chapotraphouse

I have some comments, questions, and possible suggestions. I think this is really great, and simulations are incredibly fun and I love digging into them. Some of my questions are because I know Python but not MatLab, so I may need to check I understand what your code is doing. Other comments may be due to differences in how quantities are calculated (particularly how the labor-value and the costs were calculated), and your final comparison of aggregated quantities instead of sector quantities. Keep in mind that I don’t mean any comment to sound aggressive, and it is possible that I am misunderstanding the code or the concept that the calculation represents.

Because I don’t know MatLab well, I’m going to go through the sections of the code and we can confirm my understanding of each part.

1.) You make N economic simulations. For each iterative economic simulation, i, you:

2.) First, generate a random net product vector n for the global economy (you call it o in the simulation).

3.) Then you randomly generate an input output table A.

• Warning: not every randomly generated input output table is productive, i.e. there is no guarantee that the inverse of I-A exists, or that if it does exist then you will have an economically feasible gross product. The Hawkins-Simons condition (which is an economic application of the Perron-Frobenius theorem) gives us the mathematical conditions for ensuring that an input output matrix A is economically feasible.
• • Essentially for A to be productive, (I-A)^-1^ must exist and (I-A)^-1^ n must result in a non-negative vector (you can’t have a requirement of negative gross production) which means (I-A)^-1^ must also be non-negative. -- To confirm that A is productive. You can check if the largest eigenvalue of A. If it is a positive value that is less than one then by the Hawkins-Simon theorem it will be productive. -- Alternatively, you could just randomly generate the input output matrix A and then confirm that (I-A)^-1^ exists and is non-negative. If not, regenerate A and test again. -- I am also sure that MatLab would give an error if the matrix inverse does not exist, but it won’t give an error if the resulting gross product is not non-negative.

4.) Then you calculate the gross product vector q, or as you call it O. This is calculated via q = (I-A)^-1^ n. It took me a while to realize that “\” is MatLab’s way of doing a matrix inverse followed by a multiplication. So A \ b is MatLab’s way of calculating A^-1^b, correct?

5.) You calculate the gross labor use as L=l q. This is element wise multiplication, or equivalently, the dot product. I wasn’t sure why you normalized the net product and the gross labor, though.