Problem: Change in the Rate of Surplus Value

The rate of surplus value has increased from 200% to 300%. At the same time, the duration of the workweek has decreased from 48 to 44 hours.
How has the distribution of work time between the worker and the capitalist changed?

Commentary

This is a classic example of Soviet propaganda.

Now, let’s take a closer look at the essence of the problem. In the end, the worker is actually working fewer hours, while the efficiency of production has increased.
Such changes do not happen on their own. This means that the capitalist had to make certain financial investments, likely involving organizational improvements
and other measures. The amount of necessary labor has decreased. The worker himself did not contribute any effort to this change.

However, the expected conclusion from solving this problem is that the "horrific exploitation of the worker has increased." And this, despite the fact that in reality,
the worker’s labor is being used less (since the workweek has been shortened).

If, according to Marx’s theory, the capitalist is someone who does nothing but appropriates the results of labor, then it would be logical to assume that
the worker’s exploitation has magically increased.

Solution

The rate of surplus value is calculated using the following formula:

We get:
m ₁ / v ₁ * 100%  = 200%  
m₁ + v₁ = 48  

Let's solve:
m ₁  = 48 - v ₁
where
(48 - v ₁ ) / v ₁ * 100% = 200%
v ₁ = 16
Thus
m ₁ = 32

Under the new conditions:
m ₂ / v ₂  * 100%  = 300%  
m₂ + v₂ = 44   

Let's solve:
m ₂   = 44 - v ₂
where
(44 - v ₂ ) / v ₂ * 100% = 300%
v ₂ = 11
Thus
m ₂ = 33 

As a result, we find that the time of surplus labor has increased by 33 - 32 = 1 hour a week.