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First let's get the terms to be more precise. The FairTax is the name given the movement and the legislation. The FairTax involves more than the NRST which is the National Retail Sales Tax, the FairTax also involves enforcement, administration of previous federal taxes, etc.

Secondly, your 'argument' is just that, it is not research. There is no research plan, means of data collection, data description, hypotheses, model or analytical methods defined. So it is useless as a policy instrument.

And it is flawed, very much so to the point of embarrassment but that is the advantage of an anonymous forum, you can withstand challenges without impugning your real reputation.

I will instruct you and then let you fly off the handle as I expect you to do. Because most of the FairTax haters have hot air arguments with no real research results. They are not interested in discourse but rather rants. For example, one FT hater clings to the absurdity that the current federal gas tax is a hidden tax and weaves some bizarre logic to defend this absurdity. I expect you to fall in the same category. If I don't respond to your clinging absurdities post-response it is because I really don't have time for the incorrigible. Anyways it is not for you I write but for those looking in.

For the purposes of our discussion let's say that the components of the Fair Tax (F) charged for a given product are the "hidden taxes" (H) and the open taxes (O) that are paid on said product. Both are positive numbers.

Your 'O' is undefined. This is a fatal flaw in any attempt at logical argument even in the absence of data.

However, when I buy said product with money earned before the implementation of the fair tax I have already paid taxes (T) on that money.

The federal taxes paid on present products and services are nearly all unlisted and are therefore labeled the hidden or embedded federal taxes. The federal gas tax is an exception as are various federal telecommunication taxes. So your 'T' is 'H'. This is another flaw related to the failure to properly define terms.

So, when I buy the aforementioned product, I am actually paying F + T in taxes.

You are using 'F' apparently to denote the NRST and if you had read HR 25 or studied any number of papers concerning the FairTax legislation then you would know that the NRST is only applied to products and services that came into existence post enactment of the FairTax legislation.

For example, if you buy a standard 2X4 stud from Home Depot for $2 prior to the FairTax passage, then you are going to pay the same $2 for that same stud if it is still sitting on the shelf post-enactment and there will be no NRST applied to it because it is considered pre-enactment inventory. This also applies to wholesalers and manufacturers with inventory on their loading docks.

Once that inventory clears, all post-enactment inventory will be subject to the NRST but the cost of the new inventory will have decreased. It is expected that the new lower price of that stud and the NRST applied to it will still equal $2. That is the purpose of current studies, to look at price stability across broad product categories. And that is also why the FairTax will be implemented in selected participating states first, to evaluate price stability and other issues.

I do hope you will at least understand there will be a transition period as old inventories get cleared out. Those inventories will not have the NRST applied to them. Any product manufactured before or in the process of manufacture when the FairTax is enacted will not be subject to the NRST. Anything manufactured or any service performed after enactment of the FairTax will be subject to the NRST at the retail level.