diff --git a/lectures/input_output.md b/lectures/input_output.md index 8d6d649b..4645dd46 100644 --- a/lectures/input_output.md +++ b/lectures/input_output.md @@ -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 `. -## Input output analysis +## Input-output analysis Let @@ -184,7 +184,7 @@ plt.text(1.6, -0.5, r'$d_{2}$') plt.show() ``` -**Feasible allocations must satisfy** +*Feasible allocations must satisfy* $$ \begin{aligned} @@ -264,7 +264,7 @@ $$ -For example a two good economy described by +For example a two-good economy described by $$ A = @@ -507,9 +507,9 @@ This illustrates that an element $l_{ij}$ of $L$ shows the total impact on secto ## Applications of graph theory -We can further study input output networks through applications of {doc}`graph theory `. +We can further study input-output networks through applications of {doc}`graph theory `. -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 @@ -550,7 +550,7 @@ The above figure indicates that manufacturing is the most dominant sector in the ### 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 $j$.