So, recently, I made a matlab simulation/visualization for prices in a 2-sector economy. I did this to see for myself whether labor theory of value prices are the prices at which an economy can reproduce itself exactly. That is, when the unit price of each sector matches the price predicted by the LTV, then the net financial position of both sectors of the economy (and the consumers) neither improves or worsen (so nobody is going into debt to another).
Of course, this was inspired by Marx's famous reproduction scheme method, where he did something similar. However, I have better tech than he did.
I basically randomly generated a 1000 different random economies, and in each economy, I generate 1000 different prices. Then, for each price and economy, I computed the balance of payments between the 2 sectors and the consumers. I also computed the predicted LTV prices for each of the 1000 economies
These 1 million data points are plotted on a density map in the linked image. The brighter the spot on the map, the more data points fell there. And it's exponential. A 7 on the color scale has almost 3 times as many points there as a 6.
The y-axis is the net income of sector 1. If that net income is anything but 0, the economy isn't reproducing itself. The x-axis is the ratio between the actual price ratio of the sectors (randomly generated for each point) and the price ratio predicted by the LTV.
If you look at this graph, you will see 2 black regions. There are sharp black regions both horizontally and vertically emanating from the center point (the situation of reproduction and LTV prices). This means that reproduction implies LTV prices, and LTV prices imply reproduction. So the only way for a perfectly stable economy to exist is for it to employ LTV prices, and vice versa, an economy is stable if it employs LTV prices.
This is pretty much what the theory expects. What might be an interest further avenue to research is that hourglass shape. From pretty much the moment I started coding the simulation (so even during my early attempts when I was doing things wrong), I kept seeing that hourglass shape. I don't know if it is an artefact of how I did my simulation, or if it is something more fundamental.
If I could create a model for the shape of that hourglass, I could use it to predict things like
"How much can the prices in this economy deviate from LTV prices given this much growth in a sector?"
Which would be very cool.
Unfortunately, the ability to code basic shit in MatLab does not give me the ability to do advanced mathematics, so I will really need to think about this.
For anyone interested in my actual simulation approach, I have it written out in a comment (and will also provide the code)
