And also...I'm still wondering how the price of the products we buy would not increase?
The economists that have studied the nrst actually think that retail prices will decrease. Why? because corporate income tax would also go away. This would (in theory) eliminate the built in taxes on all of the goods that we purchase. The common argument is "why would companies lose revenue by lowering their retail prices?" The answer is competition. There will inevitably be one company out there who will cut it's prices to reflect the savings it is getting in not paying taxes. In order to survive, it's competitors will have to follow suit. According to the FairTax website, the economists think that this phenomenon will eventually cause retail prices to fall about 20%. This will cover the majority of what you would pay in sales tax. The beauty of it is that you take home all of the money that you make.
With the Fair Tax plan they would actually decrease, since there would be no taxes on businesses. The cost of doing business would significantly decrease, thereby lowering prices. Besides, businesses don't really pay taxes anyway. They just pass them along in their end prices.