Need Help On Capitalist Equation

[The Vegan Marxist]

I was watching more of brendanmcooney's youtube videos, & was looking at his older ones, mainly "Felix the Cat and Capitalist Competition", & I ended up getting a little confused on how this formula works & why it's necessarily bad. If anyone can help, then much would be appreciated:

p = S / (c + v)

p = rate of profit
S = surplus value
c = constant value
v = variable capital

[Common_Means]

I was watching more of brendanmcooney's youtube videos, & was looking at his older ones, mainly "Felix the Cat and Capitalist Competition", & I ended up getting a little confused on how this formula works & why it's necessarily bad. If anyone can help, then much would be appreciated:

p = S / (c + v)

p = rate of profit
S = surplus value
c = constant value
v = variable capital

"It is of course understood that by `value of product' the political economists mean only the value newly created in a working day, the constant part of the value of the product excluded...[T]he actual degree of exploitation of labour, or the rate of surplus-value, is falsely expressed." (Capital, Vol. 1; p. 668)

Constant capital, machinery and such, is transferred value into the commodity via depreciation and so on. A true representation should read:
p = S / v. For instance, if a widget requires $10 c and $5 v, and generates $5 S, the first formula would show a a rate of 33% (5/15), whereas the real rate is 100% (5/5).

Hope this helps.

[The Vegan Marxist]

"It is of course understood that by `value of product' the political economists mean only the value newly created in a working day, the constant part of the value of the product excluded...[T]he actual degree of exploitation of labour, or the rate of surplus-value, is falsely expressed." (Capital, Vol. 1; p. 668)

Constant capital, machinery and such, is transferred value into the commodity via depreciation and so on. A true representation should read:
p = S / v. For instance, if a widget requires $10 c and $5 v, and generates $5 S, the first formula would show a a rate of 33% (5/15), whereas the real rate is 100% (5/5).

Hope this helps.

So it's taking out more profit than what it was put down, leading for the seller to gain more money than the worker? Also, where would this really lead to within the market when it shows a rate of 33% when, if went by a correct formula, it should've been a rate of 100%?

[MarxSchmarx]

Since p is a rate, we can use logarithms to understand it's long term behavior. The most intuitive way to understand it is to take the log of both sides.

Note log(p) α p so whenever profits are large log(p) is large, when profits are small log(p) is small etc...

now
p = S/(c+v)
-> log(p) = log(S)-log(c+v)

So profit is just surplus value you get after subtracting the capital costs involved.

[SocialismOrBarbarism]

This should be helpful:

http://www.marxists.org/glossary/terms/r/a.htm#rate-profit