> Both farmer and mechanic starve and then the automated systems make neither corn nor tractor while the capital owner wonders why no one is buying.

I don't think your math works out. If a tractor is worth more in the market than the corn then the mechanic is better off to sell the tractor and buy corn in the market than trade with the farmer, and vice versa if the corn is worth more in the market than the tractor. Making the trade only makes sense if the tractor and the corn have the same market value, but in that case they could both just as easily sell to the market rather than bartering.

Automation is only a problem when it lowers the price of the things you're selling but not the price of the things you're buying.

I don't see how automation of growing corn will make iPhones cheaper.

The second half of your post just gave me a vietnam flashback to Linear Systems back in college

I wonder if you could actually model economic systems using impulse response and signal filtering mathematics

I don't know about impulse response and signal filtering, but the Soviets did try to model their economy with linear models. Cosma Shalizi put up a good analysis [1] of why this is very very difficult. Simply put, any kind of "real" economy has so many variables (in the kinds of goods and services, their various quality levels, and the locations in both time and space that goods and services have to be) that any kind of linear programming quickly gets swamped by the sheer number of variables that have to be adjusted in order to compute an optimal outcome. So yes, in theory you can model an economy using a linear system. It's not even an NP problem. But in practice, the computational complexity is high enough (though still within P) that even toy economies with as few as a thousand elements become impossible to optimize with linear programming.

[1] http://crookedtimber.org/2012/05/30/in-soviet-union-optimiza...

Most real-world economic systems aren't anywhere close to linear.

Economists do love their toy models, and some of those are linear. They also make wrong predictions.

Anyone who thinks economics has useful, reliable mathematical models akin to those in physics is fooling themselves.

Absolutely you could. Indeed, it has arguably already been done, albeit indirectly: http://en.wikipedia.org/wiki/MONIAC_Computer