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If the amount of the good supplied were truly independent of price, there would be no change in the price of the good. The reason for this is that the suppliers would continue to supply the good even if they did not get as much money for it. In order to keep selling as much as they had been selling, they would accept a lower amount of money and the price for the consumer would stay the same. More of the price the consumer paid would go to the government in the form of the tax and the producer would simply take less money.
However, this is a very unlikely scenario. The law of supply says that the quantity supplied varies with the price (and is therefore not independent of it). In general, suppliers would not accept a lower price. When a sales tax is added to a good, the consumer typically has to pay a higher price to reflect that tax.
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