I could not understand why in this example ("With a value-added tax" subsection) the government charges 0.10 = $1 × 10%, but not 0.11 = $1.1 × 10%
The manufacturer spends ($1 + ($1 × 10%)) = $1.10 for the raw materials, and the seller of the raw materials pays the government $0.10.
The bigger problem is all the examples do the counting in the same way (Mankiw book, some other internet examples EU VAT overview )
With a VAT, each merchant along the supply chain needs to keep track of two numbers: the price of the item before the VAT, and the price including the VAT. The difference between the two is the amount of VAT that they have already paid.
In the Wikipedia example, the manufacturer buys raw materials from the supplier. The cost of the raw materials is $1 before the VAT, and with the 10% VAT, he pays the supplier $1.10. The supplier keeps $1 and sends $0.10 to the government.
The manufacturer wants to make $0.20 profit, so he charges a before VAT price of $1.20, which after the 10% VAT is $1.32. The wholesaler pays the manufacturer $1.32. At this point, the wholesaler has paid $0.12 in VAT. The manufacturer sends $0.02 to the government and keeps $0.10 to reimburse himself for the VAT he paid on the item earlier.
This continues down the supply chain. As long as the buyer of the item resells it at a profit, he charges VAT and keeps a portion of it to reimburse himself for the VAT he has already paid. The final consumer that does not resell the item ends up ultimately paying the entire VAT and not getting reimbursed.
$1.10 / 110% = 1$
From a consumer's point of view, the prices you see on store shelf are inclusive of VAT. This applies to online shops as well, if you look hard enough, you can often find somewhere a statement that the prices are inclusive of VAT.
As a consequence, the vendors do not pay the tax on top of what you pay them, but rather, the tax is already a part of the what they get.
Putting it differently, it is the buyers who pay the tax, and the vendors merely collect it (by adjusting the prices accordingly).
There are usually some mechanisms to ensure that the tax is not applied several times, which may cause the prices exclusive of vat to matter (e.g. the tax is not collected when I buy the goods from a supplier so as to sell them further), and you may avoid paying the tax when buying abroad (in duty-free shops, for example).
However, as far as I know, in most cases there's no reason to care about VAT (except when pressuring the politicians to change it, perhaps), rather than the total price.
