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QuantEcon
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auto publishing updates to notebooks
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about_lectures.ipynb

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}
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],
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"metadata": {
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"date": 1609475201.759867,
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"date": 1610065566.1127505,
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"filename": "about_lectures.rst",
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"kernelspec": {
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"display_name": "Python",

aiyagari.ipynb

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}
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],
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"metadata": {
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"date": 1610065566.158391,
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"filename": "aiyagari.rst",
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"kernelspec": {
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"display_name": "Python",

ar1_processes.ipynb

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}
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"metadata": {
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"date": 1610065566.2569559,
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"filename": "ar1_processes.rst",
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"kernelspec": {
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"display_name": "Python",

cake_eating_numerical.ipynb

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"### The Bellman Operator\n",
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"\n",
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"We introduce the **Bellman operator** $ T $ that takes a function v as an\n",
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"argument and returns a new function $ Tv $ defined by.\n",
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"argument and returns a new function $ Tv $ defined by\n",
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"\n",
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"$$\n",
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"Tv(x) = \\max_{0 \\leq c \\leq x} \\{u(c) + \\beta v(x - c)\\}\n",
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"source": [
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"### Fitted Value Function Iteration\n",
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"\n",
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"Both consumption $ c $ and the state variable $ x $ are continous.\n",
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"Both consumption $ c $ and the state variable $ x $ are continuous.\n",
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"\n",
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"This causes complications when it comes to numerical work.\n",
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"\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The fit is reasoable but not perfect.\n",
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"The fit is reasonable but not perfect.\n",
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"\n",
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"We can improve it by increasing the grid size or reducing the\n",
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"error tolerance in the value function iteration routine.\n",
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"source": [
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"### Exercise 1\n",
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"\n",
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"We need to create a class to hold our primitives and return the right hand side of the bellman equation.\n",
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"We need to create a class to hold our primitives and return the right hand side of the Bellman equation.\n",
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"\n",
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"We will use [inheritance](https://en.wikipedia.org/wiki/Inheritance_%28object-oriented_programming%29) to maximize code reuse."
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]
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}
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],
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"metadata": {
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"date": 1610065566.4326456,
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"filename": "cake_eating_numerical.rst",
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"kernelspec": {
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"display_name": "Python",

cake_eating_problem.ipynb

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}
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"metadata": {
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"date": 1610065566.635056,
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"filename": "cake_eating_problem.rst",
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career.ipynb

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}
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"metadata": {
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"date": 1610065566.7661104,
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"filename": "career.rst",
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"kernelspec": {
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cass_koopmans_1.ipynb

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"source": [
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"## Overview\n",
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"\n",
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"This lecture and in [Cass-Koopmans Competitive Equilibrium](https://python-programming.quantecon.org/cass_koopmans_2.html) describe a model that Tjalling Koopmans [[Koo65]](https://python-programming.quantecon.org/zreferences.html#koopmans)\n",
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"This lecture and lecture [Cass-Koopmans Competitive Equilibrium](https://python-programming.quantecon.org/cass_koopmans_2.html) describe a model that Tjalling Koopmans [[Koo65]](https://python-programming.quantecon.org/zreferences.html#koopmans)\n",
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"and David Cass [[Cas65]](https://python-programming.quantecon.org/zreferences.html#cass) used to analyze optimal growth.\n",
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"\n",
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"The model can be viewed as an extension of the model of Robert Solow\n",
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"described in [an earlier lecture](https://lectures.quantecon.org/py/python_oop.html)\n",
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"but adapted to make the saving rate the outcome of an optimal choice.\n",
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"\n",
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"(Solow assumed a constant saving rate determined outside the model).\n",
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"(Solow assumed a constant saving rate determined outside the model.)\n",
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"\n",
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"We describe two versions of the model, one in this lecture and the other in [Cass-Koopmans Competitive Equilibrium](https://python-programming.quantecon.org/cass_koopmans_2.html).\n",
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"\n",
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"cell_type": "markdown",
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"Different colors in the above graphs are associated\n",
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"Different colors in the above graphs are associated with\n",
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"different horizons $ T $.\n",
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"\n",
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"Notice that as the horizon increases, the planner puts $ K_t $\n",
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}
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],
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"metadata": {
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"date": 1610065566.9352026,
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"filename": "cass_koopmans_1.rst",
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cass_koopmans_2.ipynb

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"In this lecture [Cass-Koopmans Planning Model](https://python-programming.quantecon.org/cass_koopmans_1.html), we computed an allocation $ \\{\\vec{C}, \\vec{K}, \\vec{N}\\} $\n",
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"that solves the planning problem.\n",
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"\n",
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"(This allocation will constitute the **Big** $ K $ to be in the presence instance of the *Big** $ K $ **, little** $ k $ trick\n",
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"(This allocation will constitute the **Big** $ K $ to be in the present instance of the *Big** $ K $ **, little** $ k $ trick\n",
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"that we’ll apply to a competitive equilibrium in the spirit of [this lecture](https://lectures.quantecon.org/py/rational_expectations.html#)\n",
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"and [this lecture](https://lectures.quantecon.org/py/dyn_stack.html#).)\n",
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"\n",
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"We now turn to the problem faced by a firm in a competitive\n",
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"equilibrium:\n",
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"\n",
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"If we plug in [(8)](#equation-eq-pl) into [(1)](#equation-zero-profits) for all t, we\n",
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"If we plug [(8)](#equation-eq-pl) into [(1)](#equation-zero-profits) for all t, we\n",
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"get\n",
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"\n",
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"$$\n",
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}
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],
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"metadata": {
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"date": 1610065567.228547,
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"filename": "cass_koopmans_2.rst",
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coleman_policy_iter.ipynb

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}
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"metadata": {
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"date": 1610065567.367762,
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"filename": "coleman_policy_iter.rst",
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"kernelspec": {
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complex_and_trig.ipynb

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}
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"date": 1610065567.494145,
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"filename": "complex_and_trig.rst",
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"kernelspec": {
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"display_name": "Python",

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