You are confusing the number of shares issues versus the trading price. Trading price is NEVER (legally) set outside of the initial IPO. Also the number of shared issued is set by the Board, not by law. Therefore any company can in theory issue any number of shares that they please.
The formula to determine how much a company is worth in the number of shares outstanding time the price. Using your model above lets assume a company has 1,000,000 shares and that the shares are trading at $1. The company is worth $1 x 1,000,000 shares or $1 million. If the share price rose to $20 per share with 1 million shares, the company would now be worth $20 million. The demand does not change the number of shares is changes the price investors are willing to pay for the shares. If the company earned $.10 per share in 2013 but indicated that they were likely to earn $2 per share due to a rapid increase in sales in 2014, investors would be willing to pay a higher price as the company's shares would experience higher demand. Investors would be willing to pay more for a company whose earning were to rise sharply.
The board of directors can propose a company issue more shares and this will change the number of shares trading, but this is infrequent. On a daily basis there is no change in the number of shares a company has available for trading in the market.
So a company will see its share price rise when investors are willing to pay more for them and this in turn increases the total value of the company. This is not limited to penny stocks. This is how it works for all companies that are publicly traded.
Definition of 'Pump And Dump'
A scheme that attempts to boost the price of a stock through recommendations based on false, misleading or greatly exaggerated statements. The perpetrators of this scheme, who already have an established position in the company's stock, sell their positions after the hype has led to a higher share price. This practice is illegal based on securities law and can lead to heavy fines.
The victims of this scheme will often lose a considerable amount of their investment as the stock often falls back down after the process is complete.
Investopedia explains 'Pump And Dump'
Traditionally, this type of scheme was done through cold calling, but with the advent of the internet this illegal practice has become even more prevalent. Pump and dump schemes usually target micro- and small-cap stocks, as they are the easiest to manipulate. Due to the small float of these types of stocks it does not take a lot of new buyers to push a stock higher.
Claims about how a stock is set to break out should be met with a considerable amount of caution. It is important to always do your own research in a stock before making an investment.
They do a lot of advertising via direct mail, sending fancy brochures out to thousands of people on mailing lists that they buy. Years ago, I tracked about 20 of these stocks. They all went up and then came back down.....HARD!
My understanding of stocks is that there is a set amount of stocks made available by a company, so why are penny stocks able to grow into 20+ mil?