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.