RE: Paying tax / VAT
When you buy from amazon.co.uk, Amazon do not pay the VAT to HMRC. *You* pay the VAT to Amazon who put it in the bank for the quarter and then pass it onto HMRC, less any VAT they have paid out for products / services they have acquired.
So, in NY it would be that NYorkers would pay the sales tax to Amazon who would then pass it on to the state. The net effects would be:
Customer's would pay more
Amazon would make the same profit*
NY State would make more profit
If customer's have to pay sales tax then Amazon becomes less attractive than previously so there is a risk that customers would go elsewhere (like the shop where they can take possession of their goods immediately) or Amazon would have to lower prices and make less profits.
*I know that Amazon would be able to make some interest on the collected sales tax, but I am assuming this would be offset against the costs of processing the extra tax.