{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Job Search IV: Modeling Career Choice\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Job Search IV: Modeling Career Choice](#Job-Search-IV:-Modeling-Career-Choice) \n", " - [Overview](#Overview) \n", " - [Model](#Model) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "Next we study a computational problem concerning career and job choices.\n", "\n", "The model is originally due to Derek Neal [[Nea99]](../zreferences.html#neal1999).\n", "\n", "This exposition draws on the presentation in [[LS18]](../zreferences.html#ljungqvist2012), section 6.5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model features\n", "\n", "- Career and job within career both chosen to maximize expected discounted wage flow. \n", "- Infinite horizon dynamic programming with two state variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model\n", "\n", "In what follows we distinguish between a career and a job, where\n", "\n", "- a *career* is understood to be a general field encompassing many possible jobs, and \n", "- a *job* is understood to be a position with a particular firm \n", "\n", "\n", "For workers, wages can be decomposed into the contribution of job and career\n", "\n", "- $ w_t = \\theta_t + \\epsilon_t $, where \n", " \n", " - $ \\theta_t $ is contribution of career at time $ t $ \n", " - $ \\epsilon_t $ is contribution of job at time $ t $ \n", " \n", "\n", "\n", "At the start of time $ t $, a worker has the following options\n", "\n", "- retain a current (career, job) pair $ (\\theta_t, \\epsilon_t) $\n", " — referred to hereafter as “stay put” \n", "- retain a current career $ \\theta_t $ but redraw a job $ \\epsilon_t $\n", " — referred to hereafter as “new job” \n", "- redraw both a career $ \\theta_t $ and a job $ \\epsilon_t $\n", " — referred to hereafter as “new life” \n", "\n", "\n", "Draws of $ \\theta $ and $ \\epsilon $ are independent of each other and\n", "past values, with\n", "\n", "- $ \\theta_t \\sim F $ \n", "- $ \\epsilon_t \\sim G $ \n", "\n", "\n", "Notice that the worker does not have the option to retain a job but redraw\n", "a career — starting a new career always requires starting a new job.\n", "\n", "A young worker aims to maximize the expected sum of discounted wages.\n", "\n", "\n", "\n", "$$\n", "\\mathbb{E} \\sum_{t=0}^{\\infty} \\beta^t w_t \\tag{1}\n", "$$\n", "\n", "subject to the choice restrictions specified above.\n", "\n", "Let $ V(\\theta, \\epsilon) $ denote the value function, which is the\n", "maximum of [(1)](#equation-exw) over all feasible (career, job) policies, given the\n", "initial state $ (\\theta, \\epsilon) $.\n", "\n", "The value function obeys\n", "\n", "$$\n", "V(\\theta, \\epsilon) = \\max\\{I, II, III\\},\n", "$$\n", "\n", "where\n", "\n", "\n", "\n", "$$\n", "\\begin{aligned}\n", "& I = \\theta + \\epsilon + \\beta V(\\theta, \\epsilon) \\\\\n", "& II = \\theta + \\int \\epsilon' G(d \\epsilon') + \\beta \\int V(\\theta, \\epsilon') G(d \\epsilon') \\nonumber \\\\\n", "& III = \\int \\theta' F(d \\theta') + \\int \\epsilon' G(d \\epsilon') + \\beta \\int \\int V(\\theta', \\epsilon') G(d \\epsilon') F(d \\theta') \\nonumber\n", "\\end{aligned} \\tag{2}\n", "$$\n", "\n", "Evidently $ I $, $ II $ and $ III $ correspond to “stay put”, “new job” and “new life”, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameterization\n", "\n", "As in [[LS18]](../zreferences.html#ljungqvist2012), section 6.5, we will focus on a discrete version of the model, parameterized as follows:\n", "\n", "- both $ \\theta $ and $ \\epsilon $ take values in the set `linspace(0, B, N)` — an even grid of $ N $ points between $ 0 $ and $ B $ inclusive \n", "- $ N = 50 $ \n", "- $ B = 5 $ \n", "- $ \\beta = 0.95 $ \n", "\n", "\n", "The distributions $ F $ and $ G $ are discrete distributions\n", "generating draws from the grid points `linspace(0, B, N)`.\n", "\n", "A very useful family of discrete distributions is the Beta-binomial family,\n", "with probability mass function\n", "\n", "$$\n", "p(k \\,|\\, n, a, b)\n", "= {n \\choose k} \\frac{B(k + a, n - k + b)}{B(a, b)},\n", "\\qquad k = 0, \\ldots, n\n", "$$\n", "\n", "Interpretation:\n", "\n", "- draw $ q $ from a β distribution with shape parameters $ (a, b) $ \n", "- run $ n $ independent binary trials, each with success probability $ q $ \n", "- $ p(k \\,|\\, n, a, b) $ is the probability of $ k $ successes in these $ n $ trials \n", "\n", "\n", "Nice properties:\n", "\n", "- very flexible class of distributions, including uniform, symmetric unimodal, etc. \n", "- only three parameters \n", "\n", "\n", "Here’s a figure showing the effect of different shape parameters when $ n=50 $.\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots, QuantEcon, Distributions\n", "gr(fmt=:png);\n", "\n", "n = 50\n", "a_vals = [0.5, 1, 100]\n", "b_vals = [0.5, 1, 100]\n", "\n", "plt = plot()\n", "for (a, b) in zip(a_vals, b_vals)\n", " ab_label = \"a = $a, b = $b\"\n", " dist = BetaBinomial(n, a, b)\n", " plot!(plt, 0:n, pdf.(dist, support(dist)), label = ab_label)\n", "end\n", "plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implementation:\n", "\n", "The code for solving the DP problem described above is found below:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "get_greedy (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function CareerWorkerProblem(;β = 0.95,\n", " B = 5.0,\n", " N = 50,\n", " F_a = 1.0,\n", " F_b = 1.0,\n", " G_a = 1.0,\n", " G_b = 1.0)\n", " θ = range(0, B, length = N)\n", " ϵ = copy(θ)\n", " dist_F = BetaBinomial(N-1, F_a, F_b)\n", " dist_G = BetaBinomial(N-1, G_a, G_b)\n", " F_probs = pdf.(dist_F, support(dist_F))\n", " G_probs = pdf.(dist_G, support(dist_G))\n", " F_mean = sum(θ .* F_probs)\n", " G_mean = sum(ϵ .* G_probs)\n", " return (β = β, N = N, B = B, θ = θ, ϵ = ϵ,\n", " F_probs = F_probs, G_probs = G_probs,\n", " F_mean = F_mean, G_mean = G_mean)\n", "end\n", "\n", "function update_bellman!(cp, v, out; ret_policy = false)\n", "\n", " # new life. This is a function of the distribution parameters and is\n", " # always constant. No need to recompute it in the loop\n", " v3 = (cp.G_mean + cp.F_mean .+ cp.β .*\n", " cp.F_probs' * v * cp.G_probs)[1] # do not need 1 element array\n", "\n", " for j in 1:cp.N\n", " for i in 1:cp.N\n", " # stay put\n", " v1 = cp.θ[i] + cp.ϵ[j] + cp.β * v[i, j]\n", "\n", " # new job\n", " v2 = (cp.θ[i] .+ cp.G_mean .+ cp.β .*\n", " v[i, :]' * cp.G_probs)[1] # do not need a single element array\n", "\n", " if ret_policy\n", " if v1 > max(v2, v3)\n", " action = 1\n", " elseif v2 > max(v1, v3)\n", " action = 2\n", " else\n", " action = 3\n", " end\n", " out[i, j] = action\n", " else\n", " out[i, j] = max(v1, v2, v3)\n", " end\n", " end\n", " end\n", "end\n", "\n", "\n", "function update_bellman(cp, v; ret_policy = false)\n", " out = similar(v)\n", " update_bellman!(cp, v, out, ret_policy = ret_policy)\n", " return out\n", "end\n", "\n", "function get_greedy!(cp, v, out)\n", " update_bellman!(cp, v, out, ret_policy = true)\n", "end\n", "\n", "function get_greedy(cp, v)\n", " update_bellman(cp, v, ret_policy = true)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code defines\n", "\n", "- a named tuple `CareerWorkerProblem` that \n", " \n", " - encapsulates all the details of a particular parameterization \n", " - implements the Bellman operator $ T $ \n", " \n", "\n", "\n", "In this model, $ T $ is defined by $ Tv(\\theta, \\epsilon) = \\max\\{I, II, III\\} $, where\n", "$ I $, $ II $ and $ III $ are as given in [(2)](#equation-eyes), replacing $ V $ with $ v $.\n", "\n", "The default probability distributions in `CareerWorkerProblem` correspond to discrete uniform distributions (see [the Beta-binomial figure](#beta-binom)).\n", "\n", "In fact all our default settings correspond to the version studied in [[LS18]](../zreferences.html#ljungqvist2012), section 6.5.\n", "\n", "Hence we can reproduce figures 6.5.1 and 6.5.2 shown there, which exhibit the\n", "value function and optimal policy respectively.\n", "\n", "Here’s the value function" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem()\n", "v_init = fill(100.0, wp.N, wp.N)\n", "func(x) = update_bellman(wp, x)\n", "v = compute_fixed_point(func, v_init, max_iter = 500, verbose = false)\n", "\n", "plot(linetype = :surface, wp.θ, wp.ϵ, transpose(v), xlabel=\"theta\", ylabel=\"epsilon\",\n", " seriescolor=:plasma, gridalpha = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal policy can be represented as follows (see [Exercise 3](#career-ex3) for code).\n", "\n", "\n", "\n", "\n", "\n", " \n", "Interpretation:\n", "\n", "- If both job and career are poor or mediocre, the worker will experiment with new job and new career. \n", "- If career is sufficiently good, the worker will hold it and experiment with new jobs until a sufficiently good one is found. \n", "- If both job and career are good, the worker will stay put. \n", "\n", "\n", "Notice that the worker will always hold on to a sufficiently good career, but not necessarily hold on to even the best paying job.\n", "\n", "The reason is that high lifetime wages require both variables to be large, and\n", "the worker cannot change careers without changing jobs.\n", "\n", "- Sometimes a good job must be sacrificed in order to change to a better career. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Using the default parameterization in the `CareerWorkerProblem`,\n", "generate and plot typical sample paths for $ \\theta $ and $ \\epsilon $\n", "when the worker follows the optimal policy.\n", "\n", "In particular, modulo randomness, reproduce the following figure (where the horizontal axis represents time)\n", "\n", "\n", "\n", " \n", "Hint: To generate the draws from the distributions $ F $ and $ G $, use the type [DiscreteRV](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/discrete_rv.jl).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Let’s now consider how long it takes for the worker to settle down to a\n", "permanent job, given a starting point of $ (\\theta, \\epsilon) = (0, 0) $.\n", "\n", "In other words, we want to study the distribution of the random variable\n", "\n", "$$\n", "T^* := \\text{the first point in time from which the worker's job no longer changes}\n", "$$\n", "\n", "Evidently, the worker’s job becomes permanent if and only if $ (\\theta_t, \\epsilon_t) $ enters the\n", "“stay put” region of $ (\\theta, \\epsilon) $ space.\n", "\n", "Letting $ S $ denote this region, $ T^* $ can be expressed as the\n", "first passage time to $ S $ under the optimal policy:\n", "\n", "$$\n", "T^* := \\inf\\{t \\geq 0 \\,|\\, (\\theta_t, \\epsilon_t) \\in S\\}\n", "$$\n", "\n", "Collect 25,000 draws of this random variable and compute the median (which should be about 7).\n", "\n", "Repeat the exercise with $ \\beta=0.99 $ and interpret the change.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "As best you can, reproduce [the figure showing the optimal policy](#career-opt-pol).\n", "\n", "Hint: The `get_greedy()` method returns a representation of the optimal\n", "policy where values 1, 2 and 3 correspond to “stay put”, “new job” and “new life” respectively. Use this and the plots functions (e.g., `contour, contour!`) to produce the different shadings.\n", "\n", "Now set `G_a = G_b = 100` and generate a new figure with these parameters. Interpret." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem()\n", "\n", "function solve_wp(wp)\n", " v_init = fill(100.0, wp.N, wp.N)\n", " func(x) = update_bellman(wp, x)\n", " v = compute_fixed_point(func, v_init, max_iter = 500, verbose = false)\n", " optimal_policy = get_greedy(wp, v)\n", " return v, optimal_policy\n", "end\n", "\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "F = DiscreteRV(wp.F_probs)\n", "G = DiscreteRV(wp.G_probs)\n", "\n", "function gen_path(T = 20)\n", " i = j = 1\n", " θ_ind = Int[]\n", " ϵ_ind = Int[]\n", "\n", " for t=1:T\n", " # do nothing if stay put\n", " if optimal_policy[i, j] == 2 # new job\n", " j = rand(G)[1]\n", " elseif optimal_policy[i, j] == 3 # new life\n", " i, j = rand(F)[1], rand(G)[1]\n", " end\n", " push!(θ_ind, i)\n", " push!(ϵ_ind, j)\n", " end\n", " return wp.θ[θ_ind], wp.ϵ[ϵ_ind]\n", "end\n", "\n", "plot_array = Any[]\n", "for i in 1:2\n", " θ_path, ϵ_path = gen_path()\n", " plt = plot(ϵ_path, label=\"epsilon\")\n", " plot!(plt, θ_path, label=\"theta\")\n", " plot!(plt, legend=:bottomright)\n", " push!(plot_array, plt)\n", "end\n", "plot(plot_array..., layout = (2,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "The median for the original parameterization can be computed as follows" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.0" ] } ], "source": [ "function gen_first_passage_time(optimal_policy)\n", " t = 0\n", " i = j = 1\n", " while true\n", " if optimal_policy[i, j] == 1 # Stay put\n", " return t\n", " elseif optimal_policy[i, j] == 2 # New job\n", " j = rand(G)[1]\n", " else # New life\n", " i, j = rand(F)[1], rand(G)[1]\n", " end\n", " t += 1\n", " end\n", "end\n", "\n", "\n", "M = 25000\n", "samples = zeros(M)\n", "for i in 1:M\n", " samples[i] = gen_first_passage_time(optimal_policy)\n", "end\n", "print(median(samples))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute the median with $ \\beta=0.99 $ instead of the default value $ \\beta=0.95 $, replace `wp=CareerWorkerProblem()` with `wp=CareerWorkerProblem(β=0.99)`.\n", "\n", "The medians are subject to randomness, but should be about 7 and 14 respectively. Not surprisingly, more patient workers will wait longer to settle down to their final job." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "14.0" ] } ], "source": [ "wp2 = CareerWorkerProblem(β=0.99)\n", "\n", "v2, optimal_policy2 = solve_wp(wp2)\n", "\n", "samples2 = zeros(M)\n", "for i in 1:M\n", " samples2[i] = gen_first_passage_time(optimal_policy2)\n", "end\n", "print(median(samples2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Here’s the code to reproduce the original figure" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem();\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "lvls = [0.5, 1.5, 2.5, 3.5]\n", "x_grid = range(0, 5, length = 50)\n", "y_grid = range(0, 5, length = 50)\n", "\n", "contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,\n", " fillalpha=1, cbar = false)\n", "contour!(xlabel=\"theta\", ylabel=\"epsilon\")\n", "annotate!([(1.8,2.5, text(\"new life\", 14, :white, :center))])\n", "annotate!([(4.5,2.5, text(\"new job\", 14, :center))])\n", "annotate!([(4.0,4.5, text(\"stay put\", 14, :center))])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we need only swap out for the new parameters" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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8q1cuBw0YtHvXDtHHNTQ0uvfoeSnqYn3m8RMmDh8x8rv+2aQD55dffmE2wa79h7OycziarZmNASCNKI4cUWvBqyUpZze/LcgxtHHWMbey9PS7dyN67dKfW1tatmjZkumMTYSCokJtbe3Dhwk3b1y/fetmaWmph2fXnbv3OTm7iAb49vVXUVVVVVWtrKqqq6tzadfO3t6ht0+fkuLilJQnV69cfvQo0dnFZf+hIzwer6iw0LevX/PmJqLPcjic58+exT+4P2XqdM+uP3w2TNTFC7Gxd5cuX+ndu8+ZUydPnTrx/Pkzt87uew8ccnZpJxrD5XJ9+/plZLy8f//e/fv3qqqqfpo5e9HipRcvnG/ZqlVg/yBCiG9fP1U1tfrMzi7t7B0cJfP3Y0ZqaoqGupqhoeGnh1GiK5cY1Lln39t37stY+DEbA0C68WuEb+7S1Tk/TFhs1s6TEJKdGHNr2xK39q7rf1+vq6fHdL6mg8/n19XVycnJfdGnqqur5eXl/+tdgUBgZ9M6Pf1F6tN0I2Pjz37bjOlT/9i4/ljEKZ8+voQQHo/H4XDevafwPZWVlYqKil8UuGk4feqkmYmxs7PTp4fhHCFAk8CRowzc+bruUX8s/meRUrv2AWsjXlNqdvZtdu7cwfg/eZsMDofzpS1ICPlECxJCTkQcf/bsaUBgf3Fa8EOysrKfaEFCCDtbUHwoQoCmg1YyoM0D3hSRA1P8Es7s5XBlXAZP9Vqw7df1f3bx6CJaygQaj5qamrA1q2bP/GnC+LFycnKz585nOhFLoQgBmhaKprQdKJM+cSePHJk5qCjzmZappe+y/coO3Tp17IBFShuV6urqBfPmrP/9N0UlpZ2799nYtGE6EUvhHCFAkyUoTBYW3LfzGuQ6MIQjI1dRnH93169vs9O2btnq4dmV6XRAhEJhSUkJl8v90ut7Kysra2pqlJWVxVmAhs1wjhCA7WgtG9o8MOnG9X0TfV4lxSpp6HSdvtZ20PQhw0cMHz6sqLCQ6YBsR1GUhobGV9zloqioqKGhgRb8XlCEAE2ZaJHSGhWHyF+nRf0+p/ptqZmLZ8DaiGflQnsH2+PHwpkOCMA8FCFA00ermtIW/V+mZu0N8Uq9HimrqNxx9PwuU9fOmL+wt09v0QKVAKyFIgRgB1qG0u9ImvX8e9f68DlDSl6/1Ld08F99tFq3lbNL2/Xr12GRUmAtFCEAi4gWKS2qUDk8Y0DMwY1CodCx3zjfZQc27w9v59ru4cMEpgMCMABFCMAyFE1r29JmfolXLh6c4p+Xlqhm0Lz3oh3Newzr2avnlCmTRQ+MBWAPFCEAG1GyqpSxV4WsxYlfxl3buqy2utKiY8/+607fTX9ja9cm6uIFpgMCNBwUIQB7cdRbcVr0T3vwaG+I98t71+SUVd3GLWofvGTshND+QYH5b94wHRCgIaAIAdiNI08ZuNdpd7y4YVHkysmVJQXNbFz814Tn0pq2dm12797F+JobAJKGIgQAQis3o80CXmWX7Zvok3TxCFdGznXoNK8FW5evXe/h6fH0aRrTAQEkCEUIAIQQQmgOretCmfS5c3TP4RkD/lmkdMUBBevOnTp1XLZ0CY/HYzoigESgCAHg/1Fy6qR57zKBfvicoTd3hwnqatt4D+m3Jjz80nXHtg53bt9iOiDA94ciBID3UeqWlHnAk5jYvRN6ZyfGKGvpd5+1sXVAaMCAAVikFJoeFCEAfAQlo0gMuvBUHCJXTY/6fW7N2zIzF8/AtRHPK2g7+zb79+1lOiDAd4MiBID/RKuZcVoEvUzN3DvB++mNs7KKKh1Gzukyde2CpSu8e3tnZmQwHRDgO0ARAsAn0TKUfkehQder29dG/Dyq7M0rg9aO/daEV+u2cmnntGHD71ikFKQdihAAPo9S1KPM/POL6YNT/B+c2EkI1TYguM+y/Zv3HWnfwTUx8SHTAQG+XgMVYVFRUe/evVevXt0w0wHA90fRtI4jbe5/LzLiwOS+eU8fqRuYeC/code5X/ce3WfPnlVZWcl0RICv0UBFOHXq1OfPnz9+/LhhpgMACaFkVanmXpVyrU4sGhu9cQGvurK1p3/g2hOXE9La2NpEX4piOiDAF2uIIjx37lxhYWHfvn0bYC4AaAC0mgWnRdCLx8/3ju/5IiZaQU3TY9JK13GLR4+fgEVKQepIvAjLyspmzpy5efNmiqIkPRcANByOHKXvxtftfOnPJWd/nVK/SGmBvIGtnc32bVuxSClIC4kX4U8//TRhwgRjY+P/GlBXWyfpDAAgIbSyEW0e8CqrdP9En+RL4VwZOaegCV4Ltq3a+Je7e+fU1BSmAwLbCQSCz46RbBH+/fff9+/fHzhwYHFxcXV1dU1NTWlp6XtjuDJciWYAAMmiuZSuC2nufevgtiOzBhe/eqFlaum7bJ+CjXvnzm7Lly+rra1lOiKwF01/vuYkW4Tp6emlpaXt2rVzdnbes2fP2bNn/f39JTojADCCkteiTH1LatSPzBh058AGAZ9v5zOs3+rwIxeuOrZ1iLlzm+mAAP9JskX4448/Pv9XcHBwv379rly5ItEZAYA5FK3VhrYITLp5c+8E7+zEGGVt/R6z/2jZZ5x/YMDEiRM+PCAE0Bg03A31CgoKioqKDTYdADCCklEk+l14qo5nV/90Ye3M6vISi449+q87dT+ruE0b65MnIpgOCPA+ivEruzr37Hv7zn0ZCz9mYwDAdyaoIwUPSNmzzqNmtvb0I4TkpMTf2rq4jWWLv/78y7h5c6bzQdN3+tRJMxNjZ2enTw/DEmsAIBk0l+i2Exh0vb57w4lFY8rzXxu0duy35li1nlXbtg5rVv+KRUqhkUARAoAE0Ur6lJn/m0JycIr/g1O7KYpy8Bvt9+vh3ccjXVycHjy4z3RAABQhAEgaRdM6jpRp33unww9M6Zf/4omavrHXgq0GXfr38uo1d+6cqqoqpiMCq6EIAaAhUHJqVHPvtxyT4wtG/r19ZW1NtdUP/QLXnrh4L9nW1ubK5WimAwJ7oQgBoOFwNCw5LYJS7yfuneCdGX9TUV2r65TVbUfMHT5q1LDhwwoLCpgOCGyEIgSAhsWRo/Td6rQ6Xli34NTicRWFec0d3QJ/O/WyRtbWzmbfvr2MX8oObIMiBAAG0MqGlJl/7pva/ZP7JpzZy5GVdR02o+e8LUvW/NbFwx2LlEJDQhECAENoLq3rTBl7x0bsOzp7SPGrdC1TS9/lB1Qcunfu7LZ48SIej8d0RGAFFCEAMIlS0KJM+5ZUqx2ZOfDu4T8FfL5V9/4BYcdPXr3r5Nz2bswdpgNC04ciBADGUbSWLW3e7+HlqP2hfXKePFDS1P1hxjqL3qP7+vuHTgotKytjOiE0ZShCAGgUKBllyqhHtaLN6WWh0X/8XFNR3qJTr/6/n76XUWDbxvrM6VNMB4QmC0UIAI0IrWZOtwhKT8ncG9Ir5epJOSUVt3GLOoX+OumnGf79/F6/esV0QGiCUIQA0MjQMkSnndCw+/U9f4gWKTW0dvJffaxY2cixrf1fm/4U55njAOJDEQJAY0Qp6FCmffOLZQ5O8b93bBvN4TgHTfRdduCP3QddXJzi4x8wHRCaDhQhADRWFE1ptaFMfR+cP3loemBBeoqaQXOvn7cZeg7o5eU1derkiooKpiNCU4AiBIBGjZJTp5p7lxOjY/N/vLFzVR2vxtKjb0DY8ZspWfb2ttGXopgOCFIPRQgAUoDWaE1bBD65e29PiJdokVKP0BWOw2aPGD16xIjhWKQUvgWKEACkA8VVoAw96jRdz/829/zq6VWlRSZO7oG/nXpeybW1szl4YD/TAUFaoQgBQJrQKsa0eWBmRvHeCd4JZ/Zy5eTaj5jZfc6mhStWde/RLT39BdMBQfqgCAFA2ogWKW3uHRux/+iswcXZL3TMrX1XHCKmTq7tXFav+rWuro7piCBNUIQAIJUoeS3K1LeEp3Vk5oCbu8OEAr69748BYccPnr/q2NYh9m4M0wFBaqAIAUB6UbSmNW0R+PjWjf2T++akxCtp6XWb8bul/wS/gIDg4HFYpBTEgSIEAOn2zyKlCtanl0688udCXmW5qYtnwNoTyYU1NjatI44fYzogNHYoQgBoCmg1c9qi/7NHaXvGez2/c0lOSaX9j3M6h66aOmtOv4B+Oa9fMx0QGi8UIQA0FRxZyqCzQN/j8uYVpxYHvy3MNbRxDgg7XqRo6OBov2XzJixSCh+FIgSAJoVWMqDM+uUVCPaH9rl3fBvN4TgPmOizePe6LbvcOnd6/DiZ6YDQ6KAIAaDJoWhK24E2848/f+rglH5vniVpGJn7LNmj5tzLw9Pj558XVFdXMx0RGhEUIQA0TZScGjH2eitjEbFwzLUty2prqmy6BwWuPXE+LrlNG+vL0ZeYDgiNBYoQAJoyWs2CtghMu5+wb2KfrIe36xcpHTZyZFBQIBYpBYIiBIAmj+IqUM08azWcz4XNPr/mp6qyIhMn96Dfz+RxNK1trLZv2yoUCpnOCExCEQIAK9AqzWnzwKz0/H0Tej+5coIrK+cyZFrPuZtWrtvQy6snFillMxQhALAGzaX0XIlRrxt7N4XPG1aak6nbok3flYcFxg6uri5hYauxSCk7oQgBgF0oBW3KrG9Rpdqhn/rfObBRKBTY9x3pt/Lwnoizzi5O9+7FMR0QGhqKEABYiKI1rWnzgKS/rxyY1Dc3NUFVz6jnvM0m3Yf69PGZMnXK27dvmU4IDQdFCAAsRckokWbdqhRtTi2dGL1xAa/ybUt3n/6/n7mfXWJtZXki4jjTAaGBoAgBgNVoVVPaPOBF8rM9IV4vYv5ZpNRt0qpps+f06ePzKjub6YAgcShCAGA9jhxl0Fmg1yV60/LTS8dXFOYZWjv1C4uo1mvt5Oy4ccPvWKS0aUMRAgAQIlqk1Lxfbi5v/yTfh5H7KZq29xvtvWjXH7v2u3V2e/LkMdMBQVJQhAAA/6I4lK4TZep798SBw9ODCl+mahpb+CzZo9a2h4dHl0WLfsYipU0SihAA4H9QcupUc58yoWH4vBHXtiyrq6mx6TmgX9jx0zfuOTjY3bj+N9MB4TtDEQIAfAStYUlbBKQ9eLhvYu/MhFtKGjo/TP/NZsDUAYOHjBo1sqioiOmA8N2gCAEAPo7iKlKGHrWa7S/8Ni9yxaSqsiIzF8+g9WeeV8nY2trs37eX6YDwfaAIAQA+hVZuRpn1e/26ct+E3kkXj4gWKe02+8/Fq9Z6dvV4+jSN6YDwrVCEAACfQ3MpnbbEqOftQ9uOzR9RmpulY27VZ/kBWcuOnTp1XLJ4UW1tLdMR4euhCAEAxEIp6FCmfoXlCoemBdw7toUQoW3vYX4rDx45f6VdO5cHD+4zHRC+EooQAEBsFEVr29Hm/R5cOHtgsl9eWqKqnrHXgq3G3QZ79+49ffo0LFIqjVCEAABfhpJVoYx7VspbnVwSIlqktFWXPoG/nbiZkmlra3P+3FmmA8KXQRECAHyNfxYpfZK+Z3yvZ7ej5FXU3Scscx23ODh00oABQXm5uUwHBHGhCAEAvhZHjtLrKND3uLx5xclFY98W5BrZugasjXgjp2fvYLtxw3osUioVUIQAAN+EVjKgzQPeFJEDU/ziT++lOVynoAk+S/b+te8IFimVCihCAIBvRtGUtgPV3Cfu5MEjMwcVZj5VNzT1Xrhdq0NfD0+POXNm19TUMB0R/hOKEADg+6DkNSiTPqV1OuFzht7a+xu/jmfp4dtvdfjFmAQHB7ubN64zHRA+DkUIAPA90ZrWtHlg8s1beyf0zn50V0lT94cZv1v3nxw0aNDYsaOLi4uZDgjvQxECAHxnlIwi1awrT7Xt2VXTI1dOqiorMmvXNXDdqeTCWltb6/CjR5gOCP8DRQgAIBG0qgltEfQ6u2xviHfSxaOy8oodR831/Gn9rIW/eHl7Zbx8yXRA+AeKEABAYmgupduOMva6fXjb0TlDil+l67W09V8VLjBxdGnnvHr1r3V1dUxHBHfUpgsAACAASURBVBQhAICEUQralIlvcaXqkZkDYw5tFAoFokVK95445+TcNi4ulumAbIciBACQPIqmtW1pM//Ey1EHp/bLe/pIVc+41/wt5t6jevv4BAePKy8vZzoiezVQEVZUVAiFwoaZCwCgcaJkVSjjXpUyFicWjb22eQmvqsKiY8+gdScfZBbY2bW5cP4c0wFZSuJFuH79eg0NjWbNmikpKQ0ePLiiokLSMwIANGa0ektOi6C0hOS9Id7psVflVTW6TFzuOvaXsRMmDhw04E1eHtMBWUfiRejl5fXixYuSkpLs7OynT5+GhYVJekYAgMaOI0cZuPN1O0f9sfifRUrt2gesjcih1O3s2+zcuQOH0BqSxIuwVatWGhoahBBNTc0OHTrk5ORIekYAAKnw7iKlCWf2crgyLoOnei3Y9uv6P7t4dElLS2U6IFtwG2COFy9eREdHZ2dnX7169ejRow0wIwCAdKBoStuBqJjGnTySci2yx5QVWqaWvsv2P44+1qljh9Fjxi5evEROTo7plE1cQ1wsU1xcfP/+/du3b6uoqHC571dvXS1uowEAVqPk1Elz71K+/tE5Q2/uWsOv41l37x+47uSVhDTbNtbXrl5hOqAUE+dJWA1RhE5OTlu2bImOjvbw8Jg6dep773JlGmKvFACgkaM1LGnzgMd37uyb6PMqKVZJQ8c9dIXt4J+GDB8xfPiwosJCpgNKJZr+fM016H2ErVu3fvPmTUPOCAAgRSgZRarZDzUqDmdWTru4bk5NRbmZi2fA2ohn5cTOvs2JiONMB2yaJF6Ef/31V1xcXEZGRlRU1PLly/38/CQ9IwCAVKNVTTkt+r9MTok7toUQIquo3HH0PI/p6yZOmRIZeYbpdE2QxA9LlpSUTJo0qaCgwNDQMDQ0dMKECZKeEQBA6tEylK7L4+iIjkOn0hwuIUS/lX33mRvGjBl17dr11q2tmM7XpEi8COfOnTt37lxJzwIA0MRQcupEVv1l3DXz9t1EW3TMrdoNm+Hn1zc29p6qqiqz8ZoSXKgCANBI8VVaxEcerC9CQkirLr5vUuMdHe3U1DUZDCYtystK1qxe4+zs9OlhKEIAgEaKo9YiP21/ef5rFR3D+o0dRs0rzEhjMJUUeXTuYH7Z59f1RBECADRWNIdWb5kUdazDkMn12zhcGV0LGwZDSRFFdW1xhuExTAAAjZh66+SocKGAz3SOpkzcPcKqqqoNGzacOnUqIyOjqqrq3beKiookEAwAAAglrykQkJKcTI1mZkxnabLELcJhw4ZFRER4enoGBgYqKChINBMAANSjaC4heBiFBIlVhDwe7/Tp06tWrZo5c6akAwEAADQksc4RlpSU1NbWduvW7fNDAQAApIpYRaijo9OyZcukpCRJpwEAAGhgYh0apShq586dY8aM0dfX79q1K4fDkXQsAACAhiHuxTKjR4/OyMjo0aOHrKyskpLSu2/hqlEAAJBeX3DV6Nu3byUaBQAAoOGJW4QLFiyQaA4AAABGfMHKMklJScOHD7ezs9PU1LS2th4wYEBMTIzkkgEAADQAcYvw+vXrLi4ux44dMzY2DggIaNGixcWLF93c3I4fxxOTAQBAiol7aHTSpEk2NjZnz57V09MTbSktLR0wYEBoaKifnx+uIwUAACkl1h5hUVFRYmJiWFhYfQsSQtTU1DZs2JCbm5uSkiKxeAAAAJIlVhHyeDxCiLKy8nvbRY9Irqmp+e6xAAAAGoZYRainp2dgYLBx48b3tm/cuFFBQcHS0lICwQAAABqCuCvLLFq0aPz48Y8fPw4KCjIwMMjPz4+MjLxy5crChQvfu78eAABAioh7sUxwcLCMjMySJUtmzZol2qKnpxcWFjZt2jSJZQP4znw97bQ1VPafieHV8n/061BVXXvkwj3RW1wO3da6ubmRtpKi3OPnOXcSXjAbFUDa8Wt5KVdPKqhqmrcX64EN6bFXK0vyW7n3kZFv6Cf9iVuEhJBRo0aNGjUqMzMzPz9fQ0PDzMyMoijJJQP47uaO9XK0Mo649IBXW/XHgkG5+aWiItTXVruwdVJrM33RsL8O/40iBPhGtTVVV//6RbdFGzGL8MGJHTkpD0ydujSuIjx69Oj06dM/+xXZ2dnfLw9AA6mq5lXz6kQ/zxnTs7WZ/paj13dG3C6rqC57W81sNoAmgCKUnLKqrIIUnDv7VBGamJj4+/s3WBSAhqTjNqP+Z7tWzQghizdFFpVWMpcIoEmRU1Ydu086Vh/7VBG6urq6uro2WBRgA2VFOdERyORnr6tqat97l6Kolia62hrKpeVVKS9y+QJBw6TS1VIlhJSWf3xHUF5WxtJMT0lRLiunKCu3uGEiAXwXlSWFpbkZcoqqGsbmFPX+bQL8utri7Be1VRVKmrqqekYNkKe2uqo4+zm/rlZN31hRXfu/hlWWFJbmZsopqWoamRPJn4P7/KHRuXPnTpw40dHRMT8//6PDcGgUPu2P+QPHBLr5TtzU1tp4xsgeyopyhJDyiurZv53YGXGrftgIvw4Lgr2N9TVEL/MKy37eeHrvqRhCyJRhXVdN7zf116Obj1wXvWvXqlnskbmEEO/xG6/cTRVtDOzRdv+qUat3Ri3cePqzqYpj1uXml8Ykpg/ydhFtqbi/QfSDUdc5BcVvCSEqSvLLJvsO822vKC8reiv2UXrossOJaa++9Y8CIDF7x/csy8sas+/O31uWPrt1QSgUEELU9I17TA/Ta2krGlPHq445sCE56mht9T9HQXTMrT3GLxINOL1kXGb8zaF/nlM3NBW9G39y1609azgycmP33+HKyos2Xtm08PGlY35LdhnZfmSXqfpt6fZhHXRbtAlac5QQwququLlrVeq10/xaHiGEUJRRm3Zdgn/WaGb+7qdqKspv7Fr1/HaUKLa6oekPk5YZtG773f9K7/r8odFWrVoRQry9vcvKyiQaBZq2maO6O7Q23hlx63lWgbWF/ugAtz8XDEx9mXvrwXNCyM8hveeP88ovKl+57cKzzHwTA83xA9y3/jJUXlZma/iNq3dTCSGe7Szri9DT1bL+h/oi9GxnSQi5+u/LT5PhcmS4nGNRD5KfvZ4+opummtLCjacFQiEhpLKKRwhRkJO5sHWyk3Xz2EfpEZcSCksr2tuZ/ejf4dKOqZ2GrH6W+fF/FwI0Eud/nVxRnO8SFCKvop7x4HrGgxtnV0wcuum8rIKSgF93esm418n3dMytW3b2VlTTfPMsOenikRM/j+j/6yEtU0tjuw6Z8TezE2PqizAr8Q4hhF9bk5v6sL72shNjODJy+pb2nw0j4NedWRKck/JAx9zKulugjLxietzV53eijs8dGrTmiKqecf3I6I3zairK3MfOk1fReJUUm3zp2OnFYwNXHdZq3vL7/43+Je6h0eXLl0suBLCBQ2vjDoNX1ffH86yC1T/1G+nX8daD5842JvPG9nr5qrDjkFX1Z+l2nbx9P3z+iql+4RfvP3r6uqD4rbtzSw5Ni46Xeri0KiqtKCh+Kyo/EU9Xy2pebczDL7jg8+zfj87+/Wikf0dNNaW1u6PfPRg7d5yXk3Xz3SfvhCw5KBQKCSH7TsfcePBs9/IRK6f595+29dv/JgCSU1dbM2DtcdEVmHbeg88sG5/x4EZ67BXLLn3iT+16nXyvpZtXj2mrKZpDCGnt6Wfs0PHsiok3dv7qt2SXkV17QkhWYkybXgMJIfy62pwn9w1aO+akxGc9vCMqwrK87LK8bGP7DvU7iJ+QHHU0J+WBroVNwMoDHBlZQkhrz743dqx8GLnvxs5Vvef+UT/ybUHO4PWn5VU1CCEt3bzUDU1u7lp9c+eqvr9sl8ifiRAi/tMnLly4cPnyZdHPpaWlI0aMsLa2HjZsWHExTpmAWLYcvfHuXtShc3GEkJYmuoSQsYFuFEUt+uPMu9eq5OSXbg2/oawo16OjtVAovBaXpqGq6GhlTAjhcuhObVtcjU27cjfV0cpYU02RENLcQNPcSDsmIf3DU49fgaapMQFuNby6mWHHRS0ocvhcXOrLvF5uNkoKst8+C4DkdBgy9f/vQ6CoVl36EEJKXr8khCRdOExRtPuY+aIWFDFz8dRraZudFFtVVqRtZimvqpH9KEYo4BNC8lIf1lZXte7qp25omv3on+tfRPuIosr8rJRrpwkhLgMmiFpQxKX/eBl5hZdx16rfltZvtOs9VNSCIrZegxTUNLMS71SWFHzVn0Es4t5HOGbMmIULF/7www+EkLlz5x4+fNjX1zc6OnrkyJEnT56UXD5oMh6mZr37sqD4La+W30xXnRDS3sGcEKKprhTQ3fHdMarK8oSQVmZ6hJCrsamBPdp6trO8l5zhYmuqqiR/NTY1v6h8/AD3zk4tT1152NXVUjTsu6S1NNXTVFPMeF3Yo6PVe2+VV1TLcDnmRjqPnuJMITRe2mat332prKlLCKkozHtbmFuen6OorvUqOe69j3Bl5YlQWPLqpYFVW6M2Ls9uR+Wnp+ha2GQlxhBCjO3a5794khwVXvO2TE5ZNfufjR0+H0UoLEhPIYQY2f5Pa8qramibts5JiS9IT6k/3Gpo7fzuGI6MnH4r+/S4q/kvnpi07fyFfwNxiVWEZWVlr169ateuHSGkrq7u0KFDs2bNWrp06e3bt93c3IqKijQ1NSWUD5qMkvKqd18KhcI6Pp/LpQkhOhoqhJB1s/t/9IMqinLk3zN/nq6Wa3ZFdf33XGBhyVu+QODZzvLUlYeis4ZXvlMR6miqEEJMDLUOrB790QHKSnLfZSIACZFTVn33Jc3lEkIEAn5VaREhpLKk8MKaj68LxquqIIQY2XV4djsqOzFG18ImOzFGRcdQVc/Y2K590oXDrx/fM3PxfJUUK6ekomP+/r8UP1RbU82v5ckpqXx4p7ySlh4hpLr8//cIlTR1/2NMyWcn+mpiFWFFRQUhRF1dnRBy9+7dkpISPz8/Qoizs7NQKMzIyEARwrfg1dYSQjoNWV1U9pHb+ErLqwghL7ILMl4XdnQ0V5CT8XS1zMotfp6VTwiJf5Ll6WpJUZSHS6vSt1XxjzO/UyQ+ISQuKWP43F0fHZDzpvSj2wEaOZorQwjRNLbwmb/powMU1XXIv8c8sxNjbL0G5T1NtOrqTwgxsutA0ZysxDuqus0qSwrNXX949+Dqf+HIyBKKqq2uFPD59P8+vLbmbRkhREbu/88y8irL3/s4r6KcEMKVleA/PcUqQh0dHS6Xm5ycbGpqGh4erqWl5eDgQAgRnSCUk8M/jeGbpL18o6+tpqGmdP+TNXYtNm2EX4eu7Vu7tDEVnWIkhFyNTZ05skePjlZ6WqqRfz+q43+fWw+fZrwRCIStTHUzXhcKBMLPfwBASqjqGnG4MqU5mUqauhyZ//x/b3UDExUdw9dP7mcl3Bbw60S9KKekomPWOuvhHVVdIyL2CUKaw1HVMSx786osL6v+MlRCiFAoKHmdTghRM2hev7Hk9Usdc+t3P178SjTG5It+zS8i1sUyXC7X399/7NixI0eO3Lp168CBA0WPpI+Pj+dyuc2bN//sNwB8wvFL8YSQ0MEen169VnSbxPxgLzlZ7rV/D4FeiUklhCya6EPEvnFCHIUlb6/fe6qmrDDcV6z/qQNICxl5BRMnd35d7aPzhz890sjOta6m+t6xLYSi6s/hGdm1L85+kfr3GfLBOb9PMHFyJ4Qknjvw7sb02Kvl+TlqBs3V3ym5pItH3x2T9/RR/ovHytr6Ws1biDnXVxD3qtEtW7Z4eXnFx8cPGjSo/laKY8eOdenS5cMH9gJ8kd0nbz94ktnLzebA6lG2LZvJcDkURRnqqvfv2fbsX6H1t9hfjUsVCoVtrZoLhcKrsWmijXcSXlTV1La1ak6+35UyInPWRVTV1K6fO+CnH7s101MnhMjJci1N9WaM7L5n5Y/fcSKABtZh2HRZBaXbe8Pijm4qz88hQiG/rrYkJyPh9J6zK0Prh4l67s3zZG2TVgpq/5z/Eu0F5r94rKSho2lk/tHv/5Bj35Ey8oqPzh9OPHeAX1tDhMLMhFtX/1pECHEdGPru2jFvnj26ve+32uoqQkj+iyeXfp9NCHEODBbnGOxXE/eqUQ0NjR07dpB/L5zh8/mamprbt0vwxg5gjxpeXd/Qv/as+LFfN8d+3Rzr+AI+XyAnyyWEvK2sqT/a+aaw/MmLXGsLg+RnOXmF/yzvUM2rvfsw3aNdK9G73zFVQkp239BNu5ePWD7Fb/kUv8pqnoKcjGifNfrOk+84EUAD02hm5vvL9qi1M+4e+uPuoT+4svL8Wp5oJRe9Vnb1w4zs2hOKIkKhsX3H+o2GVk4cGVl+Le+fd8WjqmfkPWfDhbDp17ctv7lzFc3h1vGqaQ6n/ZAprdx93h3pMf6Xv7csSTi1mysnz6t8Swhp02tgmx5B3+HX/m9f8BimHTt2rFix4sWLf+5WNjQ0nD59+rRp02ha3N1KYKedEbevxqYmpr5/s8GoBXtr6/iin/OLyr3Hb+zgYN6tg1VzfY0aXl1Ofml8StaVmNRq3v/fFzh+8QFjfY3M/13wc/ZvES2a6+QVlr97w99HLd4UqammVFHFI4SMWbiv+t87DqevCldWlBN88PHr955a91ncx9O2na2ZlrpSUWnlq7zia3Fp8U+y3v9qgEajy9j5tTVVFPmfltIwNOs1c52KjqHopX4r+yF/nnsZdzUnJaGqrEheSVVJS69Zm3Z6LdrUf0RJQ6f3nD/4dTzddzZy5eR7z/2DV1WhZfK5pV4EAkII/e+enLF9x2F/XXx283x+egq/lqduaGLRoYdGM7P64a6DJ1WXl5g6dzG0dkr9+0zJ6ww5ZVUzF8+Prt/2fVGf/f8OkVWrVs2ZM6djx44BAQGiJ9SfO3cuKipq0qRJ69ev/5YEnXv2vX3nvoyF37d8CQBAk/XiWOCKHe+tydn4lbx+uX+it7nrD95zNjKV4c6+dT96u4WOHv7pYWLtEfJ4vOXLl4eEhGza9P+X206ePHn58uWLFi2aP3++ru77d34AAACbpf4dSQhRf2efr9ES66hmQUFBeXn5hAkT3tseEhLC5/MzM7/PnVsAANAEpFw9uXlA27ijm+SUVCR9eu+7EPc+QjU1tQ8fw5Sfn8/hcExMJHh7BwAASBclTT2LDt3Vm5lZuvs0zGMOv5FYRSgjI7Nw4cJJkyZFRESInspECMnOzh47duzkyZN1dHQkmRAAAKSJsX0HY3sx1iBtNMS9avTJkyf5+flWVlY2Njb6+voFBQVJSUny8vL6+vpBQf/s+Y4fP75r164SiwoAAPD9iVuEGRkZxsbGxsbGhJCioiKapu3s7Agh9XdTEELw5F4AAJA64hZhVFSURHMAAAAw4gtuqM/Nzd29e3dSUhKfzz906BAh5MyZM2pqau7u7hKLBwAAIFniFmF8fHz37t15PJ6xsXFp6T8PoElMTDx06FBSUpLE4gEAAEiWuKujBQcHW1lZvXz58s8//6zf6Ovrm5yc/OFtFQAAANJCrD3CkpKSuLi4GzduaGpqvvugHFNTU0LIq1evcAcFAABIKbH2CKuqqgghampq720vKSkhhGDRbQAAkF5idZiurq62tvaFCxcIIe/uEYaHhysqKtbfYg8AACB1xDo0yuFwJk2atGjRIoqiDA0NCSHPnj07evTo0qVLJ06cKC8vL+GQAAAAkiLuVaPz58/Pz8+fPXu2QCAghLRs2ZIQ8u7T6gEAAKSRuEXI4XA2btw4derUqKiovLw8DQ2NLl26ODg4SDQcAACApH3BDfWEEAsLi5CQEAlFAQAAaHi44BMAAFgNRQgAAKyGIgQAAFb7snOEX6e0tDQ5OVlRUdHGxkZGRqYBZgQAABCTxItw7dq1y5cvb926dWlpaU1Nzblz53ADPgAANB4SPzTq4eGRnp5++/btpKQkNze3+fPnS3pGAAAA8Um8CJ2cnESLlFIU5ejoWFBQIOkZAQAAxNdwF8tUVVVt3749KCjog3cEDZYBAADgPQ1UhHw+f+TIkaampsHBwe+/VSdsmAwAAMA2omVBP60hrhoVCARjxowpKCiIjIz88JlNHC6nATIAAAALifOgQIkXoVAoDA0Nffr06YULF/CcCgAAaGwkXoQrVqzYsWPHrFmz/vzzT0KIhobGuHHjJD0pAACAmCRehK1atZo2bVptbW1xcTHB4+wBAKCRkXgR9u/fv3///pKeBQAA4Otg/wwAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArIYiBAAAVkMRAgAAq6EIAQCA1VCEAADAaihCAABgNRQhAACwGooQAABYDUUIAACshiIEAABWQxECAACroQgBAIDVUIQAAMBqKEIAAGA1FCEAALAaihAAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArIYiBAAAVkMRAgAAq6EIAQCA1VCEAADAaihCAABgNRQhAACwGooQAABYDUUIAACshiIEAABWQxECAACroQgBAIDVUIQAAMBqKEIAAGA1FCEAALAaihAAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArMZtgDlKSkru379fVlbm7+/fANMBAACIT+JFGB0d3bt3bxMTk5ycnPLycklPBwAA8EUkfmi0Y8eO5eXlBw4ckPREAAAAX0Hie4SKioqSngIAAOCrMX+xjEAgYDoCAAA0TUKh8LNjmC9CAAAABjFfhDTNfAYAAGiSKIr67BiUEAAAsJrEL5YpKCiYMGFCUVFRdXV1UFCQvr7+hg0bJD0pAACAmBriqtH+/fsTQoKDgwkhysrKkp4RAABAfA1XhAAAAI0QzhECAACroQgBAIDVUIQAAMBqKEIAAGA1FCEAALAaihAAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArIYiBAAAVkMRAgAAq6EIAQCA1VCEAADAaihCAABgNRQhAACwGooQAABYDUUIAACshiIEAABWQxECAACroQgBAIDVUIQAAMBqKEIAAGA1FCEAALAaihAAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArIYiBAAAVkMRAgAAq6EIAQCA1VCEAADAaihCAABgNRQhAACwGooQAABYDUUIAACshiIEAABWQxECAACroQgBAIDVUIQAAMBqKEIAAGA1FCEAALAaihAAAFgNRQgAAKyGIgQAAFZDEQIAAKuhCAEAgNUaogjPnDkzfPjwkJCQpKSkD9+tqalugAwAAMBCubk5nx0j8SI8efLk6NGje/ToYWJi0rlz5+zs7PcGlJaUSjoDAACw0717Dz47hivpEGFhYUuWLBk6dCghJCEhYevWrUuWLJH0pAAAAGKS7B6hUCiMi4vr0qWL6GWXLl3u3r0r0RkBAAC+iGT3CIuKing8npaWluiltrZ2Ts77h2vl5eWFVQV1T/ZKNAkAgLQS1l1eN5MrI8t0DulTVV5q3rXrZ4dJtggVFBQIITU1NaKX1dXVioqK7425HHls48aN7200MzPT1taWaDYAAGjy3N3dPztGskWoqKiooaGRmZlpbGxMCMnMzDQyMnpvjLa29uLFiyUaAwAA4L9I/KrRgICAvXv3EkJqamqOHDkSEBAg6RkBAADERwmFQolOkJGR4enpaWxs/ObNGzMzs1OnTsnIyEh0RgAAAPFJvAgJITU1Nffu3VNSUrK3t6co6t23Ll++HBERoaSkFBwcbGFhIekkTVJmZmZsbOzz58+9vLzs7OyYjiOVBALB9evXo6Oji4qKLC0tR48erayszHQo6VNVVbVv377k5OS6ujpbW9sRI0aIrhKAr5OYmHj+/PkhQ4Z8eEYJPisrK+vgwYP1L319fa2srP5rcEOsLCMnJ9epUycHB4f3WjAyMnLAgAF2dnZcLrd9+/Z5eXkNEKbpGThw4JYtW37//ffY2Fims0irN2/eBAcHc7nctm3bRkZGdu7cmcfjMR1K+pSWlsbFxVlaWjo6Ou7Zs8fPz4/pRFKsurp65MiRv/zyS3p6OtNZpFJ6enpYWFjxvz79v+iG2CP8L+7u7oMGDQoJCSGE+Pn5tWvXbt68eUyFkXZubm4//vjjmDFjmA4ilQQCASGEpmlCSHV1tba2dnR0dPv27ZnOJcVevHjRokWL0tJSFRUVprNIpblz52poaKxevfrEiROdO3dmOo70uX79+sSJEx89eiTOYMYW3RYIBHfu3PH09BS97Nq1661bt5gKAyxH07SoBQkhlZWVNTU1mpqazEaSakKh8Pz581ZWVjjC/HUSEhKio6OnTZvGdBDpVlRUtGjRorVr16akpHx6JGNFmJ+fX1dXV3+zoI6OzuvXr5kKA1AvNDS0X79+rVq1YjqItLKxsVFQUFi6dOnBgwffOxsC4qirqxs3btzmzZtxXeG3UFJS6tGjh4KCQlpamrOz8+nTpz8xWOJrjf4XeXl5Qkhtba3oJY/Hw3l1YNzs2bPT0tIuX77MdBAplpycXFhYuG3btt69ez958gSHRr/UsmXLPD09nZycmA4i3ZycnHbt2iX62draesGCBb6+vv81mLE9QjU1NSUlpfqHUWRlZRkaGjIVBoAQsmjRogsXLly8eFFNTY3pLNJNS0trzpw5tbW19+7dYzqL9ImIiDh48KCFhYWFhUVJScnAgQM3b97MdCjp5uzsnJWV9YkBjO0REkL8/f0PHTrk4uJSW1t77NixmTNnMhgGWC4sLOzIkSPXrl2rXxoXvlRZWZmysrLobOvjx4+LiorMzMyYDiV9zp07V3+JixlL8wAABO1JREFUo5OT02+//dazZ09mI0mj0tLS+n/RHj161N7e/hODmbxqNC0tzcPDw9nZOTs7W11d/cKFC7KyWFX2i82aNevKlSupqalaWlra2trr1q3DNWZf6vnz5y1atDA3N9fQ0BBtWblyZffu3ZlNJXX27NmzaNEiOzs7Ho93586d+fPnz5o1i+lQ0k1bWxtXjX6dcePG3b1719zc/NmzZ2/fvj116tQnbrNmsggJIeXl5Tdv3lRRUenQoQOHw2EwifTKy8urqKiof6mvr//hyubwabW1te8dOdHT01NSUmIqj/R6/vx5SkqKgoKCjY2Nnp4e03GkXkZGhp6enuiKCvgiPB4vISEhNzdXT0/PwcFBTk7uE4MZLkIAAABmMXaxDAAAQGOAIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQoDGQiAQbN26NTExkekgAOyCIgRgzPbt2+Pj4+tf8vn84ODgqKioL/2egwcP3rx587tGA2ARFCEAY0JCQs6ePfvt3zN37tx3H8YNAF8ERQjQGNXU1BQVFX24vba2Njc3t7KyUpwvqaqqKiws/N7RAJoaFCEAA8rKyjQ1Nevq6lasWKGpqampqfnrr7+K3qqrq5s2bZq6urqWlpaRkVH9c9SqqqqmTJmira1tYGCgqqrq5eUlWhbOyMgoOzt7586dou+ZOnUqIWTVqlUWFhaKiora2tqampqhoaHV1dVM/bIAjRyWWANgQF1d3bVr13r16jVs2LAhQ4YQQszNzY2NjWVlZfX19d3d3SdMmCAUCmfNmvXs2bP09HRVVVUfH5+YmJgVK1a4ubllZmZOnz6doqj4+Pjbt28PHDjQ1dV18uTJhJBmzZpZWVnNmjXL2tra1tZWTk4uOjp67ty548ePX7duHdO/N0CjJAQAhnC53KVLl9a/FD18x8nJic/ni7bExsYSQk6dOiW6giYiIqJ+cHJyMiEkPDxcKBQ2b948JCTkExPNmTNHV1dXMr8EgNRj8nmEAPChnj17ih7pRwixsrIihGRlZaWnp3M4HNHuXf1IVVXVpKSkwMDAj35PdHT0rVu38vLy+Hx+WlramzdvysvL8bx4gA+hCAEal/pnIhJCRM+OqampycvLEwqFQ4cOfXckh8MpLS398Bv4fL6Pj8+1a9e6d+9uYmKiqqqqrKxMCCktLUURAnwIRQggBdTU1GRkZHJzc8V5ePWtW7cuXLhw5swZHx8f0Za1a9dGRkZKOCOAtMJVowCMUVZWrqqqEmdkly5dampq6q8g/fT3pKenE0KcnJzqt5w7d+7bkgI0ZShCAMbY2NicPHkyKirq/v37r1+//sRIf3//du3ajR8/fs+ePfn5+WVlZQ8ePJg3b969e/dE3xMdHR0ZGXn//v2MjAx7e3uKopYvX15WVpabmztz5kzRRTcA8FEoQgDGrF+/Xk1Nzd/f39nZeevWrZ8YyeVyz58/37Nnz9GjR+vq6qqpqTk7O0dFRYlO/i1fvrxVq1aDBw92dnZevny5g4PD0qVLt27dqqamZmBgEBcXt3Tp0ob6nQCkD+4jBJAmZWVlqampsrKyxsbGmpqanxhZXFz8/PlzbW1tU1PThkoHIJVQhAAAwGo4NAoAAKyGIgQAAFZDEQIAAKuhCAEAgNVQhAAAwGooQgAAYDUUIQAAsBqKEAAAWA1FCAAArPZ/7Tm6sBJPD9AAAAAASUVORK5CYII=" }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wp = CareerWorkerProblem(G_a=100.0, G_b=100.0); # use new params\n", "v, optimal_policy = solve_wp(wp)\n", "\n", "lvls = [0.5, 1.5, 2.5, 3.5]\n", "x_grid = range(0, 5, length = 50)\n", "y_grid = range(0, 5, length = 50)\n", "\n", "contour(x_grid, y_grid, optimal_policy', fill=true, levels=lvls,color = :Blues,\n", " fillalpha=1, cbar = false)\n", "contour!(xlabel=\"theta\", ylabel=\"epsilon\")\n", "annotate!([(1.8,2.5, text(\"new life\", 14, :white, :center))])\n", "annotate!([(4.5,2.5, text(\"new job\", 14, :center))])\n", "annotate!([(4.0,4.5, text(\"stay put\", 14, :center))])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You will see that the region for which the worker\n", "will stay put has grown because the distribution for $ \\epsilon $\n", "has become more concentrated around the mean, making high-paying jobs\n", "less realistic." ] } ], "metadata": { "date": 1591310614.1454165, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "career.rst", "filename_with_path": "dynamic_programming/career", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Job Search IV: Modeling Career Choice" }, "nbformat": 4, "nbformat_minor": 2 }