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[input_output] update typos
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  - change 'input output' to 'input-output' for consistency
  - change **feasible allocations must satisfy**  to *feasible allocations must satisfy* to match with style guide
  - change 'a two good economy' to 'a two-good economy'
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longye-tian committed Aug 1, 2024
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Expand Up @@ -120,7 +120,7 @@ A basic framework for their analysis is
After introducing the input-output model, we describe some of its connections to {doc}`linear programming lecture <lp_intro>`.


## Input output analysis
## Input-output analysis

Let

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plt.show()
```

**Feasible allocations must satisfy**
*Feasible allocations must satisfy*

$$
\begin{aligned}
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For example a two good economy described by
For example a two-good economy described by
$$
A =
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## Applications of graph theory
We can further study input output networks through applications of {doc}`graph theory <networks>`.
We can further study input-output networks through applications of {doc}`graph theory <networks>`.
An input output network can be represented by a weighted directed graph induced by the adjacency matrix $A$.
An input-output network can be represented by a weighted directed graph induced by the adjacency matrix $A$.
The set of nodes $V = [n]$ is the list of sectors and the set of edges is given by
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### Output multipliers
Another way to rank sectors in input output networks is via output multipliers.
Another way to rank sectors in input-output networks is via output multipliers.
The **output multiplier** of sector $j$ denoted by $\mu_j$ is usually defined as the
total sector-wide impact of a unit change of demand in sector $j$.
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