Understanding the Leontief inverse What I remember from economics about input/output analysis is that it basically analyses the interdependencies between business sectors and demand. If we use matrices we have $A$ as the input-output matrix, $I$ as an identity matrix and $d$ as final demand. In order to find the final input $x$ we may solve the Leontief Inverse:
$$
x = (I-A)^{-1}\cdot d
$$
So here's my question: Is there a simple rationale behind this inverse? Especially when considering the form:
$$
   (I-A)^{-1} = I+A + A^2 + A^3\ldots
$$
What happens if we change an element $a_{i,j}$ in $A$? How is this transmitted within the system? And is there decent literature about this behaviour around? Thank you very much for your help!

This question has languished. At the level the question was asked, there is now a short, useful lecture available:
https://www.youtube.com/watch?v=-1jT5NOk93w
If this information is insufficient, perhaps a followup question would be appropriate.
