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Sorry if this a dumb question, I am an undergrad economics student and am currently reading this paper from Okishio on the Marxist concept of Constant and Variable capital, my issue is on this following excerpt:

Passage from page 94 in Okishio, N., 1990. Constant and variable capital. In Marxian Economics (pp. 91-103). Palgrave Macmillan, London.

I can't figure out how he is able to get equation $2.16$. I have the feeling that he is dividing inequalities $2.14$ and $2.15$, but can't think of a reason he's allowed to do that. Either that or he is assuming something from the relationship between these equations/variables that I'm not seeing.

For reference, $2.3$ is $B= (wT)/p_2$, and the only assumptions are: $1-a_1>0$, i.e. net output from production, and the starting equations $p_1>a_1p_1 + \tau_1w$ and $p_2>a_2p_1 + \tau_2w$.

$i = 1$ - Means of Production
$i = 2$ - Consumable goods
$p_i$ - Unit price of good $i$
$\tau_i$ - Labour power required for production of a unit of $i$
$a_i$ - Means of production required for the production of a unit of the good $i$
$T$ - Amount of Working Hours per day
$B$ - Affordable consumable goods at a money wage rate '$w$' and working '$T$' hours a day

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    $\begingroup$ Division is allowed here, if the terms you divide by are different from zero. And that division is exactly what gives you the result (as you suspected). $\endgroup$
    – BrsG
    Sep 13, 2021 at 10:30
  • $\begingroup$ That's a relief! Thank you so much :) $\endgroup$
    – Gabriel
    Sep 13, 2021 at 11:17
  • $\begingroup$ For some reason I can't upvote your answer @BrsG? Neither can I make the question closed and answered, I'm new here sorry :( The only action it allows me to do is flag it $\endgroup$
    – Gabriel
    Sep 13, 2021 at 11:32

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Turns out it was a typo, when deducing equation $2.15$ by substituting $2.3$ into $2.2$ the result should be

$\frac{p_1}{p_2} < \frac{T-\tau_2B}{Ta_2}$

Solution

Credit to @dopplerdog from reddit for finding this out https://www.reddit.com/r/communism/comments/pnc2q6/economics_help_pls_question_on_a_passage_from/hcop5zx?utm_source=share&utm_medium=web2x&context=3

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