What happens as we move from a few agents to many to a billion ?

Markets
Acting thru time and location
Many markets by tupe of commodity
Time and location

at least one
for each commodity type
 many many firms
even more distinct
Commodities

What a scramble of crossing and double crossing decisions

The basic unit a single
if an n compounding of items
Then  itemized into n distinct transactions

  transaction data (T DATA )
Items prices
Time place buyer seller payment terms

Surely we can build a raw t data  gathering system
 and at various scales And scopes  etc

Real time info streams

Look at the real system out there
With more and more T level
Observations

Let the social production system advance in small finite leaps and transformations

The pile of commodities is always finite ...even if in prospect limitless

Analytic value theory

Hey The market economy is a discrete System With discrete money prices and transactions Yes there are results from analytic Like in number theory can be valid but ..... Models with discretion are better The uncountable infinitesmals and info its Are Zeus like powers Leave the lightening and thunder bolts to the ivory academy bell tower

Point of production v point of extraction in exploitation process

The two points neednt ever coincide at all The capitalist production system tends To equalize product level profits Thru market forces dynamic impact on firm level product Mark up realizations This is by no means a simple reflection Of the exploitation of the direct labor inputed into that product at that stage by that firm alone ..... Market mediated competion for jobs may optimally equalize wages for Certain tasks across firms But this only equalizes that tasks rate of exploitation without determining the exact rate of that exploitation or it's points of extraction in the whole system of production and circulation

Capitalist breakdown part II

Discussion of the formula Edit The number of years n down to the absolute crisis thus depends on four conditions: The level of organic composition Ω. The higher this is the smaller the number of years. The crisis is accelerated. The rate of accumulation of the constant capital ac, which works in the same direction as the level of the organic composition of capital. The rate of accumulation of the variable capital av, which can work in either direction, sharpening the crisis or defusing it, and whose impact is therefore ambivalent. The level of the rate of surplus value s, which has a defusing impact; that is, the greater is s, the greater is the number of years n, so that the breakdown tendency is postponed. The accumulation process could be continued if the earlier assumptions were modified: the rate of accumulation of the constant capital ac is reduced, and the tempo of accumulation slowed down; the constant capital is devalued which again reduces the rate of accumulation ac; labour power is devalued, hence wages cut, so that the rate of accumulation of variable capital av is reduced and the rate of surplus value s is enhanced; finally, capital is exported, so that again the rate of accumulation ac is reduced. These four major cases allow us to deduce all the variations that are actually to be found in reality and which impart to the capitalist mode of production a certain elasticity ... Much of the remainder of Grossman's book is devoted to exploring these "elasticities" or counter-crisis tendencies, tracking both their logical and their actual, historical development. Examples of each would include: Depressed interest rates, investment capital transferred to unproductive speculation, e.g. housing stock, art objects. Enlarged state sector bleeds value from the accumulation process via taxes. Wars destroy capital values. The Reserve army of labour (unemployed) created to discipline wage claims. Imperialism

Capitalist Breakdown grossman

c = constant capital. Initial value = co. Value after j years = cj v = variable capital. Initial value = vo. Value after j years = vj s = rate of surplus value (written as a percentage of v) ac = rate of accumulation of constant capital c av = rate of accumulation of variable capital v k = consumption share of capitalists S = mass of surplus value, being: {\displaystyle k+{a_{c}\cdot c \over 100}+{a_{v}\cdot v \over 100}} k+{a_{{c}}\cdot c \over 100}+{a_{{v}}\cdot v \over 100} Ω = organic composition of capital, or c:v {\displaystyle c_{0}} c_{0}: {\displaystyle v_{0}} v_{0}) j = number of years Further, let {\displaystyle r=1+{a_{c} \over 100}} r=1+{a_{c} \over 100} and let {\displaystyle w=1+{a_{v} \over 100}} w=1+{a_{v} \over 100} The formula Edit After j years, at the assumed rate of accumulation ac, the constant capital c reaches the level: {\displaystyle c_{j}=c_{o}\cdot r^{j}} c_{j}=c_{{o}}\cdot r^{j} At the assumed rate of accumulation av, the variable capital v reaches the level: {\displaystyle v_{j}=v_{o}\cdot w^{j}} v_{j}=v_{{o}}\cdot w^{j} The year after (j + 1) accumulation is continued as usual, according to the formula: {\displaystyle S=k+{c_{o}\cdot r^{j}\cdot a_{c} \over 100}+{v_{o}\cdot w^{j}\cdot a_{v} \over 100}={s\cdot v_{o}\cdot w^{j} \over 100}} S=k+{c_{{o}}\cdot r^{{j}}\cdot a_{c} \over 100}+{v_{{o}}\cdot w^{{j}}\cdot a_{v} \over 100}={s\cdot v_{{o}}\cdot w^{j} \over 100} whence {\displaystyle k={v_{o}\cdot w^{j}(s-a_{v}) \over 100}-{c_{o}\cdot r^{j}\cdot a_{c} \over 100}} k={v_{{o}}\cdot w^{{j}}(s-a_{{v}}) \over 100}-{c_{{o}}\cdot r^{{j}}\cdot a_{c} \over 100} For k to be greater than 0, it is necessary that: {\displaystyle {v_{o}\cdot w^{j}(s-a_{v}) \over 100}>{c_{o}\cdot r^{j}\cdot a_{c} \over 100}} {v_{{o}}\cdot w^{{j}}(s-a_{{v}}) \over 100}>{c_{{o}}\cdot r^{{j}}\cdot a_{c} \over 100} k = 0 for a year n, if: {\displaystyle {v_{o}\cdot w^{n}(s-a_{v}) \over 100}={c_{o}\cdot r^{n}\cdot a_{c} \over 100}} {v_{{o}}\cdot w^{{n}}(s-a_{{v}}) \over 100}={c_{{o}}\cdot r^{{n}}\cdot a_{c} \over 100} The timing of the absolute crisis is given by the point at which the consumption share of the entrepreneur vanishes completely, long after it has already started to decline. This means: {\displaystyle ({r \over w})^{n}={s-a_{v} \over \Omega \cdot a_{c}}} ({r \over w})^{n}={s-a_{v} \over \Omega \cdot a_{c}} whence n = {\displaystyle {log\left({\frac {s-a_{v}}{\Omega \cdot a_{c}}}\right)} \over {log\left({\frac {100+a_{c}}{100+a_{v}}}\right)}} {{log\left({\frac {s-a_{v}}{\Omega \cdot a_{c}}}\right)} \over {log\left({\frac {100+a_{c}}{100+a_{v}}}\right)}} This is a real number as long as s > av But this is what we assume anyway throughout our investigation. Starting from time-point n, the mass of surplus value S is not sufficient to ensure the valorisation of c and v under the conditions postulated.