sodium_nitride

I don't know if I should post them here or on lemmygrad (a place I don't go to often enough). If you have any suggestions for a community let me know.

Posting it on the free chat should be fine. Stuff gets traction there. Also, you could try posting in Chapo then linking to the lemmygrad. I think that could boost the engagement numbers and get lots of community interaction.

which can be rewritten as ...

The very last part of your comment is very interesting. At some point in my coding, I literally did randomly generate prices using that exact same equation. The vector pi was randomly generated (and so was A+). I didn't use that pricing generation strategy because it caused the deviation of the prices to clump around the average for large sector numbers. But, that was my incomplete model. I think I can try and see how my finished model reacts to these prices.

For the model in this post, there is no assumption of equal profit rates, no structual mechansim for enforcing equalizafion of r, so the profit is simply a residual.

Not exactly. It's more so that in this model, there is no class other than the working class. There is also no mechanism for profit rate equalization because this model doesn't have time steps. The only purpose of the model is to investigate the relationship between prices and economic stability.

I do have a model that I have just about finished coding that incorporates the idea of time, movement, wage rates and external trade. The post for that is in the works.

Maybe the third model in the series model will have profits and a capitalist class in it. The second version is still a massive upgrade, so I want to release it first.

Profit equalization is also something I don't plan on assuming. The agents in my 3rd model will try to maximize profits, and maybe profit equalization might emerge.

Although, the sectors in the 2nd model do hire more workers when the sector's income is high, which is something like a profit maximization behaviour. Of course, the sectors in my 2nd model can't choose prices (it wouldn't make sense, since all gross outputs are fully sold), so it's not true profit maximization behavior. The sectors in my models (so far) are also not individual firms, which limits their agency as agents.

Working under the assumption that the net product is the net consumption of workers, i.e. n = c (also, don’t worry about using a standard notation - there isn’t really much of one. I am using a mix of Ian Wright’s, Pasinetti’s and my own ) the line S = o.*P; is calculating the below, correct?

Yup, 100% correct

Works out because you couldn’t element-wise multiply a n x 1 array L with a 1 x mag array Y.

This is indeed a valid operation in Matlab, also equivalent to L*Y (I could have clearer here)

Thanks for taking the time to discuss this!

No problem

Matlab element wise multiplication indeed works in the correct way that you described.

sum(Leon.*l)

is equivalent to

l*Leon

which is why MatLab's "sum" function by default sums down columns rather than by rows. The sum(Leon.*l) notation keeps things explicit (helps me in coding consistently), but the MatLab compiler knows how to optimize these things.

I added in the explict checks. It turns out, a huge number of the matrices being produced were non-productive. Instead of trying to keep generating matrices, I made a different fix (which makes the technical matrices more realistic, so win-win)

I made it so that the average number of entries in each row of the technical matrix is (2*n)^0.5

This means that as the economy grows larger, the matrices grow sparser. This makes productive matrices much more likely (at which point, I just have a check which makes it so that non-productive matrices are regenerated).

Curiously, this change doesn't have that big of an effect on the outcome. I've verified. The model simply handles negative net production and treats it like purchasing commodities from the external market (so something like imports). Still, I have removed it for now.

Looking forward to the 10,000 year reign of the burger emperor, his golden throne (the toilet) fueled by the souls of a 1000 immigrants being sacrificed a day.

All of those sound interesting, I will check them out.

also love to hear about any updates!

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).

7. 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.

8. 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).

unit cost = A^T p

This is what I have done in C (except I also multiplied by gross output yo get total costs per sector)

If you wanted an aggregate quantity across all sectors, this would be the p q - you have already calculated this as R.

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.

And perhaps this is what you’ve done, but just in an aggregate way.

my shitty code is causing people to think I aggregated everything even though everything is disagregated.

6. uh, I haven't really read staffa or anything, but my approach for computing ltv prices was

Assume 1 unit of net output for a commodity

Calculate how much gross production would required for each sector in that case

Element wise multiply this with direct labor use to get needed labor from each sector

Add up all of the labors from all the sectors.

In formal terms, for sector 1

(I-A)^-1 * [1;0] = g = Gross product for 1 unit of sector 1

Then

sum(g.*l)

The "(eye(n)-A)\eye(n))" computes "g" for every sector at once (the output is [g1 g2 g3 g4 ...])

I believe this is equivalent to the equation you have also provided, except your equation involves fewer steps.

Also, just as a context thing, matlab, for some reason sums matrices down columns by default. So the output the ltv prices equation is a row vector of the summed labors (which I transpose using the apostrophe symbol ')

Indeed I am pretty sure that my code actually is using prices and values for each sector separately, otherwise the code should be giving me an error regarding the dimensionality of the code.

1. correct

2. correct

3. I was under the impression that since matlab's "rand" generates values between 0 and 1, all of the technical matrices should be automatically productive, but you are correct. I should add explicit checks

4. yes

5. I normalise the net product so that different economies are more comparable to one another. I am interested in the ratio of output between 2 industries, and not the scale of overall production

I normalise the gross labor use because that variable should actually be "share of workforce employed". The name is a relic from my previous attempt at the code where I had tried to incorporate the population into the sim. I seem to have forgotten to change the name.

Matlab's elementwise multiplication is not a dot product