<p>Turns out it was a typo, when deducing equation <span class="math-container">$2.15$</span> by substituting <span class="math-container">$2.3$</span> into <span class="math-container">$2.2$</span> the result should be</p>
<p><span class="math-container">$\frac{p_1}{p_2} &lt; \frac{T-\tau_2B}{Ta_2}$</span></p>
<p><a href="https://i.sstatic.net/cX60F.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cX60F.png" alt="Solution" /></a></p>
<p>Credit to @dopplerdog from reddit for finding this out <a href="https://www.reddit.com/r/communism/comments/pnc2q6/economics_help_pls_question_on_a_passage_from/hcop5zx?utm_source=share&amp;utm_medium=web2x&amp;context=3" rel="nofollow noreferrer">https://www.reddit.com/r/communism/comments/pnc2q6/economics_help_pls_question_on_a_passage_from/hcop5zx?utm_source=share&amp;utm_medium=web2x&amp;context=3</a></p>

CC BY-SA 4.0
2021-09-13T14:12:59.387Z
2021-09-13T14:12:59.387Z
Gabriel
<p>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:</p>
<p><a href="https://i.sstatic.net/Pged8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Pged8.png" alt="Passage from page 94 in Okishio, N., 1990. Constant and variable capital. In Marxian Economics (pp. 91-103). Palgrave Macmillan, London." /></a></p>
<p>I can't figure out how he is able to get equation <span class="math-container">$2.16$</span>. I have the feeling that he is dividing inequalities <span class="math-container">$2.14$</span> and <span class="math-container">$2.15$</span>, 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. <br/></p>
<p>For reference, <span class="math-container">$2.3$</span> is <span class="math-container">$B= (wT)/p_2$</span>, and the only assumptions are: <span class="math-container">$1-a_1&gt;0$</span>, i.e. net output from production, and the starting equations <span class="math-container">$p_1&gt;a_1p_1 + \tau_1w$</span> and <span class="math-container">$p_2&gt;a_2p_1 + \tau_2w$</span>.</p>
<p><span class="math-container">$i = 1$</span> - Means of Production <br/>
<span class="math-container">$i = 2$</span> - Consumable goods <br/>
<span class="math-container">$p_i$</span> - Unit price of good <span class="math-container">$i$</span> <br/>
<span class="math-container">$\tau_i$</span> - Labour power required for production of a unit of <span class="math-container">$i$</span> <br/>
<span class="math-container">$a_i$</span> - Means of production required for the production of a unit of the good <span class="math-container">$i$</span> <br/>
<span class="math-container">$T$</span> - Amount of Working Hours per day <br/>
<span class="math-container">$B$</span> - Affordable consumable goods at a money wage rate '<span class="math-container">$w$</span>' and working '<span class="math-container">$T$</span>' hours a day <br/></p>

CC BY-SA 4.0
2021-09-13T10:30:13.473Z
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).
BrsG
CC BY-SA 4.0
2021-09-13T11:17:35.510Z
That's a relief! Thank you so much :)
Gabriel
CC BY-SA 4.0
2021-09-13T11:32:11.300Z
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
Gabriel
<mathematical-economics><production-function><marxism>
Question on a passage from N.OKISHIO's Constant and Variable Capital
Gabriel
# Question on a passage from N.OKISHIO's Constant and Variable Capital

(Asked by: username_0 on 2021-09-13)

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.](https://i.sstatic.net/Pged8.png)](https://i.sstatic.net/Pged8.png)

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

**Tags:** mathematical-economics, production-function, marxism

> **Comments:**
> **username_1**: 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).  
> **username_0**: That's a relief! Thank you so much :)  
> **username_0**: For some reason I can't upvote your answer @username_1? 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  

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## 1 answers

### Answer by username_0 on 2021-09-13. Score: 1 | Accepted answer

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](https://i.sstatic.net/cX60F.png)](https://i.sstatic.net/cX60F.png)

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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