Here is the lemmygrad post I made it at (don’t wanna have to copy everything over).
Please give the post lots of 
, the post would really appreciate it
Don’t be afraid to ask questions.
Here is the lemmygrad post I made it at (don’t wanna have to copy everything over).
Please give the post lots of , the post would really appreciate it
Don’t be afraid to ask questions.
7.) Then you have a vector of randomized prices. This is an n x 1000 table, though. I am confused why there is an extra 1000 here, when the loop itself will create 1000 instances of the economy. I may be misunderstanding the intention of this step so any clarification can help.
8.) You then calculate the costs, the sales to consumers, the total wages paid out, and the net income (I am also confused why the net income is normalized)? Some of the cost calculations confuse me, so I will discuss my understanding of calculating cost and we can also check if we are converging on our understanding: Sector i will spend the following amount of money on their means of production per unit product:
unit costi = p1 a_1,i + p2a_2,i + …
This is the amount of money that sector i must shell out to all other sectors in order to built a unit quantity. You can think of it as the row vector of prices multiplied by the i-th column in the input-output matrix A.
This unit cost for each sector can be expressed via matrix algebra as
unit cost = p A where p is a n x 1 row vector of prices
This gives you a row vector of each sector’s unit cost.
Alternatively, you can calculate this as unit cost = AT p where p is a column vector. I just prefer to use column vectors for physical quantity vectors, and row vectors for prices, labor coefficients, and values. It makes the math easier to write, and you avoid transposing. It also hints at a duality present in the system.
Since this is a unit cost, we can calculate the total cost of production for sector i as
costi = unit costi x qi = (p1 a1,i + p2a2,i + …) qi
You can do this for all sectors by first calculating the unit cost vector above, so you can do p A using matrix multiplication, then you can convert these unit costs to real costs by element-wise multiplication with q. This will give you each sector’s individual costs for means of production.
If you wanted aggregate costs for the whole economy though, then you can do the matrix multiplication of p A q, but I would suggest moving from an aggregate to a sector-specific model so you can test the differences between sector prices and sector labor values. I think that would be very interesting!
The money that each sector receives would then be the element-wise multiplication of pi qi. If you wanted an aggregate quantity across all sectors, this would be the p q - you have already calculated this as R.
Then you also need to include the wage payments for each sector. Each sector pays there workers w li qi = w Li. In the aggregate if workers are spending all of their wage and they are the only consumers of the net product, then w L = p n. But if you wanted to find how much each sector was spending for their wages, then you have to disaggregate this. You could Introduce the wage as a new parameter. Then the total wage spend by each sector is w li qi = w Li
Divide the working class into sectors, just as the industry is divided, and note that the i-th working class consumes a proportion of Li/L n of the net product. Then, by conservation of the worker’s wages with their expenditure, note that wage spent by each sector is then pi ni Li/L.
With that, you can then find the net income as you have. And perhaps this is what you’ve done, but just in an aggregate way. As I mentioned, MatLab code is a little difficult for me to understand. And also, I think disaggregating this can be a good next step!
the 1000 different prices are there to see what happens to the reproduction condition with 1000 different prices. I am not directly calculating reproduction prices for each economy. I am just letting random guesses show me what happens to the reproduction condition at various price points.
The net income being normalised was there just to improve the visualisation. I have run the code with all sorts of parameters with and without the normalisation, and it is difficult to decide which is more useful for gaining insight.
I’ve tried generating economies with upto 100 sectors (my poor laptop), but right now, I am facing a different problem I am trying to solve (with more and more sectors, my current random price generation strategy rarely ever produces prices close to LTV. Law of large numbers and all).
This is what I have done in C (except I also multiplied by gross output yo get total costs per sector)
R is a vector denoting the revenue by sector. I think part of your misunderstanding might be from MatLab’s element-wise multiplication function, whose output can be difficult to understand.
O is a n long coming vector, P is a n long column vector, when element wise multiplied, the output is also a n long column vector.
And I do suppose that using standard notation (which I have never seen before tbh) would probably help greatly.
9.) The sector income then acts as a proxy for reproducibility. If the income is negative, then the sector is not sustainable and the prices must be updated. A future direction can be to have some dynamic model where each sector can adjust its prices if it is finding that the income is negative. A problem though that you will have to address if you do move in this direction is you will have to have a mechanism for modeling prices in a semi-realistic fashion and address appropriate labor reallocation.
If a sector’s income is very high then perhaps it is because the prices are very high. But the prices won’t be high in a real market economy if the supply of the product is also very high, as competition would result in competitive firms within the sector lowering prices for market advantage. A high supply would result in a downward pressure on prices. This downward pressure causes the income to lower over time, and firms would start to move out of this sector and labor will be reallocated to other sectors. This also occurs in reverse for sectors with a high demand but low supply. This mechanism is important for the operation of the law of value.
To test Wright’s non-standard value you’ll need to introduce an exploiting class. For the purpose of the simulation you would have to add some population that consumes but does not contribute labor to production. You can have separate consumption vectors for the working class and the exploiting class. The net product n would then be sum of the worker’s and the exploiter’s consumption, n = cW + cK. Start with the exploiting class consumption = 0, and you can slowly increase it to check the impact it has on prices.
For a micro model which with no exploitation and is simple commodity production you can find his paper The Emergence of the Law of Value in a Dynamic Simple Commodity Economy. For a different micro model with exploitation (but abstracts away from different commodities and input output tables) you can check out his Implicit Microfoundations for Macroeconomics or his The Social Architecture of Capitalism, both papers have similar simulations. But value isn’t discussed in the last two papers.
For a macro model, with the emergence of value and prices corresponding to values, you can check out Convergence to Natural Prices in Simple Production for simple commodity production with no exploitation and Classical Macrodynamics and the Labor Theory of Value for a macro model with exploitation.
Also, for a theoretical discussion of the work you can either check out his thesis, The Law of Value or specific papers such as a discussion paper where he discusses his non-standard value Nonstandard Labor Values, or a more detailed paper Marx’s Transformation Problem and Pasinetti’s Vertically Integrated Subsystems
I find this field fascinating and I love simulations. Hopefully I can share something of my own one day. So I’d like to congratulate you, and also love to hear about any updates!
All of those sound interesting, I will check them out.
I would love to share them. Hopefully I have something good by the end of the week.
I am very well aware that the dynamism is important for the law of value. I have tried making simulations of micro actors in the past to simulate commodity exchange, but those tended to become computationally intensive beyond what my cheap laptop could handle. (Either that, or trying model various effects to make it more accurate would start becoming like a full time job, forcing me to focus on my actual studies instead. )
This simulation is intended only to model a single time step (for now, adding more time steps comes in once I perfect the simulation for a single time step).
I was in that same boat with my micro models. It got to where I felt like I had to add X, but to add X properly it felt like I also needed to handle Y, and so on and so on. So I get the struggle! I can have a problem of not knowing when and how to set the level of abstraction and not let the perfect be the enemy of the good. I have so many scrap projects that stall out because of this. And proletariat science unfortunately has to deal with the fact that we have other jobs that take away our time.
I will give it another look now that I understand what you were doing with the 1000 prices and that you did disaggregate. It isn’t bad code, it just isn’t my first language!
Don’t know when I will get back, but I hope do it soon as I genuinely love this sort of stuff!