70V8ZYBUGRK4w5nqgexgxbzkHpGeIffVtGV86zR60Xjl7jpD2OSD2ePLZ9Nq4ZDZoNF1bouAcnmjHNiJfQdK6NRWDMVmf8z2t+45UMX07bwOhLNw92vehs/e+ZO451sfnvo8ad9wEsld3qC9A+6oWicDNgsShY4Z7MFZkNxjvZXIM6NADi4e/3Ob7kEdv7YMiOis+O/tAB4G8GjmMQXALwD4t4seZF1EigGNBSAWIsptqEr/852YV6Zbp29d6L3k5qHvDmHG3tQBluwO/ixFRRlCxYAW+9CYv7LKPWydwTbbS3JmAWCwy2+Gij258XWg9KB5u5lMzeIvq1TGxP5otmy0AGRvQacIo6EIO0FYi9x1MWHKagR11IGqaXjT3/+n6MzYHLT7fKU67wDQUULaVIeHvJVaJnudBUnu7XB/8T0Qow2DIvheaoVd5qd/nJDdg1oFFtW5f4qI/hLA7wP4EGNsF8D7iOhrAL4C4AUAv7nge9RGLAiQ4nCiclc1DSFTYFKAAbMXnhCUftyBN4KJ6dIwNWM9jJrh2BKRYkCLPegrbMtQ5ywMinCwm+6FDETaktaZnNIcqn0Y/m6SB1k2Up+EAgcO1NCZqiwqggypOBTulHWDkE3R62ZTEpXWgWTatsT3/jhDOplKm2dlwcq9Ex/MncKUvJZQ8DjDwzR9bYEe/rqgJylSqyH3hebXGWNvKXjs4wA+vsjrLopIMaGxoHQ8PYAGDT72lR4WXaBLco+8EUzmTU0WUrLaW2O+CzpSDKgsEGkzqyF3rc9bVftXn8fWaf7/I9FjNQrI3dG30favYSjI3Soh9+RGGoygRQ6CKda4hcfV3hbHch24+HJ+DuqQu5i+JWsxP6FF0dvmlXt8Atsy0slUcbhHT1XL5jxIpKP12SGenTOFSUJJ5JkHSWj6SRhiko6gcqBv2djICVWmGtCZD4WFiGlyEjEQ1fxgQV8ZIFO5u0O0yJtakY8lQtUMx5aIFf7ZdBaUhmIsCmuLE/rh9eeTx/xD3saSSUJZ+MY2OtE+ELoImVKqfFBUFS7TQYEDLXZry0ENQe7OAScWjQW1bnCnz9+Fq9hG947X1HrfZUM3TBwye+Yk63GEKUzxdJfvyWhztmWkuECnaOEN7qzqhNUITT9qyFVQtCJy37iwDoAvdw1wci8acgmEVa6rL07u8u4bCjtcNmWZms1ynbfiiVW+KjHgr6xy7wpvcnfvcvKYLz5fuz+pbIqsbfT3DkChCx/61ItKOvgZsYtDvV4FLW1/feFOqddMue/2T6H7S09judqs+fDkm38Nt1y676gPozakJ48VCDfHGjGBWVAm4zRacIM7VZ0MEptv/QRsqMo9KDnQt2xsJLkz1YTOAihxiLiA3KU80jcXz6KUqUvRkJMfTWm3ZOVZakU3xDyYasBgPgyKgBX1bLeEN3m4n5J7POJf5qzdb3JM7TOwyYfq7sIjc+pwvwwUN2J3pntiHi2xagiGKbmfhJT7Irz2b/y9oz6EuaBqGlymox1yT5iqxm95ZL8Li+6BSHmm7wy41TdORuVui1WQHOhbNja0LWPCRMC9RwoqO+kBHlmLk7u8+9JI9CCnjJ5nK3dtznACpppoM3GnX1Ffsbe1w7NRB+mGKnN2ETFCt0AJogrzsJbz4ky/FJ9MqJEDk7m1TafkjSUe7SIKQ27fe0LJ/STDIRvdmHvC1MmAzSK7/0Q1wsqLoMvVszMARIaqvuT4yVVAly6vwWqi9jaS3KGZMCjkQy5FlbvcZF3UVwaAafOLWxE9SGXKMlXLVCt6DcOsLJhq8ig7ALSiKTxSFNygLWijK8ljiruHQ2oXuinKoZx+cGXm1KWv8FBgEx5YzZ5zt7eNmBHg7COQZkvqarT+DcrhwkSf8anKMtnrLCiZQofmjNiTkEHzoTdIMxxOgBSSFAV/duH9aL98QpeyFGxkW0ZWtGbs4HAKuSudxbuvMsNR5oiWmWYB434X8oKsC5bdlF3hiPWhtg3TS8OoVW8fA+qiaJfCFv4yZ+LreE67MPV1A2HPajMPcc1BLkVVsU8tkLuHIPBh4WQk7mwaPMWCGoskqTnbi9lVrFozKD4PmVkcuUMg8uEzFcYJ8cl/0wc+trLXPhlnoCZkEpDNRoXj6dJN0egtTu6KqsJjOqxAJMpM6UFmByuq+phPvsh6yH2o76AdpORuBPsYqcXH3N7mFgQmBQhnDCaFigEjGsGgcKZ7YhEG1IHq7yP0T46166Yh62iqzxkTmHVtlLm980I6i8b+EBT5lXN1Nx2bSe4iSq/FnMIJRqmgWdRXRsIjA62IT03qU1Qw2baMPWe1Qmsid9/aQT9K/WWs8ACuVnzMvVOphcOskfpQtZPM1XlG10cKt/2ViTtNW2b9yJrjWfZ8bZls5W4uELEHpNp75g9BcVArV3eTsZHkLvXkLfIKh1ykk2Dn1GLWAxIeDPRiTu7TK/eU+KzOvOSebhTNOx1YBVHrLLbYAaKQRxW2Cux+Jbpbp/nGEIBwhoInUq3kXE1TFpXB1bowg0ME/skJQt40yADwiBGMOTcus6H1ZmcxcrcTch8BcbCSbOGTiI0kd1m5Ayhuy4ix/f7pxUzDJDwy0RMbTOYUf/LsBW3P2ZbJVuurNEeizlloFGPvOpdDdtghIrP4S8h74fzzRDOmTiPVRpe4OmCasqgMgd6FHR8iEiZlStOWWTukhNWDMXcGbLZyt7uLqdakPJP8YaET7M2KjST3MQ1tUVtG0eExHe0FKwaJgEwuywNgTFHBSEdKhxljua51kL1xrdLWVO/zVc3BtecRRxG6bJgkCBXhUOErkVl+KdmpWnUOjXRo9NGOBwiD1SqGGpQjEhYbdY3fslAzfzcZyr4IHLJAwVBYjjTkDmwouatGtnKfJHemaNin7tKS57PpS9YUcpcbqs6c4dhAbhBKX52W197mq5rB9RdweLDLIwkLHCElhhon/lmZmlnvnVmhFkWIzD56bIBQSCGzkroG60EsHE09LEDuGRO9zgIpTBIuLCihI3ruzTUBbKgUUs32ogvaMvTNP4Cnrr4ey9lOHSf3qW0ZVUPMCG5Nw6yx18h8NnWFU3jd07cBALy9yxjuXUMfqStjETx9G/CBeMZgUtaeQZ9HRmdtwaAQ3kDMFZyAMfNNg5xP8BdwJZXGXkNmoT3nKjYLT7Gghg6IRYg2k9ZqYyPPwljlXqCmeOA7f3Cp7yf7zDEjmCX5oQAfWgigwqP5N0KzZKatcAqvf4br1cODyxgKu1+js1P6/MDaBoaY6ooJYMxYbZ7RdXmDcfd5WMRJcP/bOIiN8EUyYOWQ0ZBaWEbooa/Y0CIHjKhWru4mYyPbMmNOdWv4Q0eiz+xW2GAKoMFfpHLPfLZVknu3tw2X6cDgKtwDYfc7ZeMrtgXxz2gVZeWP0/YnyiBtf0NB7k3lvn5IlVNdy+YspLjAUZaTZyuH43j6WkPuwMaSe0YLvgY1hfRIcStUMiGpCGoaZmWRbcVoK+y5k6LghrINbXQlcWFs9cvtGqglyH1Gzz2rkDHmGICRfvJswK0Rmsp9/ZD+6eECbRlpC+0qy7E9DlUbRuxALXGCvRmxmeSe9XdRV/+Hln3mKhtMITQE6vwXtG5ke9ar07kDwKHKLQhCQe6dArtfCa3DiZ9m3HCy3jvWHINcMn9UHfFW0UnIytw0SEfTcIHKXVry+otG7AmEqg2DuVDjoNAJ9mbERpL7mCPcGiYYYykNq3Cxh9DmDscGxlsxq3a+Gxk76AQ3EDt887KzXV65m2Lad9ZgVdZ7x5qy+VyGVp+Tu+HxG85JsHbdNEhyr+vqmYWiqogYIVhSWHmktWDGLtQVBsefNGzkLU7PbGrSGshdbiJW6UE+88DPoHvr3XO/l56pfPUpm7fLgG+dRn/0OF5y9uAwA/aUNoq9Jch9RjJPdlVVFsc3DW0R2NEKOLk3lfv6oQu76lnKqFkIoSFcMGJPgmk2LLgYsaghd4GNJPesDelajKVEK6IKub/+PT++0FsZGUI3zNVW7nH7LLauH0J1ruOQOphG25de9RA++6c/hFe86b1TX1PaM4yYidYccwZd4eneC0XM2wmwdt00SLvqWTMNs7BHPUTd25ZxSIj1NmzmQUVTuUtsJrmb623LSAXIIj3IqtAzn21eX4+qUDpnoRBDb/g0hsp0uwRNNyrZl0r5ozsjsakMqqbhkNnYxh5A4349DdaDJB5ulux1Fn70M3jN9pKmTYwWDAphxm5D7gIb2XPPkp6yTnJfcJlaBXJV4jNtaRO2pe8lgrJvDZ+BU+IIWRdycGmR6cYBdWAST9xpyH39MEWO6qIB7ecu3JVEzS0KEns5XTYonEq/GbGR5E6KAo/xPzCtYTxdkvuiPcgqkG0ZH6v/XPYW95fpYQRPW86X0Ht3SFAAAAkeSURBVBR99iqbz2XI+so3G6rrh7TYnTXTsE5I7X2ZE+zNiI0kdwDwZNrSGoylpLwvWnSZWgGqpiFgKoI1DGp0z5xP/j8wFvf/ANIl/SIDMG6G3PWG3NeO3vYZPNZ9O7Zf/c6jPpQEWZ+ikxqavmxsZM8dAHwYAEZQluBbMQtS3lc3E3ReBNDWUrlvZcg9LrH7rQuZObvIlK6n9wBuCpnopRusD4qq4nU//btHfRhjULOB803lDmCDK/dQkN86/L6lJcDCG0wV4ZGxlsq93d3CiHHyZPZyKnfpmrnI5nNo8J5vyJS5rZMbbBayITlFflI3IzaW3CX5raPnLi8sWlvlrq/N1nRX4aSuTLH7rQNFVeEyfaEWVmzyY2oSdxpIjDmMNm0ZABtM7iHxP7C2hp57Mlg0Y4BnWQhITz7fqnGoiXH/zmJpOVm4ZCZpPnNBhIYEzZh5AwHdzrRlmsodwAb33APFAGJAWcOQiy7kieuq3EMy1uZ8NzJ2gAAwp9j91sVXd94B9Y43zf37ZPP+fxOn1kDCzDiMrmVw8QRgY78dkvzWoXPfvuUSrmELvdvvXfl7AUBABsI1bRoF1g4wBMzu8sj9DT/xHxb6fVXa/m7u5dugJqxsJnFD7gA2mNylHam6hsq9v30a+KVvoNxWa7kYmGcRastx05uFuH0OuA60t9b16WbDaPMWUROn1kDCzAxDUWMDDWCDyT0S0Xeb6D1y94/9NhRFXct7de56I5579vdw+pY71vJ+VWB2Jblv7OXboCZa7XSCuiF3jo39dsSycl/Dhuq60V5CoHBV3Pe2h4G3Pby296sCafvbZGU2kFA1DR7TYVKwllbsScBCahki+jARPU5EXyaij4jHXkNEnyOi/0dEXyCih5ZzqPUQq7It0/yhNw1tkQjVJO40yMIRSWhN5c4xN7kT0b0APgDgIQD3A3g3Ed0N4F8A+GXG2GsA/KL4ee1IK/fmD71pkLa/TVZmgyxc8MG4dViOnAQsUvq8EsDnGGMjACCiPwLwfQAYANkA6wN4YaEjnBPSsW7VaUUN1g/dMDFkVpNy32AMnmJx+XNT0AFYjNwfB/DPiGgHgAPgXQC+AOAjAP4XEf06+MrgzUW/TEQfBPBBALj99tsXOIxiMFVuqDYEsIk4pE7TlmkwBp+ayj2LudsyjLEnAPwqgM8A+DSALwEIAfwYgI8yxi4C+CiAR0p+/zcYYw8yxh48c6Y8eHnu4xM9901UyzQABmof4SJTrg02Dr64HtYhfz4JWGhDlTH2CGPstYyxtwK4AeBJAO8H8DviKf8NvCe/dihbF3Ed/cY1cEPB3v0xnPqeXznqw2hwjCBv9uuYSj8JWFQtc1b893YADwN4FLzH/jbxlLeDE/7a8eDDH4X5U1+Coq5HD95gvbj7gbfijle+7qgPo8ExgvQratK5OBZtWn5K9NwDAB9ijO0S0QcAfJyINAAuRF993VA1DZ3ecpwMGzRocPwRadzbSV2DE+xJwELkzhh7S8Fj/xdAU1I1aNBgrYg12XNvKndggy1/GzRocHMhFq6s2jHKdj1KNOTeoEGDzYDOzfSa0HSOhtwbNGiwESBDVu6NWgbYYOOwBg0a3Fy4/Vvfh8/6I7zx9K1HfSjHAg25N2jQYCNw26V7cNsPH4mV1bFE05Zp0KBBgw1EQ+4NGjRosIFoyL1BgwYNNhANuTdo0KDBBqIh9wYNGjTYQDTk3qBBgwYbiIbcGzRo0GAD0ZB7gwYNGmwgiDF21McAIroK4Btz/vppANeWeDibgOacjKM5H5Nozsk4Tur5uIMxVhhldyzIfREQ0RcYYw8e9XEcJzTnZBzN+ZhEc07GsYnno2nLNGjQoMEGoiH3Bg0aNNhAbAK5/8ZRH8AxRHNOxtGcj0k052QcG3c+TnzPvUGDBg0aTGITKvcGDRo0aJBDQ+4NGjRosIE40eRORH+TiL5KRF8nop896uNZN4joIhH9IRE9QURfJqIPi8dPEdFniOhJ8d/toz7WdYKIVCL6IhH9D/Hzy4jo8+J8/Bciuqly2Ihoi4g+SURfEdfKm27ma4SIPiq+L48T0aNEZG3iNXJiyZ2IVAD/GsB3AXgVgPcR0auO9qjWjhDATzPGXgngjQA+JM7BzwL4A8bY3QD+QPx8M+HDAJ7I/PyrAP6VOB+7AH7kSI7q6PBxAJ9mjL0CwP3g5+amvEaI6DyAnwTwIGPsXgAqgL+DDbxGTiy5A3gIwNcZY08xxnwAvw3gPUd8TGsFY+xFxtifi/8/BP/Sngc/D78lnvZbAN57NEe4fhDRBQDfDeAT4mcC8HYAnxRPudnORw/AWwE8AgCMMZ8xtoeb+BoBjxe1iUgD0ALwIjbwGjnJ5H4ewLOZn58Tj92UIKJLAB4A8HkA5xhjLwL8BgDg7NEd2drxMQD/CEAsft4BsMcYC8XPN9t1cieAqwB+U7SqPkFEbdyk1whj7HkAvw7gGXBS3wfwGDbwGjnJ5E4Fj92Uuk4i6gD4FICPMMYOjvp4jgpE9G4AVxhjj2UfLnjqzXSdaABeC+DfMMYeADDETdKCKYLYW3gPgJcBuA1AG7y1m8eJv0ZOMrk/B+Bi5ucLAF44omM5MhCRDk7s/4kx9jvi4ZeI6Fbx77cCuHJUx7dmfAuA7yWip8HbdG8Hr+S3xBIcuPmuk+cAPMcY+7z4+ZPgZH+zXiPvBPDXjLGrjLEAwO8AeDM28Bo5yeT+ZwDuFrvcBvimyO8d8TGtFaKf/AiAJxhj/zLzT78H4P3i/98P4L+v+9iOAoyxn2OMXWCMXQK/Hv43Y+zvAvhDAH9bPO2mOR8AwBi7DOBZIrpHPPQOAH+Jm/QaAW/HvJGIWuL7I8/Hxl0jJ3pClYjeBV6ZqQD+PWPsnx3xIa0VRPStAP4PgL9A2mP+efC++38FcDv4xfz9jLEbR3KQRwQi+jYAP8MYezcR3QleyZ8C8EUAP8gY847y+NYJInoN+AazAeApAD8EXtjdlNcIEf0ygB8AV5t9EcCPgvfYN+oaOdHk3qBBgwYNinGS2zINGjRo0KAEDbk3aNCgwQaiIfcGDRo02EA05N6gQYMGG4iG3Bs0aNBgA9GQe4MGDRpsIBpyb9CgQYMNxP8HNlDDWhVeIGEAAAAASUVORK5CYII=\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# double check that state sequences are well prepared\n", "var_names = ['y', 'shock', 'b']\n", "for i, var_name in enumerate(var_names):\n", " plt.plot(range(T-S), x1[i, :], label=\"original\")\n", " plt.plot(range(T-S), x2[i, :], label=\"innovations\")\n", " plt.title(f\"{var_name}\")\n", " plt.legend()\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ax.plot(range(S+1, T+1), ev1, label=\"original representation\")\n", "ax.plot(range(S+1, T+1), ev2, label=\"innovation representation\")\n", "ax.legend()\n", "ax.set_title(\"discounted expected values\")\n", "\n", "ax1_ = ax.twinx()\n", "ax1_.plot(range(S+1, T+1), y_seq[S+1:], color='g', label=\"income\", alpha=0.4)\n", "ax1_.set_ylabel(\"income\", color='g')\n", "span = (max(y_seq[S+1:]) - min(y_seq[S+1:])) / 2\n", "center = (max(y_seq[S+1:]) + min(y_seq[S+1:])) / 2\n", "ax1_.set_ylim(center-span*1.1, center+span*1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stop here -- the remaining cells are things to be deleted or edited" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Zejin Nov 21 Consider the expected total wealth in each state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For “original representation” consumers, given $y_{t}$, $\\epsilon_{t}$, and $b_{t}$:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\sum_{j=0}^{\\infty}\\beta^{j}E_{t}\\left[y_{t+j}\\right]-b_{t}\t&=y_{t}+\\sum_{j=1}^{\\infty}\\beta^{j}E_{t}\\left[y_{t+j}\\right]-b_{t} \\\\\n", "\t&=y_{t}+\\sum_{j=1}^{\\infty}\\beta^{j}\\left(y_{t}-\\beta^{-1}\\epsilon_{t}\\right)-b_{t} \\\\\n", "\t&=\\sum_{j=0}^{\\infty}\\left(y_{t}-\\epsilon_{t}\\right)-b_{t} \\\\\n", "\t&=\\frac{y_{t}}{1-\\beta}-\\frac{\\epsilon_{t}}{1-\\beta}-b_{t}. \n", "\\end{aligned}\n", "$$\n", "\n", "For “innovations representation” consumers, given $y_{t}$, $a_{t}$, and $b_{t}$:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\sum_{j=0}^{\\infty}\\beta^{j}E_{t}\\left[y_{t+j}\\right]-b_{t}\t&=y_{t}+\\sum_{j=1}^{\\infty}\\beta^{j}E_{t}\\left[y_{t+j}\\right]-b_{t} \\\\\n", "\t&=y_{t}+\\sum_{j=1}^{\\infty}\\beta^{j}\\left(y_{t}-\\beta a_{t}\\right)-b_{t} \\\\\n", "\t&=\\sum_{j=0}^{\\infty}y_{t}-\\sum_{j=0}^{\\infty}\\beta^{2}a_{t}-b_{t} \\\\\n", "\t&=\\frac{y_{t}}{1-\\beta}-\\frac{\\beta^{2}a_{t}}{1-\\beta}-b_{t}.\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "code", "execution_count": 240, "metadata": {}, "outputs": [], "source": [ "ew1 = x1[0, :] / (1 - β) - x1[1, :] / (1 - β) - x1[2, :]\n", "ew2 = x2[0, :] / (1 - β) - β ** 2 * x2[1, :] / (1 - β) - x2[2, :]" ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(T-S), ew1)\n", "plt.plot(range(T-S), ew2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Zejin Nov 21: try to simulate consumption with the same debts" ] }, { "cell_type": "code", "execution_count": 242, "metadata": {}, "outputs": [], "source": [ "# set the initial state\n", "c1_hypo = np.empty(T-S)\n", "\n", "for i in range(T-S):\n", "\n", " # orginal representation\n", " c1_hypo[i] = y_seq[S+i+1] - ϵ_seq[S+i+1] - (1 - β) * b2[i]" ] }, { "cell_type": "code", "execution_count": 243, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 243, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(S+1, T+1), c1_hypo, label=\"original representation\")\n", "plt.plot(range(S+1, T+1), c2, label=\"innovation representation\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## compare consumptions, expected discounted wealth, and expected utility (resized)" ] }, { "cell_type": "code", "execution_count": 244, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 244, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(T-S), c1_hypo / c1_hypo.max(), label='$c_t$')\n", "plt.plot(range(T-S), ew1 / ew1.max(), label='ew')\n", "plt.plot(range(T-S), ev1 / ev1.max(), label='ev')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 245, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 245, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(T-S), c2 / c2.max(), label='$c_t$')\n", "plt.plot(range(T-S), ew2 / ew2.max(), label='ew')\n", "plt.plot(range(T-S), ev2 / ev2.max(), label='ev')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 246, "metadata": {}, "outputs": [], "source": [ "# construct b1 so that two types of consumers have the same expected discounted wealth\n", "x1_hypo = x1.copy()\n", "\n", "x1_hypo[2, :] = x1[0, :] / (1 - β) - x1[1, :] / (1 - β) - ew2\n", "ev1_hypo = np.diagonal(x1_hypo.T @ P1 @ x1_hypo) + d1" ] }, { "cell_type": "code", "execution_count": 247, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 247, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(T-S), x1_hypo[2, :], label=\"original\")\n", "plt.plot(range(T-S), x2[2, :], label=\"innovations\")" ] }, { "cell_type": "code", "execution_count": 248, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "ax.plot(range(S+1, T+1), ev1_hypo, label=\"original representation\")\n", "ax.plot(range(S+1, T+1), ev2, label=\"innovation representation\")\n", "ax.legend()\n", "ax.set_title(\"discounted expected values\")\n", "\n", "ax1_ = ax.twinx()\n", "ax1_.plot(range(S+1, T+1), y_seq[S+1:], color='g', label=\"income\", alpha=0.4)\n", "ax1_.set_ylabel(\"income\", color='g')\n", "span = (max(y_seq[S+1:]) - min(y_seq[S+1:])) / 2\n", "center = (max(y_seq[S+1:]) + min(y_seq[S+1:])) / 2\n", "ax1_.set_ylim(center-span*1.1, center+span*1.1);" ] }, { "cell_type": "code", "execution_count": 249, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158,\n", " -4.00263158, -4.00263158, -4.00263158, -4.00263158, -4.00263158])" ] }, "execution_count": 249, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the gain of information\n", "ev1_hypo - ev2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## more income does not make consumers worse off?" ] }, { "cell_type": "code", "execution_count": 250, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 250, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_seq = np.arange(-1000, 1000)\n", "plt.plot(y_seq, [np.array([y, 0, 0]) @ P1 @ np.array([y, 0, 0]) + d1 for y in y_seq])" ] }, { "cell_type": "code", "execution_count": 251, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2000.0000000003936 -2004.002631579302\n" ] } ], "source": [ "# the initial state\n", "# the last entry is the initial state of debt\n", "x0 = np.array([10, 0, 0])\n", "\n", "print(- x0 @ P1 @ x0 - d1, - x0 @ P2 @ x0 - d2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Equation numbering from Zejin\n", "\n", "Hi Tom, if you want to modify the ipython notebook directly, you would need to add HTML tags. For example, you may check the sourse code of the following equation by double-clicking this cell, and do copying and pasting.\n", "\n", "\n", "\n", "\n", "
\n", "$$\n", "\\text{equation here}\n", "$$\n", "\n", "(1)\n", "
\n", "\n", "If you want to use equation numbers when you construct .rst files, it would be much simpler. You can use the `label` tag:\n", "\n", "```\n", ".. math::\n", " :label: equation_name\n", "\n", " E_0 \\sum_{t=0}^\\infty \\beta^t u(c_t)\n", "```\n", "\n", "and then you can use `eq` to refer to it: \"the consumer maximizes :eq:\\`equation_name\\` by choosing a consumption...\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell evaluates optimal values (maximized expected sum of utilities) at the initial condition." ] }, { "cell_type": "code", "execution_count": 252, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 252, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a_seq = np.arange(-100, 1000)\n", "plt.plot(a_seq, [np.array([10, 0, a]) @ P1 @ np.array([10, 0, a]) + d1 for a in a_seq])\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }