dynamic_programming/coleman_policy_iter.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<a id='coleman-policy-iter'></a>\n",
    "<div id=\"qe-notebook-header\" style=\"text-align:right;\">\n",
    "        <a href=\"https://quantecon.org/\" title=\"quantecon.org\">\n",
    "                <img style=\"width:250px;display:inline;\" src=\"https://assets.quantecon.org/img/qe-menubar-logo.svg\" alt=\"QuantEcon\">\n",
    "        </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimal Growth II: Time Iteration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "- [Optimal Growth II: Time Iteration](#Optimal-Growth-II:-Time-Iteration)  \n",
    "  - [Overview](#Overview)  \n",
    "  - [The Euler Equation](#The-Euler-Equation)  \n",
    "  - [Comparison with Value Function Iteration](#Comparison-with-Value-Function-Iteration)  \n",
    "  - [Implementation](#Implementation)  \n",
    "  - [Exercises](#Exercises)  \n",
    "  - [Solutions](#Solutions)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "In this lecture we’ll continue our [earlier study](optgrowth.html) of the stochastic optimal growth model.\n",
    "\n",
    "In that lecture we solved the associated discounted dynamic programming problem using value function iteration.\n",
    "\n",
    "The beauty of this technique is its broad applicability.\n",
    "\n",
    "With numerical problems, however, we can often attain higher efficiency in specific applications by deriving methods that are carefully tailored to the application at hand.\n",
    "\n",
    "The stochastic optimal growth model has plenty of structure to exploit for this purpose, especially when we adopt some concavity and smoothness assumptions over primitives.\n",
    "\n",
    "We’ll use this structure to obtain an **Euler equation**  based method that’s more efficient than value function iteration for this and some other closely related applications.\n",
    "\n",
    "In a [subsequent lecture](egm_policy_iter.html) we’ll see that the numerical implementation part of the Euler equation method can be further adjusted to obtain even more efficiency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Euler Equation\n",
    "\n",
    "Let’s take the model set out in [the stochastic growth model lecture](optgrowth.html) and add the assumptions that\n",
    "\n",
    "1. $ u $ and $ f $ are continuously differentiable and strictly concave  \n",
    "1. $ f(0) = 0 $  \n",
    "1. $ \\lim_{c \\to 0} u'(c) = \\infty $ and $ \\lim_{c \\to \\infty} u'(c) = 0 $  \n",
    "1. $ \\lim_{k \\to 0} f'(k) = \\infty $ and $ \\lim_{k \\to \\infty} f'(k) = 0 $  \n",
    "\n",
    "\n",
    "The last two conditions are usually called **Inada conditions**.\n",
    "\n",
    "Recall the Bellman equation\n",
    "\n",
    "\n",
    "<a id='equation-cpi-fpb30'></a>\n",
    "$$\n",
    "v^*(y) = \\max_{0 \\leq c \\leq y}\n",
    "    \\left\\{\n",
    "        u(c) + \\beta \\int v^*(f(y - c) z) \\phi(dz)\n",
    "    \\right\\}\n",
    "\\quad \\text{for all} \\quad\n",
    "y \\in \\mathbb R_+ \\tag{1}\n",
    "$$\n",
    "\n",
    "Let the optimal consumption policy be denoted by $ c^* $.\n",
    "\n",
    "We know that $ c^* $ is a $ v^* $ greedy policy, so that $ c^*(y) $ is the maximizer in [(1)](#equation-cpi-fpb30).\n",
    "\n",
    "The conditions above imply that\n",
    "\n",
    "- $ c^* $ is the unique optimal policy for the stochastic optimal growth model  \n",
    "- the optimal policy is continuous, strictly increasing and also **interior**, in the sense that $ 0 < c^*(y) < y $ for all strictly positive $ y $, and  \n",
    "- the value function is strictly concave and continuously differentiable, with  \n",
    "\n",
    "\n",
    "\n",
    "<a id='equation-cpi-env'></a>\n",
    "$$\n",
    "(v^*)'(y) = u' (c^*(y) ) := (u' \\circ c^*)(y) \\tag{2}\n",
    "$$\n",
    "\n",
    "The last result is called the **envelope condition** due to its relationship with the [envelope theorem](https://en.wikipedia.org/wiki/Envelope_theorem).\n",
    "\n",
    "To see why [(2)](#equation-cpi-env) might be valid, write the Bellman equation in the equivalent\n",
    "form\n",
    "\n",
    "$$\n",
    "v^*(y) = \\max_{0 \\leq k \\leq y}\n",
    "    \\left\\{\n",
    "        u(y-k) + \\beta \\int v^*(f(k) z) \\phi(dz)\n",
    "    \\right\\},\n",
    "$$\n",
    "\n",
    "differentiate naively with respect to $ y $,  and then  evaluate at the optimum.\n",
    "\n",
    "Section 12.1 of [EDTC](http://johnstachurski.net/edtc.html) contains full proofs of these results, and closely related discussions can be found in many other texts.\n",
    "\n",
    "Differentiability of the value function and iteriority of the optimal policy\n",
    "imply that optimal consumption satisfies the first order condition associated\n",
    "with [(1)](#equation-cpi-fpb30), which is\n",
    "\n",
    "\n",
    "<a id='equation-cpi-foc'></a>\n",
    "$$\n",
    "u'(c^*(y)) = \\beta \\int (v^*)'(f(y - c^*(y)) z) f'(y - c^*(y)) z \\phi(dz) \\tag{3}\n",
    "$$\n",
    "\n",
    "Combining [(2)](#equation-cpi-env) and the first-order condition [(3)](#equation-cpi-foc) gives the famous **Euler equation**\n",
    "\n",
    "\n",
    "<a id='equation-cpi-euler'></a>\n",
    "$$\n",
    "(u'\\circ c^*)(y)\n",
    "= \\beta \\int (u'\\circ c^*)(f(y - c^*(y)) z) f'(y - c^*(y)) z \\phi(dz) \\tag{4}\n",
    "$$\n",
    "\n",
    "We can think of the Euler equation as a functional equation\n",
    "\n",
    "\n",
    "<a id='equation-cpi-euler-func'></a>\n",
    "$$\n",
    "(u'\\circ \\sigma)(y)\n",
    "= \\beta \\int (u'\\circ \\sigma)(f(y - \\sigma(y)) z) f'(y - \\sigma(y)) z \\phi(dz) \\tag{5}\n",
    "$$\n",
    "\n",
    "over interior consumption policies $ \\sigma $, one solution of which is the optimal policy $ c^* $.\n",
    "\n",
    "Our aim is to solve the functional equation [(5)](#equation-cpi-euler-func) and hence obtain $ c^* $."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Coleman Operator\n",
    "\n",
    "Recall the Bellman operator\n",
    "\n",
    "\n",
    "<a id='equation-fcbell20-coleman'></a>\n",
    "$$\n",
    "Tw(y) := \\max_{0 \\leq c \\leq y}\n",
    "\\left\\{\n",
    "    u(c) + \\beta \\int w(f(y - c) z) \\phi(dz)\n",
    "\\right\\} \\tag{6}\n",
    "$$\n",
    "\n",
    "Just as we introduced the Bellman operator to solve the Bellman equation, we\n",
    "will now introduce an operator over policies to help us solve the Euler\n",
    "equation.\n",
    "\n",
    "This operator $ K $ will act on the set of all $ \\sigma \\in \\Sigma $\n",
    "that are continuous, strictly increasing and interior (i.e., $ 0 < \\sigma(y) < y $ for all strictly positive $ y $).\n",
    "\n",
    "Henceforth we denote this set of policies by $ \\mathscr P $\n",
    "\n",
    "1. The operator $ K $ takes as its argument a $ \\sigma \\in \\mathscr P $ and  \n",
    "1. returns a new function $ K\\sigma $,  where $ K\\sigma(y) $ is the $ c \\in (0, y) $ that solves  \n",
    "\n",
    "\n",
    "\n",
    "<a id='equation-cpi-coledef'></a>\n",
    "$$\n",
    "u'(c)\n",
    "= \\beta \\int (u' \\circ \\sigma) (f(y - c) z ) f'(y - c) z \\phi(dz) \\tag{7}\n",
    "$$\n",
    "\n",
    "We call this operator the **Coleman operator** to acknowledge the work of [[Col90]](../zreferences.html#coleman1990)  (although many people have studied this and other closely related iterative techniques).\n",
    "\n",
    "In essence, $ K\\sigma $ is the consumption policy that the Euler equation tells\n",
    "you to choose today when your future consumption policy is $ \\sigma $.\n",
    "\n",
    "The  important thing to note about $ K $ is that, by\n",
    "construction, its fixed points coincide with solutions to the functional\n",
    "equation [(5)](#equation-cpi-euler-func).\n",
    "\n",
    "In particular, the optimal policy $ c^* $ is a fixed point.\n",
    "\n",
    "Indeed, for fixed $ y $, the value $ Kc^*(y) $ is the $ c $ that\n",
    "solves\n",
    "\n",
    "$$\n",
    "u'(c)\n",
    "= \\beta \\int (u' \\circ c^*) (f(y - c) z ) f'(y - c) z \\phi(dz)\n",
    "$$\n",
    "\n",
    "In view of the Euler equation, this is exactly $ c^*(y) $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Is the Coleman Operator Well Defined?\n",
    "\n",
    "In particular, is there always a unique $ c \\in (0, y) $ that solves\n",
    "[(7)](#equation-cpi-coledef)?\n",
    "\n",
    "The answer is yes, under our assumptions.\n",
    "\n",
    "For any $ \\sigma \\in \\mathscr P $, the right side of [(7)](#equation-cpi-coledef)\n",
    "\n",
    "- is continuous and strictly increasing in $ c $ on $ (0, y) $  \n",
    "- diverges to $ +\\infty $ as $ c \\uparrow y $  \n",
    "\n",
    "\n",
    "The left side of [(7)](#equation-cpi-coledef)\n",
    "\n",
    "- is continuous and strictly decreasing in $ c $ on $ (0, y) $  \n",
    "- diverges to $ +\\infty $ as $ c \\downarrow 0 $  \n",
    "\n",
    "\n",
    "Sketching these curves and using the information above will convince you that they cross exactly once as $ c $ ranges over $ (0, y) $.\n",
    "\n",
    "With a bit more analysis, one can show in addition that $ K \\sigma \\in \\mathscr P $\n",
    "whenever $ \\sigma \\in \\mathscr P $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison with Value Function Iteration\n",
    "\n",
    "How does Euler equation time iteration compare with value function iteration?\n",
    "\n",
    "Both can be used to compute the optimal policy, but is one faster or more\n",
    "accurate?\n",
    "\n",
    "There are two parts to this story.\n",
    "\n",
    "First, on a theoretical level, the two methods are essentially isomorphic.\n",
    "\n",
    "In particular, they converge at  the same rate.\n",
    "\n",
    "We’ll prove this in just a moment.\n",
    "\n",
    "The other side to the story is the speed of the numerical implementation.\n",
    "\n",
    "It turns out that, once we actually implement these two routines, time iteration is faster and more accurate than value function iteration.\n",
    "\n",
    "More on this below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equivalent Dynamics\n",
    "\n",
    "Let’s talk about the theory first.\n",
    "\n",
    "To explain the connection between the two algorithms, it helps to understand\n",
    "the notion of equivalent dynamics.\n",
    "\n",
    "(This concept is very helpful in many other contexts as well).\n",
    "\n",
    "Suppose that we have a function $ g \\colon X \\to X $ where $ X $ is a given set.\n",
    "\n",
    "The pair $ (X, g) $ is sometimes called a **dynamical system** and we\n",
    "associate it with trajectories of the form\n",
    "\n",
    "$$\n",
    "x_{t+1} = g(x_t), \\qquad x_0 \\text{ given}\n",
    "$$\n",
    "\n",
    "Equivalently, $ x_t = g^t(x_0) $, where $ g $ is the $ t $-th\n",
    "composition of $ g $ with itself.\n",
    "\n",
    "Here’s the picture\n",
    "\n",
    "<img src=\"_static/figures/col_pol_composition.png\" style=\"width:40%;\">\n",
    "\n",
    "  \n",
    "Now let another function $ h \\colon Y \\to Y $ where $ Y $ is another set.\n",
    "\n",
    "Suppose further that\n",
    "\n",
    "- there exists a bijection $ \\tau $ from $ X $ to $ Y $  \n",
    "- the two functions **commute** under $ \\tau $, which is to say that\n",
    "  $ \\tau(g(x)) = h (\\tau(x)) $ for all $ x \\in X $  \n",
    "\n",
    "\n",
    "The last statement can be written more simply as\n",
    "\n",
    "$$\n",
    "\\tau \\circ g = h \\circ \\tau\n",
    "$$\n",
    "\n",
    "or, by applying $ \\tau^{-1} $ to both sides\n",
    "\n",
    "\n",
    "<a id='equation-cpi-ghcom'></a>\n",
    "$$\n",
    "g = \\tau^{-1} \\circ h \\circ \\tau \\tag{8}\n",
    "$$\n",
    "\n",
    "Here’s a commutative diagram that illustrates\n",
    "\n",
    "<img src=\"_static/figures/col_pol_bij1.png\" style=\"width:50%;\">\n",
    "\n",
    "  \n",
    "Here’s a similar figure that traces out the action of the maps on a point\n",
    "$ x \\in X $\n",
    "\n",
    "<img src=\"_static/figures/col_pol_bij2.png\" style=\"width:50%;\">\n",
    "\n",
    "  \n",
    "Now, it’s easy to check from [(8)](#equation-cpi-ghcom) that $ g^2 = \\tau^{-1} \\circ h^2 \\circ \\tau $ holds.\n",
    "\n",
    "In fact, if you like proofs by induction, you won’t have trouble showing that\n",
    "\n",
    "$$\n",
    "g^n = \\tau^{-1} \\circ h^n \\circ \\tau\n",
    "$$\n",
    "\n",
    "is valid for all $ n $.\n",
    "\n",
    "What does this tell us?\n",
    "\n",
    "It tells us that the following are equivalent\n",
    "\n",
    "- iterate $ n $ times with $ g $, starting at $ x $  \n",
    "- shift $ x $ to $ Y $ using $ \\tau $,  iterate $ n $ times with $ h $ starting at $ \\tau(x) $, and shift the result $ h^n(\\tau(x)) $ back to $ X $ using $ \\tau^{-1} $  \n",
    "\n",
    "\n",
    "We end up with exactly the same object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Back to Economics\n",
    "\n",
    "Have you guessed where this is leading?\n",
    "\n",
    "What we’re going to show now is that the operators $ T $ and $ K $\n",
    "commute under a certain bijection.\n",
    "\n",
    "The implication is that they have exactly the same rate of convergence.\n",
    "\n",
    "To make life a little easier, we’ll assume in the following analysis (although not\n",
    "always in our applications) that $ u(0) = 0 $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A Bijection\n",
    "\n",
    "Let $ \\mathscr V $ be all strictly concave, continuously differentiable functions $ v $ mapping $ \\mathbb R_+ $ to itself and satisfying $ v(0) = 0 $ and $ v'(y) > u'(y) $ for all positive $ y $.\n",
    "\n",
    "For $ v \\in \\mathscr V $ let\n",
    "\n",
    "$$\n",
    "M v := h \\circ v' \\qquad \\text{where } h := (u')^{-1}\n",
    "$$\n",
    "\n",
    "Although we omit details, $ \\sigma := M v $ is actually the unique\n",
    "$ v $-greedy policy.\n",
    "\n",
    "- See proposition 12.1.18 of [EDTC](http://johnstachurski.net/edtc.html)  \n",
    "\n",
    "\n",
    "It turns out that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $.\n",
    "\n",
    "A (solved) exercise below asks you to confirm this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Commutative Operators\n",
    "\n",
    "It is an additional solved exercise (see below) to show that $ T $ and $ K $ commute under $ M $, in the sense that\n",
    "\n",
    "\n",
    "<a id='equation-cpi-ed-tk'></a>\n",
    "$$\n",
    "M \\circ T = K \\circ M \\tag{9}\n",
    "$$\n",
    "\n",
    "In view of the preceding discussion, this implies that\n",
    "\n",
    "$$\n",
    "T^n = M^{-1} \\circ K^n \\circ M\n",
    "$$\n",
    "\n",
    "Hence, $ T $ and $ K $ converge at exactly the same rate!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation\n",
    "\n",
    "We’ve just shown that the operators $ T $ and $ K $ have the same rate of convergence.\n",
    "\n",
    "However, it turns out that, once numerical approximation is taken into account, significant differences arises.\n",
    "\n",
    "In particular, the image of policy functions under $ K $ can be calculated faster and with greater accuracy than the image of value functions under $ T $.\n",
    "\n",
    "Our intuition for this result is that\n",
    "\n",
    "- the Coleman operator exploits more information because it uses first order and envelope conditions  \n",
    "- policy functions generally have less curvature than value functions, and hence admit more accurate approximations based on grid point information  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Operator\n",
    "\n",
    "Here’s some code that implements the Coleman operator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using InstantiateFromURL\n",
    "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.6.0\")\n",
    "# uncomment to force package installation and precompilation\n",
    "# github_project(\"QuantEcon/quantecon-notebooks-julia\", version=\"0.6.0\", instantiate=true, precompile = true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using LinearAlgebra, Statistics\n",
    "using BenchmarkTools, Interpolations, Parameters, Plots, QuantEcon, Roots\n",
    "using Optim, Random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "using BenchmarkTools, Interpolations, Parameters, Plots, QuantEcon, Roots\n",
    "\n",
    "gr(fmt = :png);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "K (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function K!(Kg, g, grid, β, ∂u∂c, f, f′, shocks)\n",
    "# This function requires the container of the output value as argument Kg\n",
    "\n",
    "    # Construct linear interpolation object\n",
    "    g_func = LinearInterpolation(grid, g, extrapolation_bc=Line())\n",
    "\n",
    "    # solve for updated consumption value\n",
    "    for (i, y) in enumerate(grid)\n",
    "        function h(c)\n",
    "            vals = ∂u∂c.(g_func.(f(y - c) * shocks)) .* f′(y - c) .* shocks\n",
    "            return ∂u∂c(c) - β * mean(vals)\n",
    "        end\n",
    "        Kg[i] = find_zero(h, (1e-10, y - 1e-10))\n",
    "    end\n",
    "    return Kg\n",
    "end\n",
    "\n",
    "# The following function does NOT require the container of the output value as argument\n",
    "K(g, grid, β, ∂u∂c, f, f′, shocks) =\n",
    "    K!(similar(g), g, grid, β, ∂u∂c, f, f′, shocks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has some similarities to the code for the Bellman operator in our [optimal growth lecture](optgrowth.html).\n",
    "\n",
    "For example, it evaluates integrals by Monte Carlo and approximates functions using linear interpolation.\n",
    "\n",
    "Here’s that Bellman operator code again, which needs to be executed because we’ll use it in some tests below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "T (generic function with 2 methods)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Optim\n",
    "\n",
    "function T(w, grid, β, u, f, shocks, Tw = similar(w);\n",
    "                          compute_policy = false)\n",
    "\n",
    "    # apply linear interpolation to w\n",
    "    w_func = LinearInterpolation(grid, w, extrapolation_bc=Line())\n",
    "\n",
    "    if compute_policy\n",
    "        σ = similar(w)\n",
    "    end\n",
    "\n",
    "    # set Tw[i] = max_c { u(c) + β E w(f(y  - c) z)}\n",
    "    for (i, y) in enumerate(grid)\n",
    "        objective(c) =  u(c) + β * mean(w_func.(f(y - c) .* shocks))\n",
    "        res = maximize(objective, 1e-10, y)\n",
    "\n",
    "        if compute_policy\n",
    "            σ[i] = Optim.maximizer(res)\n",
    "        end\n",
    "        Tw[i] = Optim.maximum(res)\n",
    "    end\n",
    "\n",
    "    if compute_policy\n",
    "        return Tw, σ\n",
    "    else\n",
    "        return Tw\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing on the Log / Cobb–Douglas case\n",
    "\n",
    "As we [did for value function iteration](optgrowth.html), let’s start by\n",
    "testing our method in the presence of a model that does have an analytical\n",
    "solution.\n",
    "\n",
    "Here’s an object containing data from the log-linear growth model we used in the [value function iteration lecture](optgrowth.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "##NamedTuple_kw#253 (generic function with 2 methods)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isoelastic(c, γ) = isone(γ) ? log(c) : (c^(1 - γ) - 1) / (1 - γ)\n",
    "Model = @with_kw (α = 0.65,                            # Productivity parameter\n",
    "                  β = 0.95,                            # Discount factor\n",
    "                  γ = 1.0,                             # Risk aversion\n",
    "                  μ = 0.0,                             # First parameter in lognorm(μ, σ)\n",
    "                  s = 0.1,                             # Second parameter in lognorm(μ, σ)\n",
    "                  grid = range(1e-6, 4, length = 200), # Grid\n",
    "                  grid_min = 1e-6,                     # Smallest grid point\n",
    "                  grid_max = 4.0,                      # Largest grid point\n",
    "                  grid_size = 200,                     # Number of grid points\n",
    "                  u = (c, γ = γ) -> isoelastic(c, γ),  # utility function\n",
    "                  ∂u∂c = c -> c^(-γ),                  # u′\n",
    "                  f = k -> k^α,                        # production function\n",
    "                  f′ = k -> α * k^(α - 1),             # f′\n",
    "                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we generate an instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "m = Model();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need some shock draws for Monte Carlo integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "using Random\n",
    "Random.seed!(42) # for reproducible results.\n",
    "\n",
    "shock_size = 250 # number of shock draws in Monte Carlo integral\n",
    "shocks = collect(exp.(m.μ .+ m.s * randn(shock_size))); # generate shocks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a preliminary test, let’s see if $ K c^* = c^* $, as implied by the\n",
    "theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "verify_true_policy (generic function with 1 method)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function verify_true_policy(m, shocks, c_star)\n",
    "    # compute (Kc_star)\n",
    "    @unpack grid, β, ∂u∂c, f, f′ = m\n",
    "    c_star_new = K(c_star, grid, β, ∂u∂c, f, f′, shocks)\n",
    "\n",
    "    # plot c_star and Kc_star\n",
    "    plot(grid, c_star, label = \"optimal policy cc_star\")\n",
    "    plot!(grid, c_star_new, label = \"Kc_star\")\n",
    "    plot!(legend = :topleft)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_star = (1 - m.α * m.β) * m.grid # true policy (c_star)\n",
    "verify_true_policy(m, shocks, c_star)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can’t really distinguish the two plots, so we are looking good, at least\n",
    "for this test.\n",
    "\n",
    "Next let’s try iterating from an arbitrary initial condition and see if we\n",
    "converge towards $ c^* $.\n",
    "\n",
    "The initial condition we’ll use is the one that eats the whole pie: $ c(y) = y $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "check_convergence (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function check_convergence(m, shocks, c_star, g_init; n_iter = 15)\n",
    "    @unpack grid, β, ∂u∂c, f, f′ = m\n",
    "    g = g_init;\n",
    "    plot(m.grid, g, lw = 2, alpha = 0.6, label = \"intial condition c(y) = y\")\n",
    "    for i in 1:n_iter\n",
    "        new_g = K(g, grid, β, ∂u∂c, f, f′, shocks)\n",
    "        g = new_g\n",
    "        plot!(grid, g, lw = 2, alpha = 0.6, label = \"\")\n",
    "    end\n",
    "    plot!(grid, c_star, color = :black, lw = 2, alpha = 0.8,\n",
    "          label = \"true policy function c_star\")\n",
    "    plot!(legend = :topleft)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_convergence(m, shocks, c_star, m.grid, n_iter = 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the policy has converged nicely, in only a few steps.\n",
    "\n",
    "Now let’s compare the accuracy of iteration using the Coleman and Bellman operators.\n",
    "\n",
    "We’ll generate\n",
    "\n",
    "1. $ K^n c $ where $ c(y) = y $  \n",
    "1. $ (M \\circ T^n \\circ M^{-1}) c $ where $ c(y) = y $  \n",
    "\n",
    "\n",
    "In each case we’ll compare the resulting policy to $ c^* $.\n",
    "\n",
    "The theory on equivalent dynamics says we will get the same policy function\n",
    "and hence the same errors.\n",
    "\n",
    "But in fact we expect the first method to be more accurate for reasons\n",
    "discussed above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "compare_error (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function iterate_updating(func, arg_init; sim_length = 20)\n",
    "    arg = arg_init;\n",
    "    for i in 1:sim_length\n",
    "        new_arg = func(arg)\n",
    "        arg = new_arg\n",
    "    end\n",
    "    return arg\n",
    "end\n",
    "\n",
    "function compare_error(m, shocks, g_init, w_init; sim_length = 20)\n",
    "    @unpack grid, β, u, ∂u∂c, f, f′ = m\n",
    "    g, w = g_init, w_init\n",
    "\n",
    "    # two functions for simplification\n",
    "    bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n",
    "    coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n",
    "\n",
    "    g = iterate_updating(coleman_single_arg, grid, sim_length = 20)\n",
    "    w = iterate_updating(bellman_single_arg, u.(grid), sim_length = 20)\n",
    "    new_w, vf_g = T(w, grid, β, u, f, shocks, compute_policy = true)\n",
    "\n",
    "    pf_error = c_star - g\n",
    "    vf_error = c_star - vf_g\n",
    "\n",
    "    plot(grid, zero(grid), color = :black, lw = 1)\n",
    "    plot!(grid, pf_error, lw = 2, alpha = 0.6, label = \"policy iteration error\")\n",
    "    plot!(grid, vf_error, lw = 2, alpha = 0.6, label = \"value iteration error\")\n",
    "    plot!(legend = :bottomleft)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compare_error(m, shocks, m.grid, m.u.(m.grid), sim_length=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, time iteration is much more accurate for a given\n",
    "number of iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "Show that [(9)](#equation-cpi-ed-tk) is valid.  In particular,\n",
    "\n",
    "- Let $ v $ be strictly concave and continuously differentiable on $ (0, \\infty) $  \n",
    "- Fix $ y \\in (0, \\infty) $ and show that $ MTv(y) = KMv(y) $  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "Show that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "\n",
    "Consider the same model as above but with the CRRA utility function\n",
    "\n",
    "$$\n",
    "u(c) = \\frac{c^{1 - \\gamma} - 1}{1 - \\gamma}\n",
    "$$\n",
    "\n",
    "Iterate 20 times with Bellman iteration and Euler equation time iteration\n",
    "\n",
    "- start time iteration from $ c(y) = y $  \n",
    "- start value function iteration from $ v(y) = u(y) $  \n",
    "- set $ \\gamma = 1.5 $  \n",
    "\n",
    "\n",
    "Compare the resulting policies and check that they are close."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4\n",
    "\n",
    "Do the same exercise, but now, rather than plotting results, benchmark both approaches with 20\n",
    "iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution to Exercise 1\n",
    "\n",
    "Let $ T, K, M, v $ and $ y $ be as stated in the exercise.\n",
    "\n",
    "Using the envelope theorem, one can show that $ (Tv)'(y) = u'(c(y)) $\n",
    "where $ c(y) $ solves\n",
    "\n",
    "\n",
    "<a id='equation-cpi-foo'></a>\n",
    "$$\n",
    "u'(c(y))\n",
    "= \\beta \\int v' (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz) \\tag{10}\n",
    "$$\n",
    "\n",
    "Hence $ MTv(y) = (u')^{-1} (u'(c(y))) = c(y) $.\n",
    "\n",
    "On the other hand, $ KMv(y) $ is the $ c(y) $ that solves\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    u'(c(y))\n",
    "    & = \\beta \\int (u' \\circ (Mv)) (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n",
    "    \\\\\n",
    "    & = \\beta \\int (u' \\circ ((u')^{-1} \\circ v'))\n",
    "        (f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n",
    "    \\\\\n",
    "    & = \\beta \\int v'(f(y - c(y)) z ) f'(y - c(y)) z \\phi(dz)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We see that $ c(y) $ is the same in each case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution to Exercise 2\n",
    "\n",
    "We need to show that $ M $ is a bijection from $ \\mathscr V $ to $ \\mathscr P $.\n",
    "\n",
    "To see this, first observe that, in view of our assumptions above, $ u' $ is a strictly decreasing continuous bijection from $ (0,\\infty) $ to itself.\n",
    "\n",
    "It [follows](https://math.stackexchange.com/questions/672174/continuity-of-an-inverse-function) that $ h $ has the same properties.\n",
    "\n",
    "Moreover, for fixed $ v \\in \\mathscr V $, the derivative $ v' $ is\n",
    "a continuous, strictly decreasing function.\n",
    "\n",
    "Hence, for fixed $ v \\in \\mathscr V $, the map $ M v = h \\circ v' $\n",
    "is strictly increasing and continuous, taking values in $ (0, \\infty) $.\n",
    "\n",
    "Moreover, interiority holds because $ v' $ strictly dominates $ u' $, implying that\n",
    "\n",
    "$$\n",
    "(M v)(y) = h(v'(y)) < h(u'(y)) = y\n",
    "$$\n",
    "\n",
    "In particular, $ \\sigma(y) := (Mv)(y) $ is an element of $ \\mathscr\n",
    "P $.\n",
    "\n",
    "To see that each $ \\sigma \\in \\mathscr P $ has a preimage $ v \\in \\mathscr V $ with $ Mv = \\sigma $, fix any $ \\sigma \\in \\mathscr P $.\n",
    "\n",
    "Let $ v(y) := \\int_0^y u'(\\sigma(x)) dx $ with $ v(0) = 0 $.\n",
    "\n",
    "With a small amount of effort you will be able to show that $ v \\in \\mathscr V $ and $ Mv = \\sigma $.\n",
    "\n",
    "It’s also true that $ M $ is one-to-one on $ \\mathscr V $.\n",
    "\n",
    "To see this, suppose that  $ v $ and $ w $ are elements of $ \\mathscr V $\n",
    "satisfying $ Mv = Mw $.\n",
    "\n",
    "Then $ v(0) = w(0) = 0 $ and $ v' = w' $ on $ (0, \\infty) $.\n",
    "\n",
    "The fundamental theorem of calculus then implies that $ v = w $ on $ \\mathbb R_+ $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution to Exercise 3\n",
    "\n",
    "Here’s the code, which will execute if you’ve run all the code above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "# Model instance with risk aversion = 1.5\n",
    "# others are the same as the previous instance\n",
    "m_ex = Model(γ = 1.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "exercise2 (generic function with 3 methods)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function exercise2(m, shocks, g_init = m.grid, w_init = m.u.(m.grid); sim_length = 20)\n",
    "\n",
    "    @unpack grid, β, u, ∂u∂c, f, f′ = m\n",
    "    # initial policy and value\n",
    "    g, w = g_init, w_init\n",
    "    # iteration\n",
    "    bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n",
    "    coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n",
    "\n",
    "    g = iterate_updating(coleman_single_arg, grid, sim_length = 20)\n",
    "    w = iterate_updating(bellman_single_arg, u.(m.grid), sim_length = 20)\n",
    "    new_w, vf_g = T(w, grid, β, u, f, shocks, compute_policy = true)\n",
    "\n",
    "    plot(grid, g, lw = 2, alpha = 0.6, label = \"policy iteration\")\n",
    "    plot!(grid, vf_g, lw = 2, alpha = 0.6, label = \"value iteration\")\n",
    "    return plot!(legend = :topleft)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0s8y8SJGiqOlh7YwcHBymg02fKWptbW28Lnj6wnyGYS47PWdmn337Q1cAMGscTyqaus+XKySqQREhcg/v8IwM50V6RsxVoAhNw8fHxyRjBeTm5i5ZssRUo50BAPw3pzsvNpUUSwa7JYRIrW2WJyUvWb6MWOQ5cShC0wgNDTUOxXKTnnrqqZvfCADAVfQMjNQUFPG9HRKeF4klPhFRoTGRZjRrkslZ7ncOAGBpRsanSosqdWdqKE5PM6zryvDIhGiRxU/1gyIEAFj8dAautKppsLZMpFXTNGUTEBydlmRts0DPiJlnuI5wvj377LOXjSB6nV544YXPPvvMOHbozQTQarUzp0pJS0vDlEkAixhPSFXTuS8/+Pto2QmRVi13cY+9c0v6rWvRgtOwRzjfTp8+PX3m56x4eno6Ojq+/vrrHR0dxuFeb8zHH3988ODBAwcOGL8MDg423zmtAODq2noGGxWFzMA5ESEia7tliQkBK5Zb5hkxV4EiNA21Wt3Z2Tl9DcPk5GRTU1NkZKRarS4uLh4aGgoODo6IiJhe/9y5cxKJxDg2qVqt7u7uDgkJIYS0tLTU19d7e3snJCRcdqFMYmIiIeTAgQMDAwPV1dVyuTw4OJgQ0tzc3NDQ4Ovraxw7rb+/X6vVsiybl5eXlpbm5eVVVVXV3t7u4uKSlpbGcZxxyNPq6mqxWLxq1apt27YZR5Dp6Oioqalxc3NLTk6maVqlUp0/f97Hx+fIkSO2trbZ2dkMw8zTqwkAN+2icryisIzramB4nhZLvCJiwmMjKBrv4itAEZpMUlJSXV3d0qVLCSGffPLJhx9+mJube++99zo6Ojo6Ov7ud7+75ZZbXn75ZePKv/vd7/z9/Y2DXNfW1j722GMNDQ3PPPPMvn371q5dW1lZ6eXlNT0cmtHzzz/v7e1dUVExOjr6zjvv+Pr6PvXUU7t37z58+HBOTs5rr70WFBS0Z8+ePXv27N27l6KoiIiIpUuX7t27V6FQBAUFNTc3/+QnPzlw4EBBQUFXV9c777zj6Oj4wgsvJCcnDw8P79u379lnn920aZOxYr/++uvKysoHH3zQz88vJCSkrKzsgw8++OSTT+b/VQWA2dLoDMWlpzSNFYxeS9OUU/Dq6JQEscWfEXMVi6cIDWPD2vb6+Xkuxs5JErBq5hJra+uNGzd+/PHHTz/9NCFkz549DzzwACHkwIEDxh27X/3qVz4+Ple5OqK6uvqDDz5oamqytrbmOC4qKio3NzczM3PmOi4uLnfeeWdHR8fbb79NCCktLd27d+/p06dlMpnBYAgLCysuLiaEXLx4sbW11TgcTGJi4q5du4wPv/3224uLi7dv337w4EHjFoxUKtWuXbtyc3Ojo6MNBkN0dPSHH37o5+fX19enUCh8fX2VSqWbm5tSqZy7WbQA4OYZeFJa19FfWSQeVzKEWHv7RaSnOjgttlmTTG7xFCHFsIz1PA19Qkutvr3wvvvue/TRR5966qnu7u6ampqvvvqKEFJQUPCHP/zh7Nmz4+Pj4+PjXV1d/22bRUVFcrn8+eef1+l0Go1mYmLi1KlTlxXhZQoLC2Uy2XPPPWd8iE6nO3XqFCEkJSVlepzSCxcu/PrXv66rqxscHBwaGoqKivr2EcrW1lZbW1vjdEsMw9xyyy2VlZV+fn4BAQG+vr6EEAcHBxcXl76+PhQhwILV0N57pqRYrLwgJkRm7xCckubt7yd0KPOweIqQtrKVLLvG7H1zKjMz02AwlJSUnDx58q677rK2tr548eLmzZs/++yzhIQEqVTq5eU1Pc8RRf17lFfjQr1e7+7unp2dbVy4ZcuWgICAqz+jXq/38PCY+ZCgoKB//OMf00OmEULuu+++tLS0l156yd7efseOHVNTU1fc1MwhZ6ezicXi6YU0TXMcN5vXAwDmyfmBsZp8BdXbLiaElcr8omNCIsIJToK7bounCAVHUdTWrVs/+OCDvLy89957jxDS2dnp4OCQkZFBCDl16lRfX9/0yu7u7tMz6CoUCkJIUlLSyy+/HBUVNb3XdcXisba21mg0xttJSUlvvfVWbGzs9JwS335IU1PT66+/bm9vPzU1lZubu2XLlplbMAoKChobG6uvrw8LC+M47tixY9czFSIACE45PlVaVKk9U8NwepoVua6KiEyIZkXiaz8SZkARmtL27dtDQkK8vb1TU1MJIWFhYYSQ73znO35+fgqFws3NbXrN//mf/4mPj6coSqPR9Pb2EkLi4+Mfeuih6OjoTZs26fX64uLi1157zXim6EyZmZm/+tWvNm/eHBQU9OKLL95zzz3R0dEbN27U6XSFhYXfvqzijjvu2L59+4YNG/Ly8ox9mZyc/IMf/GDjxo2enp5vvfUWIcTW1vb3v//9hg0b7rnnnsrKSplMtn379qKiorl8qQDgpug4UlTbPlylEE+OsTRlG7AiOi3JanFNizFvMA2TiRUWFjo6Ok7PHTEyMnL48GGaptevX9/Y2BgaGnr+/HlHR0cPD49z587l5+f7+vpGRES0tLQYL35oaWmprq4mhERHR09PSWHU0tJibW3t7e2tVCqbmppEIlFsbCwhpKmpqaamhqbpmJiYoKCgrq6uiYkJ45UVhBDjHl5vb29qairP8zRNBwQEqFSq06dP6/X65OTk/Pz85ORklmVbWloqKiq8vLzS09MZhhkeHm5tbZ2ezr6wsDAiIsI4W8XVYRqmOYVpmAQn+DRMPE9q2i60lZXKlT2EELmz66q0dDdvTwEjzae5mIYJRQgmhiKcUyhCwQlbhGd7BuoKFMzgeUKIVCYNiEsICFtFKAs6HIj5CAEALNTAiKZCUarvamJ4jhZLvFZHrI6JoEUSoXMtBihCAIAFbVLPF5XWqepLGb2WommHkMiYpFipDBfImwyKEABggeJ4UtnU3V1WIFEPMYTIvfyiMtMcHHE5r4mhCAEAFqIz5y41FBeLB85JCJHY2AanpPsG+QsdanFCEQIALCz9yvEKRQnfdVpMeFYi8YmMCY0Kpyx4Bvm5hlcWAGChUOsMxaV1msZyVq9laMZpZXh0UoxIgsOBcwtFCAAgPANPyuvbe8uLxBMjIkKsvf0iM9LscDhwXqAIAQAEdrrzYnORQjx8QUyI1N4xJCXF23+p0KEsiBkX4d///ncMA7YAqdVqoSMAmI1epaYir4g63yImPCuV+cXGh4SHYQb5eWauRfjuu+/u2bPHOEonzKepqamrD2vy0EMPCTsAFYBZUGu5wtJTE43lrEFLM4zLyvCoxFhWggvkBWCuRRgWFvbKK68IncISCT7QIoC50xv4svr2vspiycSIiBBb36VRmRnWdrZC57Jc5lqEAADmqLG9t7VYwY70SwiROziEJKd64nCg0FCEAADzoXdwrCpfwfd2sDzPyq38Y+JXrA7F4cCFAEUIADC3VFpDcXH15OkKmtPTrMgtLDIqPprBFCILBooQAGCuGHhSWtfRV1kkGVcyhFgvXRGTkWxtc+15PWE+oQgBAOZEY0dfS3GRWHnBeDhwZXqmh6+P0KHgClCEAAAm1js4WplfRHrbxTwvksmXRscuD19F0YzQueDKUIQAACaj1upLCsonWmoo3kAzrGtYZGRCNCsSC50LrgZFCABgAgaelNW195cXiiZHKUJZB4bEpibicKBZQBECANys5o4LzcVFrLJPRIjE0XVVRqant7vQoeB6oQgBAG5cv1JdmVvA97SxhDBSmX9sfHD4KkLRQueCWUARAgDciHGdobS8TlVfRut1hBXZhUQmJkWJxDgcaH5QhAAAs8MTUnO6s6tUIdIoaULkPoExWel2djgcaK5QhAAAs9DRM9RRc0I0eE5EiNTOISQ1zdvfT+hQcFNQhAAA12VgRF2RV6TrahbRFCuR+EbFhUaFExqHA80eihAA4Bq0eq6opE5VX0obdBRDO6+MiE6KFUulQucC00ARAgD8VzxPqlp7u4rzJKoBmhCZj39wTLS3j6fQucCUUIQAAFd29pKqOr9I3N8q4XmJje2KlPQlQf4qlUroXGBiKEIAgMuNqCZKiqp07XUSTs+yrFd41Kq4GJrFH8zFCT9XAIB/m+L40vKGodoSZmqSoSjHwOVRKYlSWzuhc8EcQhECAHyjvuNia2GuePQiQ4jU3TciPdnFzVXoUDDnUIQAAKR3WF2eX0yfbxETXmRlHZiUGhS8TOhQME9QhABg0TRafXFxtaapijFM0SzrHhoekRjHiERC54L5gyIEAAvF8aSirq23XMFOqlhCbPwCo9NTrO1wONDioAgBwBK19Y3V5eWKB7pYQsSOrmFpaZ6+XkKHAmGgCAHAsgyNTRYVVXEdp8ScnpVIfOOSQyNCCaGEzgWCQRECgKXQ6g2lJTXKxipmSiuiKeegFRHpqRK5XOhcIDAUIQBYhNrm7q6SPEatZAix8vSNTE1ycHMTOhQsCChCAFjkegbVVXkKureVIYSxcQhJz1jq7yt0KFhAUIQAsGipdYbCoprJpgrGMEWzIo/wmIiEKJpmhM4FCwuKEAAWIY4npafP9ZbmS8aVLCG2S4OiM1KtbGyEzgULEYoQABabtn5VTX6B7GK7hBCpveOq9AyPJT5Ch4KFC0UIAIvH0Li+qLCaa62UcXqRWOQbFbsyOgqTyMPVoQgBYDGY0nMlFQ1DdRWsTiOiKefAZRHpqRIra6FzgRlAEQKA2atv6zmryKXVwywhVi5u4WkpTl7eQocCs4EiBAAz1jcyUZpbyPQ00zxP2zisSEwKXB5AKAwTA7OAIgQAszQxxSlK6zUNZax+kmYYt9UxUYkxNINLI2DWUIQAYGZ4nlQ1d3WVFkrUQyJCbL19IzIybB0dhM4F5gpFCADmpLtfWZ1XwFzqkhAisbELSUnxCQoUOhSYtxspwosXL7733nuDg4O33XZbRkbG9PLm5uaDBw/OXHP79u3t7e0lJSXTSx5//HGZTHbDcQHAYqkmp4oUldqWaoY30GKJd0RMWHQ4zeK/ebhZs768RqPRxMfHd3Z2Ll269J577tm7d+/0XTqdTvkvNTU1zz77rEQiOX78+L59+6aXcxxn0vwAsPhxPCmpP3tsz0dTzRUM4eyXh2Ztvy88PhotCCYx61+jjz/+2MPD49133yWEODg4vPDCC1u2bDHetXr16tWrVxtvP/HEE3feeaejoyMhJDk5+cUXXzRdZgCwIG19I7X5CumlsyJCpE7OqzOy3Lw8hA4Fi8qsi1ChUGRnZxtv5+TkbNu2bWxszNbWduY6Op3u73//+8cff2z8srGx8cUXX/T29r7zzjutrKxuPjQAWIIRjU5RWMm11Uo5vUgsWRIbFxIZgUsjwORmXYT9/f1xcXHG287OzjRN9/X1XVaEX3zxhVQqzczMJIS4ubn5+/trNJp33333qaeeKi8vd3d3n7nyxMTEb37zG2dn55kLd+3atWzZsm8/u8Fg0Ol0FN4JwpmcnBSJREKnsFxarZamaYPBIHSQuaU38OV17cpTxSLdBENT9v5B4cnxIpnVpFYrdDS8BQQ2OTnJMMz1t4BYLKavNcberItQJBLp9XrjbY7jeJ4Xi8WXrfPee+89+OCDDMMQQr7//e9PL1+7du2rr7760ksvzVyZYZiwsLClS5fOXOjk5HTFXzWapnmex2+hgEQiEV5/AXEcR9P04v4RNJ8falYUiJU9IkLkrh7h6amOC2kGXbwFhGV8/a+/CK9nzVkXoaen54ULF4y3e3p6KIq6bA+vp6fn5MmTb7311rcfm5iY2NjYeNlCsVh8xx13TO9lXhPDMAyumRUOXn9hMQxD0/Ri/REMjk0WF5SSznoJz4uk8sCklKCVwQvts1C8BYRlfP1N+7ngrM8avf3227/88kutVksI2bt3b05Ojkwma29vb2hoMK7w17/+NSMjw9/f3/jlxMSE8YZOp/v6669DQ0NNlBwAFg+dnssrOqX48APqbB1DEfeQsJz77w8KDVloLQiL0qz3CDds2PDmm28mJycvX7786NGjhw4dIn0F7/MAACAASURBVIS88847bW1tn3/+Oc/zf/vb355//vnp9aOiopYsWeLk5FRSUuLm5rZr1y5TxgcA81ffdPZsaSGtVrKEWHn6RGWm2zs5CR0KLMisi5Bl2SNHjuTn5w8PD7/yyitubm6EkMcff3xycpIQotfrP/3001WrVk2vn5ubW11drVarH3/88ZiYGJznAgDT+pSaihO5VG8HTQhr47AiOdl/WYDQocDi3MjlqAzDZGVlzVzi7f3NjCcikSgqKmrmXe7u7hs2bLjhfACwKGn1XGFpvaqhlJnSUqzIPTIhKjacZjCDLggA4zIAwHyrae7uLCkQqYcYQmx8lsZkZ1rb2ggdCiwXihAA5k/vgLIir5DuOysiRGxjG5ycumQZhswGgaEIAWA+TOr0xQVl6pYamuNokdgzIjo8NpJm8CcIhIffQgCYWzxPqtp6uxXHRRoloWirwNCEtES5tVzoXADfQBECwBzqGVKXFZSKzjeJCC+ycwzNXuPj7X7thwHMIxQhAMyJcZ2+SFGtaakSG6ZYlvEKiwxLjKcwJgssPChCADAxnidVLee6i/JE4yMsITZ+AbFpKXJ7e6FzAVwZihAATOnC8HjZiTxRX5uIEJG906qMDG9fb6FDAVwNihAATGNiis8vrZ9oKBHptQzLekXFrY6JonCNPCx4KEIAuFk8x9c2tndWlIg0ShEhdkuWRmdkyO1sr/1IgAUARQgAN+X8ReWpkyf5gR4RIRJb+9DkZK8gXCMP5gRFCAA3aGKKU5ScmqgvoTk9kch9YuLDw0PxWSiYHRQhANyIxvbeFkWuWDXIEGIdEByXmSaXS4UOBXAjUIQAMDu9Sk1ZbhFzoUXM8xIbu5Vpad4B/kKHArhxKEIAuF6TU5yi5JSmoZw1aFmW9QqPCouLoVj8GQHzht9gALgutS3dnUX5rGaYJcR2iX90RpqVnZ3QoQBMAEUIANdwcVhdnltALrSxhIhsHULT0nz8/YQOBWAyKEIA+K90eq6opHqsvoI2TFGsyCMyLjIugqYxXigsKihCALiyhraedkUuox6mCbHyWxaXmWptYy10KADTQxECwOUGRydKTxZwPWcYnmdtHILT05f6LxE6FMBcQRECwL/pOb6o8vRwVRGrn6RZ1m11THRCNI25k2BRQxECwDdaugca83LFI30sIVaeS6Kzs+wcMF4oLH4oQgAgI2ptUX6J4WyDmOdYmXxZclpgyHKhQwHMExQhgEXjOL60tuVSRSGjG6dpyjkkIiY1nhVLhM4FMH9QhACWq6NXWZd7kh3qYQiRunlFZ2c6OjsJHQpgvqEIASyRelKvKKiYOlPN8gZGJg9ISFkRuoJQlNC5AASAIgSwLDxPaurbussLmYkxilD2y0Pj05PFUkwcAZYLRQhgQc5fHKk9mUsGuhlCxI7OEZlZbl4eQocCEBiKEMAiTE5xhYVVmtMVNKenJNIlMQlhkasIhUl0AVCEABagrrWnozCXVQ/TFGUbGBKXmSqT4bNQgG+gCAEWs8GR8ZLcAr6nleV5ka1DaEamj5+P0KEAFhYUIcDiZOD58or6S9Ul9JSWZlmXsJjYRAyWBnAFKEKARait+2JDfh6r7KcJkXsvjc1Kt7XHJLoAV4YiBFhUVBptUX6JrqOB5TlWbr0sJT1wRaDQoQAWNBQhwCLBE1JR29JbrmC04xRNO6+MikmJF4lFQucCWOhQhACLQc/AWNXJk/TFcwwhYlfPqOxsFxdHoUMBmAcUIYB50+r5gsLq8cYymtNTYqlffPKq8JUYLA3g+qEIAcxYY3tvqyKXVQ3ShMiXrkjMSpVbyYUOBWBmUIQAZmlobKLoZBE538TyvMjGbmV6pq//EqFDAZglFCGAmeE4vqji9EB1MaMbpxjGLSwqOjGWZvFeBrhBePMAmJNzF0cb8vJEI30MIXIPn6jsTAdHB6FDAZg3FCGAedBopwoLqydOV7C8gZbJAxNTVoQG46QYgJuHIgQwA6caO86WFLATYwwhdkEhCVlpmEEQwFRQhAAL2oBSXXHshKG/iyVEZO8ckpzs6eslEuEyeQCTQRECLFAGnhSVNyiri2i9logkXtEJkdGrdVM6oXMBLDYoQoCFqKN3+NTJXNFwD02IzCcgPifTxsZK6FAAixOKEGBhGdfqC/NLJ1prRRzHyuSBianLQlcIHQpgMUMRAiwgp9t7zuSdYMdHaIq2Wx6WkJ4klkqEDgWwyKEIARaEgbHJotwiuvs0y/MiB+eI7DXunq5ChwKwCChCAIEZOL64smmwppjVjdMM4xkRExEfSzG00LkALAWKEEBIZ3uVp3JPskM9LCHWnj7RWRm2jpg+CWBeoQgBhDGu1RcVVo03VbK8gZHJgxJTloUGCx0KwBKhCAEEUNd8rqMojx0foSnKPmhlfGYKRooBEAqKEGBeDY2Ol5xU8OdbWEJE9k6rMzI9fb2EDgVg0VCEAPOE4/jSmuZLlYWMboKwIo/IuOi4SIrGSTEAAkMRAsyHnn5ldW4uNXCeIUTi4Rubk+ngYC90KAAgBEUIMNe0ekOxokLVWEXxBloq909IDgkLEToUAPwbihBgDrWc7WvOP86ohilC2SwLTUhPlspwUgzAwoIiBJgTqkl9YV7xVFsdw3O0jcOqzKwlft5ChwKAK0ARApheVUvPucITovERmqKcVsfEJccxLN5rAAsU3pwApjQwoinOLaJ6WkTfDBma4+7pJnQoALgaFCGAaXA8Ka5qGqxQMPpJhmW9wmNWJ0RTNCN0LgC4BhQhgAl0D4xVHjshGuxmCJF7+MZkZ9g5OggdCgCuC4oQ4Kbo9JyiuEbVUC4yTDESaWBS6vJVuDoCwJygCAFuXEtnX3PeCUY1xBJit3RZbFaa1MpK6FAAMDsoQoAboZ6cKswtnmqrYwjP2tivTMtYErBE6FAAcCNQhACzdqqpq7Mol5kYIzTtHBodl4KrIwDMGN69ALOgHBsvOlnIdzczhIid3CKyc9zcnYUOBQA35QaLUKvVUhQlFouvc32NRiOTyWgMtA9mi+dJZU3ThYpCRjdBMaxzREJ8YgRF4VcawOzN+m08NTV1//33u7q6uri4PProowaDYfouhULhOMOXX35JCOnp6UlMTPTx8XFxcXn33XdNmR1gvvQNjh78ZF9/0TFGNyFx9025d3tCUhRaEGBxmPUe4V/+8pf6+vre3l6DwZCYmPjxxx9v377deNfU1JSPj09+fr7xSysrK0LIrl27wsLCiouLGxoakpKScnJy/Pz8TBYfYI4ZOL6wvHGkppDW6yip3D8+eeVqXB0BsKjMugj/9re/PfbYY8aSe+SRR/bs2TNdhIQQhmEcHP59HfHY2NiBAweam5spigoLC8vJyfnoo4+efvppk0QHmGvn+kcqT+aKB7tpQqz8liVkZ8itZEKHAgATm3URtre3BwcHG28HBwe/+uqrM+9tbm62sbFxcHDYtGnT7373u+7ubkJIQEDA9Ppnz569bIM8zw8ODvb19c1c6OTkdP0HIAFMTqfnFIoq9ekKMadnpLLlKRmBIcuEDgUAc2LWRTg6Omr1r0uGra2tlUrl9F0hISFVVVVBQUFtbW3btm3bvXv3PffcYzXj+mIbG5vTp09ftsGxsbHt27eLRKKZCz/++OPY2NhvP7vBYNDpdHq9fraxwVTUarXQEeZc+/mBjmIFqx4mFGXlFxSRFCeSSlUqldC5CCFEq9XSNH3Z+wXmkyW8BRYyjUbDcRxFUde5vlwuZ5hrDPk76yJ0cXEZHR013h4ZGXFxcZm+y8PDw8PDgxCycuXK3/zmN4899tjOnTtVKhXHccbzRUdGRlxdXS/boJ2d3Z49e+Li4q7n2Y1FKJPh4ykh2djYCB1hrmi0U4q8cl1rtZjnGVuH0MysJUt9hQ71H8RiMYpQcIv4LbDwURRlZWV1/UV4PWZ92tvKlStramqMt2tqalauXHnF1bRarUgk8vX1lcvldXV1xoXV1dX/bX0AwTW09x758O9TZ6poQjmHRq69b9tCa0EAmAuz3iN89NFHn3jiiYyMDL1e/+abb/71r38lhDz++ONJSUkURbm4uPj5+bW1te3evfu73/2uTCa77777fv7zn7/99tvFxcWVlZX/+Mc/5uC7ALgpoxP6gpPFfMcpEeFF9k6ROWvcMIkggMWYdRFu2rTp/Pnz27dvp2n6mWeeWbduHSFELBYzDKPRaJ555pne3l53d3fj56KEkBdffPGnP/3pmjVr3NzcDh486OTkZPpvAuAmTM8mz9CUa1hsTEocJhEEsCgUz/PCJoiLi3vjjTdwjNBcqFSqRXOARKnWFpwspM6dpnhe6ugcmZPj7L7QdwRxsozgFtNbwByp1WqTHyPEWKNgiXielNe19pbms7pxhmG8I2PC4mOwIwhgmVCEYHEuKlVlx/OovrMsITI3r5icLHsnR6FDAYBgUIRgQTiOL6lsHKwqovVaSiRZmpAcGh5KTPoZCwCYHRQhWIrewdGKYyfpgW6aEJmPf0JOprWNtdChAEB4KEJY/GYOnM1IJAHxySvCVwkdCgAWChQhLHLnL41WHjvGDl2gCbFeEpSwJlMmx1nHAPBvKEJYtAwcX1pSPVRbxnJ6WipbnpoZFBwkdCgAWHBQhLA4dV4YrDt+lB4doAixDVgRn5kqlcuFDgUACxGKEBabKQNXoKhWN5TRvIGysluZluEf5Cd0KABYuFCEsKh0XBiqO36UHb1EU5Td8rCEzBSxGIOwAMDVoAhhkdAZ+AJFlaahjOUNjNwmNDsHc0cAwPVAEcJi0HFh6NTxo6LRSzRFOS4PjctKFYnEQocCAPOAIgTzptUb8gtrJxrLRJyetbYNzczyXbpE6FAAYE5QhGDG2i4M1584JhrppynKaUVoXGYqix1BAJglFCGYJa2eyy+sGW8sE3F6kdw6NDvHBzuCAHBDUIRgftrOXWzIPc6ODbIUcVq+MjYzlRVLhA4FAOYKRQjmRKvnCgoqJk6XszzPWtuuzsry8sOOIADcFBQhmI22nqH6E9+cGuoQEhGfkcSy+AUGgJuFvyNgBrRT+oL8ionmahFvYK1tw7LXeC/xFjoUACwSKEJY6NrO9TedOEqplRShnFasistIxhFBADAhFCEsXFMGPq+odqKumOINlK1jeHa2j4+n0KEAYLFBEcICdfbCUE1unni4h6Ioh+DVCZmpLMsIHQoAFiEUISw4U1P64rzi0ZZTYp4XyWQrM3N8A/2FDgUAixaKEBaWrt6h+qOHyNgwoWj74LCE1ESRFEcEAWAOoQhhodAb+IKyxrFaBWOYomwcwnLW+fm4CR0KABY/FCEsCD19Q5UncpnhCywhtoHBCTmZmEcQAOYHihAExvF8cWGVsq6U4ThGbhWckua/YpnQoQDAgqAIQUh9w+ryI0fpgfOEoqyWhSVnJkkkOCIIAPMKRQjC4Hm+uLLpUmUhq5+kpfJlGWuWLfMTOhQAWCIUIQhgcHi09OgJ/tJ5lhBrb7/4dWvkVnKhQwGAhUIRwrzieVJZ29JXkksZdJRUHpiYErwqWOhQAGDRUIQwf0bU2oJj+dT5ZooQiW9g8posKyuZ0KEAwNKhCGGe1Da0dRXnM1oNzbK+CWlhkauETgQAQAiKEOaBekJbdOSkrruVIUTi4hm/LsfO0UHoUAAA30ARwtxq6ug7c/IIMzHKs2LvmMSo2NWEUEKHAgD4NxQhzBXtlCEvr1zbUsnwvMjRLXbDeidHO6FDAQBcDkUIc6Kju7/+xDFGNUxTlEtYdFxaIkXTQocCALgCFCGYmJ7jFAWVqoYyhucZG4eInBxPzKYLAAsYihBM6cLAaOWRI/RwH0Uou+CI5MwkhsXvGAAsaPgjBabB83xJef1AVRFtmKJl1iuz1y719xE6FADAtaEIwQQGR9Slh4/yA+dpQqyXLk/MSZfKcKU8AJgHFCHcrOq6M+eLc+kpLZHIlqVmrQgJFDoRAMAsoAjhxqkntIojefruFpoQsZd/8rpsa2uMnQ0AZgZFCDeouf38mdzj9MQYYUXecamR0RgyDQDMEooQZk2n5/LzSiebqmjCs84esWvXODtjyDQAMFcoQpidnoGxZsWX7OglQlFOYXGJafEUhSHTAMCMoQjhenEcX1RaN1hdyPIGxso2bO06H1wpDwDmD0UI12VQqS75+igZOE9znG1QSGJOhlgiEToUAIAJoAjh2moa2rsLT9BTk0QiWxqbtDoyVOhEAAAmgyKEq9FMTuUfUxg6G2hCxJ5Lk2/J4XmD0KEAAEwJRQj/VXt7d2PuCXpijKIZr9jkyNhwQlEqlUroXAAApoQihCuY0htKcotGW07RPM84uMauW+Pi6ix0KACAOYEihMv1K9XlXx6ilH08xTiExyWnxNA0LpAAgEULRQj/ofzUmQsl+ezUBJHbhK27damPm9CJAADmFooQvqFWTyiOntT3tLOEWHn5JW5YJ5NJhQ4FADDnUIRACCFn2rvP5B4lExrCipfEp6yODCUYLwYALAOK0NLpDbwiv1TdWEkIT7l4J96y1snBRuhQAADzB0Vo0S4OjZYdOkIp+whFO66OS0yJpWla6FAAAPMKRWi5Kmuae0vyKIOOklmvWrPOz89b6EQAAAJAEVoizeRU/tE8Q1cTRYjMNyh5XbZMhoFDAcBCoQgtTvv5gfqjX7OaYYphfZLSwyMwcCgAWDQUoQXheF5RVDNSW8LyBtbeKWb9ehcXJ6FDAQAIDEVoKQZHVMWHj1IDPTRFOQSvTspMoVn89AEAUISWob7pbKfiBKUdp6Ty4IzswGX+QicCAFgoUISL3JTekHu8aLLtFMXzYnff5A3rrK3lQocCAFhAUISLWe/ASMWhw/ToJYqm3aOTYuKjKAyfDQDwn1CEi1ZFdVNvWT6t19FWtuHr1nt7uwudCABgIUIRLkKaSW3B13n67haaELnfspRbsiVisdChAAAWKBThYtPZc6n+yGFKM0JYkV9SRlh4iNCJAAAWtBspwsnJyffff//cuXPx8fEbN26cXs7zfFlZWUFBwfj4eHh4+MaNG2marqqqqqmpmV5n+/btUikm95kTPCFFZQ3DlQUUp6fsXRJu3eDsZC90KACAhe5GRli+44479u/f7+7uvnv37t/+9rfTy8vLy7dt2zY0NCSTyX7xi1/ce++9hJCDBw+++eab1f+i1+tNlh1mGBvXfbn/a2X5SYrT2y1bdcu930ELAgBcj1nvEVZUVFRVVfX09MhkspSUlJycnF27dslkMkJIeHh4a2urcfqCLVu2BAUFvfHGG4SQ7OzsV1991eTRYVrruYuNx75mx0doVhSQlhkcGix0IgAAszHrPcL8/PzU1FRj80VFRTEMc+rUKeNdUql0ehIfg8FA07TxU9Dm5uZXXnll7969ExMTpksOhBDCcXxuYU3TF/9kx0dEjs6J93wXLQgAMCuz3iPs7e11dXWd/tLNza23t/eydXie/9GPfvToo4/a2Ng4OTm5u7v39fV99tlnP//5z0tLS11cXGauPDEx8eKLL87cJiHkBz/4QWBg4Lef3WAw6HQ6CpOnE0IIGdVMlhzLoy92UYTYLlsZk5rIsOzk5OScPunk5KRIJJrTp4Cr0Gq1NE0bDAahg1guvAWENTk5yTDM9beAWCy+5jSrsy5ClmU5jpv+cmpq6rLfCZ7nd+7cqVKpXn75ZULID3/4w+nlOTk5r7zyyosvvjhzfYZhAgMDlyxZMnOhnZ3dFX/VaJrmeR6/hYSQls7e1pNH6UkVJZEuT8sKXB4wP88rEonw+guI4ziapvEjEBDeAsIyvv7XX4TXs+asi9DLy6upqcl422AwXLx40dPTc+YKP/7xj6uqqo4fPy6X/8dQXhRFpaSkNDY2XrZBsVh81113xcXFXWcAhmEYhplt7MWE4/mCgsqx+lKG50UuXkm3rre1tZ63Z8frLyyGYWiaxo9AQHgLCMv4+pv2c8FZHyNcv369QqEYGBgghJw4ccLGxiY8PHxgYKC6upoQ8otf/CIvL+/rr7+2tbU1rq/T6Yw39Hr9sWPHQkJwWdtNGR7VfPXpAVVdCcUTp1XR6767ZT5bEABg8Zn1HuHy5cvvvffelJSU9PT0zz///OWXX2ZZ9siRI7/+9a/fe++9F154ISoq6jvf+Y5x5TfffHPLli3+/v6Ojo4lJSVWVla7du0y9bdgQZrbe86cPEJPqimpPDhrTWCgn9CJAADMHsXz/A08rLCwsKOjIy4uLjg4mBAyMDDQ3d3t5+dXW1s7c7XY2NiRkZHq6urR0dGAgICkpKRvH7SMi4t74403rvOjUePJMsZzVi0Kx/EFRdVjp4opnhe5eiVtWGdrayNIEpVKZWMjzFMD+dfJMjhGJSC8BYSlVqutrKxM+9HoDQ6xlpKSkpKSMv2li4uL8VzQ7Ozsy9a0tbX19fW94XxACBlRTSgOHyP9nRRFOYXFJKYn4rxZAABTwVijC92Zrv6mY4eZiTFKIgvOWhMYtFToRAAAiwqKcOHiCSkoqRupUjC8QeTikXTrBpwXAwBgcijCBWpsQpt/6AS50EYT4hgSnpiVQtM4YxsAwPRQhAvR2Z6B+iOHaM0IzYqDMrKXhywTOhEAwKKFIlxYeJ6UVjddKs2lOT1r7xJ/2wZHR0wiAQAwh1CEC8iETn/ySAHX2UATYrssNCUnnWHxAwIAmFv4O7tQ9A6MlH91iBkboFl2SWL6qohQoRMBAFgEFOGCUFPfel5xgjHoaGv72A3rXd1dr/0YAAAwBRShwPQcn3u8aOJMDcXz8iXLUtdni8VioUMBAFgQFKGQlKoJxRdfUkO9FM14xqVEx4ULnQgAwOKgCAVzpqu/+ehX9KSaklmvXrfe19fz2o8BAABTQxEKgOeJoqxeWVlA8waxi2fK7bdaWcuv/TAAAJgDKML5NqHTnzx0kutupglxDF6dlJ1GfWtGDgAAmDcownnVO6Cs+OoremyIYkWBaZnBocFCJwIAsHQowvlTd7qjM/8YrdfSNg5xt97q4uokdCIAAEARzguO5/NzS9WnK2mel/kGpq5fI5HgGgkAgAUBRTjn1JO6vC8O8/1dhKJco5PjE6MIptUFAFgwUIRzq+eisuqrg7RaScTSkJz1gYG+QicCAID/gCKcQzWNZ7sLjtJ6LePgnHjbbQ4OdkInAgCAy6EI5wTH8bl55ZrGcprwVkuCUjesEYlEQocCAIArQBGannpCm/vlUdJ3lqJoj5ikmHgcFAQAWLhQhCbW0z9cfehLSq0kYumqteuX+uOgIADAgoYiNKW6prNduUcog462d066HQcFAQDMAIrQNHieLyioGKsrowgvW7IsbcMasQivLQCAGcAfaxOY1OlPfnXccP4MIZRLdHICrhQEADAfKMKbNaDUFB38ghm5RLHiZdnrli/3FzoRAADMAorwprSe6z/99VeMVk1b2cXcdpubm7PQiQAAYHZQhDeuvKqpvzSX4fQSV6+U2zfIrTCnIACA+UER3giO508eK55oqaIIsVu2KnVtBuYUBAAwUyjCWdNM6HIPfs33dxKa9klMj4gKEzoRAADcOBTh7FwcGi09+CU9NkjE0lVrNyz19xE6EQAA3BQU4Sy0nr3QfOwQrR2nbR0T7rjdydFe6EQAAHCzUITXq6rqdG9JLsUbRB5+GbffIpVKhE4EAAAmgCK8Np7weceL1U1VhBCb4Ij0nBSKwqkxAACLBIrwGrS6qZNfHdWfbyc07ZWQERW9SuhEAABgSijCqxkZG1d8cZAM9xORJGTNBswvDwCw+KAI/6uefmXVwQP0xCixsou9/XZ3VyehEwEAgOmhCK+sqb2n9dhX9NQk6+SeducdVlYyoRMBAMCcQBFeQXldW7/iKM3ppT6BmbevY1m8SgAAixb+xP8Hnie5iir1qWKK8PbBq1Oy0zB2GgDA4oYi/De9gTt2OFd/tpEilFdsclRCtNCJAABgzqEIv6GZ0OZ+8RV/8TzFsEGZa1eEBAmdCAAA5gOKkBBChsfGCz8/QI1cIhJ55K13eHm7CZ0IAADmCYqQXLg0UvHF58z4KGVtn7TpTkcHO6ETAQDA/LH0Imzvvth46ACjm2Ad3dLuvN3K2kroRAAAMK8sugjrW851nviKNkxJPf0yNm4QiURCJwIAgPlmuUVYXtPcX3yc4jhr/+CMDTm4TAIAwDJZaBEWFFaP1BZRPO8UGpWUmUwoSuhEAAAgDIsrQp7nTxxVTJyppQjlFZ8aFRcpdCIAABCSZRWhwcAd//KY7lwLoZmAjJyVoSuETgQAAAKzoCLUTelP7D+o7+/mWXHI2luDMKcSAABYThFOaHUnP/uCG7zAi2URt2709cEl8wAAQIiFFKF6fDLvs8955UUitY7dtNnDxUHoRAAAsFAs/iIcU03k79tHRgd5K7ukzZudHWyFTgQAAAvIIi9C5ahasW8/pRqmbBxTN2+yt7MWOhEAACwsi7kIB0fURZ99RmtGKHvnjM2bra0xyzwAAFxu0RbhwPBYyb7P6PEx2tE1Y/OdVnK0IAAAXMHiLMJB5WjJvn3U+Bjj6JZ51yaZTCJ0IgAAWKAWYRFeGhop3bePmlAxTh5ZW+6USsRCJwIAgIVrsY00PTA8VrJ/PzWhYpw9su7aiBYEAICrW1RFOKAcK963jx4fY5w8sjZvlErxiSgAAFzD4vlodHhEXbxvPz0+ik9EAQDg+i2SPcIx1UTh/v20ZoRxdMvEJ6IAAHDdFkMRaiZ1efs/p1TDtK1T+uY7ZfhEFAAArpvZF6FWbzix/yA1comytk+7a5OVXCp0IgAAMCfmfYyQ4/gTX52gBnpoqTxh40YbGyuhEwEAgJkx7z3Co0cLDeeaKVYcfcedTk72QscBAADzY8ZFqCiumWqtoWhm1fpb3d1dhI4DAABm6QaLcGpq6r/dZTAYOI67/vVvTF3dmZGqQkJR/qlZfksx1zwAANygWRdhf39/Z+6TOgAAB3ZJREFUZmamk5OTi4vLnj17Zt6l1+u/973vOTg42NvbP/HEE8Y67Ovry8jIuOL6N6zrXG+X4hghvGtU0srVISbZJgAAWKZZF+GPf/xjPz8/pVJ59OjRnTt3njt3bvqu9957r6Kioqenp6ur68iRI59++ikhZNeuXf7+/kql8siRIzt37uzu7r7JxOMTk/XHjlCcQb5sdXxS9E1uDQAALNzsilCtVu/bt+9nP/sZwzCRkZE5OTkfffTR9L0ffPDBzp07bW1tHR0dH3nkkQ8++EClUu3fv9+4flRUVHZ29sz1b0zpCQUZH6Mc3NJyUm9yUwAAALMrwu7uboPBEBQUZPwyJCSkvb19+t729vaQkJCZd3V3d/M8HxgYeMX1jXieHxsbG/5Per3+igGqqk7rL3TwIkn8retFLDOr8AAAAN82u+sIR0ZGrKysKIoyfmljYzM8PDzzXmtr6+m7lErlt9c/ffr0ZdscGxvbvHkzw/xHq+3duzc+Pv7bAXz9PHrbvL2CQ2RiRq1Wzyo8mIRGo5n+gcL802q1NE2LRCKhg1guvAWEpdFoeJ6//h+BXC6n6Wvs8s2uCJ2dnVUqFcdxxu0qlUo3N7eZ946Ojhpvj4yMuLq6Xn19Izs7uz179sTFxV1PAJlMtm7zbTIZppsXDM/z0//uwPwTiUQoQmHhLSC4mftXJjG7j0Z9fHzkcnl9fb3xy1OnTq1YsWL63uDg4Nra2pl3+fr6ymSyhoaGK64PAAAguNkVoUwm27Zt2y9/+cv+/v79+/eXlpZu3bqV47i1a9e2trZ+73vfe+2111paWhoaGv70pz9973vfk8lkW7duffrpp/v7+/ft21dWVrZ169Y5+k4AAABuwKzHGv3973//ox/9KDY21t3dfd++fa6urhzHabVanufvueeerq6u22+/nWGY3bt3r1+/nhDy0ksvGdf38PDYv3+/iwuGgAEAgAWE4nle2ARxcXFvvPHGdR4jNBgMOp0OxwgFpFKpbGxshE5huXCyjODwFhCWWq0W+Bih4HJzc//4xz8KncKibd26VavVCp3Ccu3Zs+fAgQNCp7Bc/f39O3fuFDqFRXv++edrampMu00zK8Lz589Pn3oDgjh+/LjBYBA6heVqbm4+e/as0Cks1/j4eEFBgdApLFp1dfWlS5dMu00zK0IAAADTQhECAIBFE/5kmf/3//7foUOHWPa6zl/V6XRTU1NWVpiJXjBKpdLe3h4jawhlYmKCoiipVCp0EAvFcZxKpbKzsxM6iOVSqVRSqfT6zxc7evTo9Nif/43wRTg5OTkwMCBsBgAAWJTc3d2v2ZrCFyEAAICAcIwQAAAsGooQAAAsmjkV4ZEjR9asWZOcnPzGG2/gE915xnHcJ5988uMf//juu+/u6OgQOo4lOnHixP3335+YmHjrrbd+9tlnQsexOL29vQ8//HBKSkpycvJPfvKTwcFBoRNZqMnJyfvvv/+ll14y4TZnPdaoUJqbm+++++733nvP29t727ZtNjY2DzzwgNChLMjU1NSHH34YFRV18ODBJ598Uug4lujLL7+MjY195JFHOjs7H3roIZFIdMcddwgdyoLodLro6OgHHniA5/kXX3zxnnvuOXHihNChLNGvfvUrhUKhVCpNuE2zOVnmiSeeUKvVf/nLXwghH3300R/+8Ifq6mqhQ1kia2vr/Pz86OhooYNYtB07dvA8/3//939CB7FQlZWV6enpGo1G6CAWp7a2dufOnevXr6+oqPjiiy9MtVmz+Wi0vr5+emDu2NjY+vp6juOEjQQglIaGhqCgIKFTWKLOzs6GhobXXntty5YtQmexODqd7qGHHnrzzTcZhjHtls3mo9FLly7Z29sbbzs6Our1+qGhIUzqBBbo9ddfv3jx4o4dO4QOYonWrl07NjYmk/3/du7XdXEwgOP4niSnODAYZtlg/gMi/geCDP8AYRiNZoPBJggGm00waBGGxSIINpNRyzAsiCDKoeAvUPAb5K7ewfl17J73Ky2NDwi+2SPzxxsfR/CX6vW6ZVmpVGo8Hr/3zoEJYTQavVwur+vT6SSEUFXV30nA5/V6vWazOZ1Ow+Gw31tk5LquoijdbjebzXqex6fwMcvl0nGc+Xz+HTcPTAgNw1itVq/r1WqlaVooFPJ3EvBhg8GgUqlMJhPORf1VLBZLpZLneX/87y68y2Kx2Gw2iURCUZTb7fZ4PJLJ5O8o/KPA/EZo23a/3z8cDs/ns91u27bt9yLgo4bDYblcHo1GfPn6wnXd4/GoKMrz+ex0Oqqqmqbp9yiJFAqFn7/UajXLst5VQSVAIczn87lczjRNXdf3+321WvV7kXRM0xRCnM/nTCYjhFiv134vkkuj0djtdul0WgghhODdiQ+bzWaGYei6Ho/HW62W4zgcSv03AvP6xMvhcLher5qm+T0EgHTu9/t2u41EIrFYzO8teKeAhRAAgPcKzNEoAADfgRACAKRGCAEAUiOEAACpEUIAgNQIIQBAaoQQACA1QggAkBohBABIjRACAKRGCAEAUiOEAACpEUIAgNS+AIzQo8p2Q5J8AAAAAElFTkSuQmCC"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exercise2(m_ex, shocks, m.grid, m.u.(m.grid), sim_length=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The policies are indeed close."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution to Exercise 4\n",
    "\n",
    "Here’s the code.\n",
    "\n",
    "It assumes that you’ve just run the code from the previous exercise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "coleman (generic function with 1 method)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function bellman(m, shocks)\n",
    "    @unpack grid, β, u, ∂u∂c, f, f′ = m\n",
    "    bellman_single_arg(w) = T(w, grid, β, u, f, shocks)\n",
    "    iterate_updating(bellman_single_arg, u.(grid), sim_length = 20)\n",
    "end\n",
    "function coleman(m, shocks)\n",
    "    @unpack grid, β, ∂u∂c, f, f′ = m\n",
    "    coleman_single_arg(g) = K(g, grid, β, ∂u∂c, f, f′, shocks)\n",
    "    iterate_updating(coleman_single_arg, grid, sim_length = 20)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  153.31 MiB\n",
       "  allocs estimate:  89472\n",
       "  --------------\n",
       "  minimum time:     360.784 ms (4.25% GC)\n",
       "  median time:      371.484 ms (4.14% GC)\n",
       "  mean time:        371.766 ms (4.42% GC)\n",
       "  maximum time:     379.611 ms (5.34% GC)\n",
       "  --------------\n",
       "  samples:          14\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark bellman(m_ex, shocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  153.31 MiB\n",
       "  allocs estimate:  89472\n",
       "  --------------\n",
       "  minimum time:     356.676 ms (4.31% GC)\n",
       "  median time:      369.395 ms (4.22% GC)\n",
       "  mean time:        369.309 ms (4.51% GC)\n",
       "  maximum time:     382.332 ms (5.42% GC)\n",
       "  --------------\n",
       "  samples:          14\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark bellman(m_ex, shocks)"
   ]
  }
 ],
 "metadata": {
  "date": 1589496355.3399575,
  "download_nb": 1,
  "download_nb_path": "https://julia.quantecon.org/",
  "filename": "coleman_policy_iter.rst",
  "filename_with_path": "dynamic_programming/coleman_policy_iter",
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