They do have a way to credit back producers. The NST does this simply by not taxing anything but the end product, so intermediate products aren’t taxed at all.
The VAT does this by taxing backproducers for only the value they added to the product, not the entire value of the product when it leaves their hands (as you have in your first example). The backproducer then presumably passes this tax to the person who buys the intermediate product from him. The end result is the tax collected by the gov’t and the tax paid by the final buyer are the same as it would be if they had just used a NST of the same rate.
Say a product goes through one back producers and a retailer before it gets in your hands. Each producer and the retailer adds a constant amount J to the value of the product.
The enters the chain at price A.
Without a tax the value of the final produt will be:
A+J+J=A+2J
And the gov’t gets nothing
With a national sales tax, the final value will be
A+J+J+Tax
Where the tax is simply 10% of the final value of the product, that is:
(A+J+J)*.1
So we get a final cost of
(A+J+J)+.1(A.+J+J) = 1.1(A+2J)
The end consumer ends up paying 10% extra, which the retailer passes to the gov’t.
For the 10% VAT, the price paid by the back producer is:
A+Tax where the Tax is 10% of A, or .1A
the guy that provided A passes the tax on to the gov’t and this first producer adds a value J.
The retailer pays:
A+.1A+J+Tax
where the tax is 10% of the value added, or .1J, giving us
A+.1A+J+.1J
and the first producer passes the .1J to the gov’t and keeps the .1A to reimburse him for the tax he paid on the original product (A).
Finally, the retailer adds his value J and charges the extra tax .1J to the final consumer for the value he’s added, meaning the final consumer pays.
A+.1A+J+.1J+J+.1J = 1.1(A+2J)
and the retailer passes on .1J in VAT to the gov’t, and gets to keep the .1A+.1J to reimburse him for the cost of the taxes the first producer (and indirectly, the person that produced A) charged him.
Also notice that the gov’t gets .1(A+2J), the same amount as if we had a simple NST, the final buyer ends up paying for all this tax, and all the backproducers are reimbursed.
