Comradeship // Freechat

pancake also did some simulations about LTV a while ago, here are their posts about it: Marxist Game Theory? et Marxist Game Theory: correction.

God I know I'm a fucking nerd by the fact that I thought this was cool as hell, and could comprehend it a little (though I'm much more familiar with Python and industry specific coding, rather then economic analysis.)

`

mag = 1000;
n = 2;
N = 1000;

Data = zeros([n N*mag]);

%%%%%%%%%%LOOP

for i = 1:N

    %Net production of [MOP; MOC]
    o = rand([n 1]); %[MOP; MOC] of net production
    o = o./sum(o); %Normalise the net production
    
    %Direct Labor use for [MOP; MOC]
    l = rand([n 1]);
    
    %Technical matrix:  [MOP to MOP, MOP to MOC;
    %                    MOC to MOP, MOC to MOC]
    A = rand([n n]);
    
    %Gross production
    O = (eye(n)-A)\o;
    
    %Gross labor use
    L = O.*l;
    L = L/sum(L); %Normalising gross labor use
    
    %LTV prices calculation
    LTV = sum(((eye(n)-A)\eye(n)).*l)';
    
    %Randomised prices
    P = rand([n mag]);
    
    %Interindustry flows
    %F = A.*(O'); %Physical flows, NOT USED IN THIS SIM
    
    %Inter-industry sales
    R = O.*P;  %Market value of gross production
    C = A' .*O*P; %Costs of inputs to production
    
    %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
    
    M = R - C - W; %Net Income by industry
    M = mag*M./sum(abs(M),2); %Normalise net income
    
    specific_price = log((P(2,:)*LTV(1))./(LTV(2)*P(1,:))); %the x-coordinate variable

    Data(:,(1+ (i-1)*mag ):(i*mag)) = [specific_price; M(1,:)]; 

end
%%%%%%%%%%LOOP

pts = linspace(-3, 3, 251);
H = log(histcounts2(Data(1,:), Data(2,:), pts, pts));
imagesc(pts, pts, H);
axis xy;
set(gca, 'XLim', pts([1 end]), 'YLim', pts([1 end]), 'YDir', 'normal');
colormap copper
a=colorbar;
a.Label.String = "Density of simulation outcomes [natural log scale]";

xlabel {Ratio of actual price to LTV price [natural log scale]}
ylabel {Net income of sector 1 [linear scale]}

saveas(gcf,"repro.png");
`

My approach in the sim was:

1. Randomly generate a 2-sector economy

   a. generate 2x1 net production vector (total product sold to consumers)

   b. generate 2x1 direct labor vector (direct labor needed to produce 1 unit of gross output)

   c. generate 2x2 technical matrix (row i column k tells how many units of product i is needed to make 1 unit of product k)

2. Calculate the economy

   a. Calculate gross production as (Identity_matrix - technical_matrix)^-1 * net_production

   Gross production is a 2x1 vector of the total production of both sectors. The gross products of both sectors have to be consumed as intermediate goods to support the production process (ex - some electricity is needed to make steel, and some steel is needed to make electricity). This formula for computing the gross product can be found from Paul Cockshott's Towards a new socialism

   b. Calculate the gross labor use for each sector by multiplying their gross production and direct labor use per product.

   c. Predict LTV prices for sector k by calculating how much gross production would be needed to produce 1 unit of net output (formula in 2a), then finding how much labor would be used to do that gross production (formula in 2b)

3. Randomly generate a 1000 pair of prices (1 per sector) and compute financial flows (so this step is repeated 1000 times for each pair of prices)

   a. Each sector pays the other for the product it purchased from that sector and at the price that was generated.

   b. Each sector sells its net output to consumers at the randomly generated prices.

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

4. Repeat steps 1-3 a thousand times. This gives an overall 1 million data points from 1000 distinct economies.

There's a little bit of discussion on the hexbear post going on.