Here is the lemmygrad post I made it at (don’t wanna have to copy everything over).

Please give the post lots of heart-sickle, the post would really appreciate it

Don’t be afraid to ask questions.

  • Sebrof [he/him, comrade/them]@hexbear.netEnglish
    2·
    3 days ago

    Can you explain how you are calculating the wages paid out to workers? In words you state:

    c. It is assumed that consumers are not going into debt, which means the total money they spend on net consumption comes from the wages (or dividends) paid by industry. Wages are paid by each industry proportionally to their gross labor usage

    And in the code you have:

    ` %Industry to consumer sales (assuming consumers save/lose nothing)

    S = o.*P; %Sales to consumers

Y = sum(S); %Total consumer spending = wages paid out

W = L.*Y; %Wages paid out vector by industry

    I have a couple of questions about this, but I still start with the calculation of Y (the answer may clarify my remaining questions).

    You start with S = o.*P; %Sales to consumers where you are performing an element-wise multiplication of a n x 1 vector of net-products by a n x mag array of prices.

    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 sans-shrug ) the line S = o.*P; is calculating the below, correct?

    Each of these elements, si = pi ci is the part of sector i’s revenue which it receives from its sales to consumers. (It isn’t the total revenue of the sector, though. That is given earlier by Ri = pi qi).

    Then you are summing along each column (you mentioned that MatLab’s sum function sum’s matrices down the column). For a single instantiation of a price vector, this is results in

    Y = p1c1 + p2c2 + … = p c

    which gives us a global wage bill, i.e. the total expenditure of the working class for the economy. This is an aggregated quantity over the entire economy.

    Y is a row-vector, though, in your code since you are testing multiple prices - mag of them in fact. if I have the correct understanding, your Y vector is

    Y = [Y(1) Y(2) … Y(mag) ]

    where I am using superscripts to designate distinct price instantiations.

    But I think I must be misunderstanding something, because if the above is true, then I am not certain how the line

    W = L.*Y; %Wages paid out vector by industry

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

    My understanding is that your L vector is a n x 1 array of normalized labor-times for each sector.

    L = O.*l;

    L = L/sum(L); %Normalising gross labor use

    So I need your help in understanding the calculation here.

    I have more questions, but I will save them for later. Thanks for taking the time to discuss this!

    • sodium_nitride [any, any]@hexbear.netOPEnglish
      2·
      2 days ago

      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

      • Sebrof [he/him, comrade/them]@hexbear.netEnglish
        1·
        2 days ago

        Okay great! This answers my next questions

        So you calculate an average wage-rate (price per labor hour)

        w=pc/L

        and pay out to each worker sector i their eage using this wage-rate

        wLi

        Now we have a price equation that we can represent as

        p = wl + pA + π

        where the profit of each sector i I’m defining as Profiti=πiqi. I.e. πi is a profit per gross output of a sector.

        The above is in a style that is close (but not completelt identical) to a Sraffa-Pasinetti framework. But setting it up that way can allow you to compare with the Sraffian framework that you may find in the literature. In this framework, it is assumed that due to competition of capitals, an equilization of profit rates emerges. A single profit rate r emerges. So π becomes written in terms of the rate of profit, π= r pA, or it is sometimes defined as r (w l + pA) which is more in line with how the classical political economists such as Marx defined the rate of profit.

        Also, if we assume the capitalists take their profits and spend it all on commodities such as luxury items, then we will need to introduce a capitalist consumption vector cK and add it to the worker consumption so it is included in the net product. This will increase the gross product, and also increase the labor that workers must provide (i.e. now workers must perform surplus labor to create commodities for capitalists). Ian Wright’s contribution is finding a measure of value which incorpotes that surplus labor and is proportional to the price. It is a measure of total labor embodied in a unit of workers’ consumed product.

        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.

        If ever interested more in any of the above I’d always be down to talk. I find it fun!

        Here are some extra tidbits about the equation. You may or may not find this worthwhile for the purposes of the simulation.

        Again, the equation you have is

        p = wl + pA + π

        We can rewrite it as

        p = wv + π(I-A)-1

        This tells you the difference between the price and the standard labor value in terms of your residual.

        Another alternative way to view the original equation is purely in terms of quantity flows, if we note that w=pc/L, then the term wl can be written as

        wl = p [(cl) (1/L)]

        The term in brackets, [(cl) (1/L)], is actually a consumption matrix, C(W), for the working class. Recall c is a column vector while l is a row vector. It is like the workers’ consumption analog to the industrial sectors’ input output matrix A.

        Element i,j of A tells us how much of product i the sector j requires to produce one unit of gross output in j.

        Similarly, element i,j of C(W) tells us how much of product i workers in sector j consume per unit of gross output in sector j.

        Some interesting properties of C(W)

        C(W)q = c(W) (for the workers)

        pC(W) = wl

        So if C(W) is known data, or constructed by a model, you can write the equation

        p = wl + pA + π

        as

        p = pC(W) + pA + π

        which can be rewritten as

        p = π (I - A(+))-1

        where A(+) = A + C(W)

        • sodium_nitride [any, any]@hexbear.netOPEnglish
          2·
          2 days ago

          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.

        • sodium_nitride [any, any]@hexbear.netOPEnglish
          2·
          2 days ago

          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.

          • Sebrof [he/him, comrade/them]@hexbear.netEnglish
            2·
            2 days ago

            Yeah and I noticed that the profits don’t go toward any class consumption. But I realize that this is fine as it is the scope of this first model - I just wanted to clarify the assumptions that a Sraffian model uses. And I agree, that in computational models one shouldn’t assume it - one checks if they emerge. That’s the more fascination approach. It would be interesting to see if a future model generates an equalization of profit rates and/or equalization of wage rates if the wage rate is an endogenous variable determined by a labor market.

            I have models that I would like to share as well. 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.

            In the meantime thanks for the great discussion! I don’t have more questions at the moment but I’m looking forward to updates!

            Thanks again! And best of luck in your future projects cyber-lenin rat-salute-2

            • sodium_nitride [any, any]@hexbear.netOPEnglish
              2·
              2 days ago

              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.