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lectures/input_output.md

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name: python3
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(input_output)=
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In this lecture, we will need the following library.
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# Input-Output Models
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source_hidden: true
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pip install --upgrade quantecon_book_networks
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pip install quantecon
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```
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In this lecture, we will need the following library.
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```{code-cell} ipython3
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import numpy as np
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import pandas as pd
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plt.show()
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```
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An arrow from $i$ to $j$ implies that sector $i$ supplies some of its output as raw material to sector $j$.
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In this lecture, we introduce the standard input-ouput model and approach it as a [linear programming](link to lpp lecture) problem.
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## Input Output Analysis
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```
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#### Feasible allocations must satisfy
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where $^*$'s denote optimal choices for the primal and dual problems.
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```{code-cell} ipython3
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```
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## Exercise
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where $L$ is a vector of labor services used in each industry.
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```{code-cell} ipython3
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```
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```{code-cell} ipython3
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```

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