Edit: tl;dr: all tools seem to be capable of 28 nm process, except the lithography machines. However, the report (why?) doesn't include the most advanced lithography tools that are known to be manufactured.

Source

This is a sequel to my previous post. The idea is the same, but I'm using better methods as was suggested in the comments.

As u/Sodium_nitride (thank you!) explained, here...

• ...I use a production matrix instead of the Cobb-Douglas function.
• ...I use capital-time instead of capital, to handle depreciation.
• ...classes consume commodities, seeking to maximize the amount consumed.

Also, I purchased the book suggested by u/davel :)

We use the following definitions:

• Labor is measured relative to A's total labor power.
• B has b labor power, assumed to be proportional to population.
• Capital-time and commodities are measured in units of what can be produced directly from 1 unit of labor.
• Labor sold is represented with w, and the salary is used to purchase capital-time s_k and commodities s_c.
• Consumption of A is c, while that of B is z*b*c, where z is the ratio of per capita consumption.

Production matrix:

        /0 0 0\
    A = |1 m 0|
        \1 n 0/

Input vectors:

          /  1 - w  \
    x_A = |k_A + s_k|
          \    0    /

          /  b + w  \
    x_B = |k_B - s_k|
          \    0    /

Demand vectors:

          / w - 1 \
    y_A = | -s_k  |
          \c - s_c/

          /  -b - w   \
    y_B = |    s_k    |
          \z*b*c + s_c/

Payoff functions:

	X_A = c
	X_B = z*c

Case 1: full equilibrium

In this case, we assume that A and B can negotiate w, s_k and s_c freely, with no party being able to obtain a better bargaining position.

The Nash equilibrium is:

    w = s_k = s_c = 0
    c = (m - n - 1)/(m - 1)
    z = 1

That is, both groups are independent and produce their own capital-time and commodities. Their consumption is directly proportional to their labor power. Effectively, there is no difference between A and B, any member of either group belongs to the same class.

Case 2: asymmetric capital ownership

Here, we set k_A = s_k = 0, so A owns no capital-time. A and B can negotiate w and s_c under the same conditions as in Case 1.

The Nash equilibrium is:

    w = 1
    s_c = c = (1/2)*(m - n - 1)/(m - 1)
    z = 2 + 1/b

As can be seen, in this case A works for B and obtains a salary. Interestingly, this salary is exactly half of what A would have obtained in Case 1. From this and z's non-dependence on m and n, we can deduce that increases in productivity scale both A's and B's earnings with the same coefficient, so it's impossible for B to force A's income to any specific minimum.

We also see that B's per capita income is higher when less people belong to the group. For a small enough group, B's total income approaches that of A, just extremely concentrated.

A plausible hypothesis here is that, if the initial situation is Case 2 but productivity is more than high enough to sustain A's needs (thanks to the inevitable scaling described before), then A would be able to eventually negotiate their way to the final equilibrium, Case 1, provided a minimally feasible way to obtain capital.

If that is the case, the (surreal, but theoretically interesting) requirements to get to the equilibrium could be summarized like this:

1. All members of A cooperate perfectly (obviously false).
2. B has no way to gain an advantage (bourgeois state in general).
3. The productive forces have developed beyond a critical point.

Further questions

• How could one verify the hypothesis above? I know how to use production matrices in a state of equilibrium, but what about transient states?
• What if individuals can freely move across groups as their economic status changes and so do their interests? I know nothing about cooperative game theory, so this could be an interesting start.
• What if members of A and/or B do not cooperate perfectly?
• What are the minimum requirements for a mechanism that could allow the cooperative result in a non-cooperative Nash equilibrium?

Today they published a new report in the series. To my surprise, it includes a second chart with revenue-based data. Enjoy!

I'm learning game theory these days, and I've tried my hand at some problems inspired by ML theory. Here's one I found really interesting.

Let's assume the following (clearly unrealistic) situation:

1. Working class (A) and bourgeoisie (B) form perfectly cooperative coalitions.
2. They may negotiate salaries, with no class having any mechanism to obtain a better bargaining position.
3. A cooperatively owns some amount k of capital, while B owns (arbitrarily) 1. In principle, k < 1.
4. B has some labor power b, while A has (arbitrarily) 1. Again, b < 1.
5. Production follows a Cobb-Douglas function, where the sum of the output elasticities of capital and labor is 1.
6. Both classes consume the same proportion of their income and use the remainder to acquire more capital.

Therefore, the payoffs in our problem can be stated like this (where w is the labor given to B and s is the compensation given to A for this labor):

X_A = A k**α (1 - w)**β + s
X_B = A (b + w)**β - s

We would like to find how the ratio of A's capital to B's changes over time, so we compute its derivative using the quotient rule, and note that the proportion of income (p) spent on capital is the same for both classes:

R = p X_A - k p X_B

Finally, we find the Nash equilibrium and its corresponding R at each combination of k and b:

Note the attractor curve coinciding with k = 1/b. In other words, ~~if both k and b are higher than 0~~, the eventual equilibrium will be for A and B to own capital proportional to their labor power.

Edit: fixed some missing solutions near k = 0.

I have been thinking about implementing this for quite some time, but I would like some feedback from people more knowledgeable than me on the matter.

There's been some great progress in the field of Private Information Retrieval (PIR) protocols. Recently, in a 2022 article, Lin et al. describe an "updateable DEPIR", with both read and write times that can be made sublinear to database size.

I wonder if one couldn't use a combination of this technique and regular public-key cryptography to provide fully anonymous message routing. One could write outgoing messages to a fixed address and issue private reads to their contacts' addresses, with the messages themselves being encrypted with the receiver's public key.

The benefit of this would be a messaging protocol wherein the server wouldn't just be oblivious to the content of all messages, but also the social graph itself, plus all message-sending operations becoming deniable as a side effect.

First of all, I'm sorry if my question could be easily answered by finding the right source. Overall I'd say I read very little theory written by contemporary comrades, and that's something I need to fix once I have the time.

Remember this post (tl;dr: did an A2 Russian language examination after nothing more than Duolingo lessons for two years)? Well, I passed the tests! Performed kind of poorly in the essay, as expected, but still well enough not to hurt my overall score; spoken test went fine (to my surprise), as did the comprehension tests.

1 more year has passed, and I'm still tracking these numbers, albeit now posting with a different username. The upward tendency has not just continued, but even increased; now Linux is nearing 4 % market share globally and over 2 % on Steam.

I'm taking a CEFR A2 Russian language exam in a few minutes. Let's see if a massive Duolingo addiction is all it akes to crack it.

Two weeks ago the Human Development Report 2023/24 was published. As I did last year, here's a comparison of current and past socialist and capitalist economies' HDI (not weighed), along with the standard error of the latter group and a p-value computed via Mann-Whitney U-test.

Looks like socialist countries are now (in 2022) fully on par with their capitalist counterparts. All of them except Cuba saw a sharp increase in their HDI, while capitalist countries are yet to recover from the COVID-19 pandemic and its economic consequences.

Ok, so I was reading about solarpunk and circular economy and such, and came across this. Seems pretty reasonable, but also very vaguely worded, both by Wikipedia and the Capital Institute. I don't yet understand what they actually advocate for in terms of economic power dynamics, and I was wondering if any of you have heard of this concept before and think it's worth reading more into it.

Ps. if you think it's some sort of lunatic pseudo-science please let me know, that can help me keep myself safe.