"x dollars allowed to exist at a given time"- nonsense!

This little lesson in economics from Welker's "Shanghai American School" deals with money creating transactions and the banking system's lending system and money multipliers. These methods have been understood since ancient times.

Over-simplified, but reasonably accurate, this formula shows how a deposit multiplies money:
Monetary Multiplier = 1/required Reserve ratio
or M=1/R
"e. g., if you deposit $500 into a bank, and the reserve ratio is 20%, $500 x 1/0.2 = $2500 dollars" created.

http://welkerswikinomics.wetpaint.com/page/Multiple-Deposit+Expansion

As the reserve ratio changes, the result changes, e. g. if the reserve ratio increases, the monetary multiplier decreases.

The Federal Reserve System in the U. S. sets policies that affect the money market.

The above is Chapter 13 of this beginner's economics; click on Chapter 14 on Interest Rates and Monetary Policy for further basics.

Did this help that worker in Lower Slobovia who is paid $0.25 for his labor?
How much would he get before he took that job? $0
Did he have any other opportunities? No, so he took the job.
The alternative is starvation.
That $0.25 pays for his bread and a place to sleep. There may be a cent or two left over to send home, when before there was $0.
That little bit sent home may keep his sister out of prostitution or slavery.

Where did that money come from? Someone saw an investment opportunity (Nike, etc.) and set up a factory. A skill was learned. Materials are needed, and a ripple effect created more jobs supplying the materials.
Was the guy who set up the factory one of the super-rich? Possibly, or just a company supported by thousands of little investors whose savings have been put together by a bank and loaned to the guy so that he could built the factory.

We can see how the system operates in India, where the multipliers have led to a fast growing economy and a prosperous middle class. The Indian government now is able to invest a billion or so in improving the lot of the peasants who have been little touched by India's capital growth (program announced today- BBC). More and more will come under the capitalist umbrella; another 50 years and India will be a major power equal to or surpassing North America.