I encountered that nobody, even my profs and lecturers so far, has an intuitive way to explain what the Leontief inverse represents. Does somebody here?
As most people here would know, it goes:
$\ x=Ax+y $ where $x$ is the output and $y$ the final demand. So
$\ x - Ax =y $
$\ x (1 - A) =y $ or
$\ x = (1-A)^{-1} y $ or
$\ x = Ly $
While $A$ is clearly the proportion of total output that comes from intermediate value exchanges and not from transactions to final demand $1 - A$ should be the proportion of total output caused by final demand. However $L = (1-A)^{-1}$. So what would this be? The inverse proportion of what in total output is related to final demand? You can also just say of course $L$ represents the multiplier or scaling factor of how $x$ responds to changes in $y$, but that is not what I am asking for. I wonder if there is any real world interpretation possible on what L represents. Or is it an entirely abstract multiplier?