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rst_files/optgrowth.rst

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@@ -330,7 +330,7 @@ function
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In our setting, we have the following key result
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*A feasible consumption policy is optimal if and only if it is* :math:`v^*`-*greedy*
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* A feasible consumption policy is optimal if and only if it is :math:`v^*`-greedy
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The intuition is similar to the intuition for the Bellman equation, which was
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provided after :eq:`fpb30`
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We will hold the primitives of the optimal growth model in a class
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The distribution $ \phi $ of the shock is assumed to be lognormal,
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and so a draw from $ \exp(\mu + \sigma \zeta) $ when $ \zeta $ is standard normal
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The distribution :math:`\phi` of the shock is assumed to be lognormal,
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and so a draw from :math:`\exp(\mu + \sigma \zeta)` when :math:`\zeta` is standard normal
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.. code-block:: python3
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@@ -595,7 +595,7 @@ Here's a function that generates a Bellman operator using linear interpolation
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def bellman_function_factory(og, parallel_flag=True):
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'''og is an OptimalGrowthModel'''
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'''og is an instance of the OptimalGrowthModel'''
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f, u = og.f, og.u
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y_grid, shocks = og.y_grid, og.shocks
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return T, get_greedy
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The `generate_T_operator` function takes a class that represents the growth model,
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and returns a function `T` that we will use to solve the model
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`bellman_function_factory` takes a class that represents the growth model,
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and returns the operator `T` and a function `get_greedy` that we will use to solve the model
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Notice that the expectation in :eq:`fcbell20_optgrowth` is computed via Monte Carlo, using the approximation
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.. index::
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single: Optimal Growth; Policy Function
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To compute an approximate optimal policy, we will write a function
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that backs out the optimal policy from the optimal wage rate
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To compute an approximate optimal policy, we will use the second function
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return from `bellman_function_factory` that backs out the optimal policy
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from the optimal wage rate
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The next figure compares the result to the exact solution, which, as mentioned
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above, is :math:`\sigma(y) = (1 - \alpha \beta) y`

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