# [OPEL:6170] L] Addendum, Marx and historical costs

aramos@aramos.bo
Wed, 11 Feb 1998 16:18:37

Re Andrew K''s PIAF:

> Date: Sat, 7 Feb 98 18:31:17 UT
> From: "andrew kliman" <Andrew_Kliman@CLASSIC.MSN.COM>
> To: ope-l@galaxy.csuchico.edu
> Subject: RE: Addendum, re Marx and historical costs

Andrew writes:

> Let me anticipate one additional point. If wages are zero and
> theres no circulating constant capital, then profit in period t
> is
>
> Pr[t] = v[t]*X[t] = L[t].
>
> Given L[t] = Lo*b^t, then the profit rate is
>
> r[t] = Lo*b^t/[(Lo/Xo)Fo + H*{b + b^2 + ... + b^t}]
>
> = 1/[(Fo/Xo)*b^(-t) + (Fo*(a-1)/Xo)*{(1/b) + (1/b)^2 + ... +
> + (1/b)^t}]

I couldn''t follow the last algebraical stept. Let me re-write the
derivation:

Give the assumptions of the model, we know that:

1 Lo*Fo*(a-1)
H = --- * ------------
b Xo

Pr[t] = L[t] = Lo*b^t

Therefore, the profit rate, assuming K[t] (losses are NOT written
down) is:

Lo*b^t
r[t] = -----------------------------------
(Lo/Xo)Fo + H {b + b^2 + ... + b^t}

Lo*b^t
r[t] = ------------------------------------------------------
Lo 1 Lo*Fo*(a-1)
---- Fo + [--- * -----------]{b + b^2 + ... + b^t}
Xo b Xo

Then, Lo is cancelled out, and the numerator and denominator of r[t]
is multiplied by b^(-t), which gives:

1
r[t] = -----------------------------------------------------------
Fo Fo*(a-1) b^(-t)
---- * b^(-t) + [-------- * ------]*{b + b^2 + ... + b^t}
Xo Xo b

I think I made a mistake here, because the term

b^(-t)
------ *{b + b^2 + ... + b^t}
b

would not be equal to:

{(1/b) + (1/b)^2 + ... + (1/b)^t}

So, where is the mistake?

Alejandro Ramos