Whether a tax is paid by a seller or the buyer does not affect the market equilibrium price or quantity. When the tax is paid by the buyers, it has the effect of increasing the purchase price of the buyers. This in effect shifts the demand curve to the left, assuming that the price considered are prices without tax. Extent of this shift will be exactly same as the change in price equal to the tax amount. However, there is no change in the cost of the suppliers. Therefore the supply curve remains same. The net result is that the equilibrium quantity will reduce in general. For perfectly elastic demand the demand curve will be vertical and the reduction in equilibrium quantity will be same as that in change in supply corresponding to change in price equivalent to tax amount.
In case the tax is paid by the seller the demand curve will not shift, but the supply curve will shift to the right, to an extent equal to the price change corresponding to tax amount. This will again shift the equilibrium quantity equivalent to change in supply corresponding to change in price equivalent to tax amount.
So, in sum we can say that shifting of responsibility for payment of tax between seller and buyer has no effect in equilibrium quantities. The equilibrium prices will change only if the tax rate is changed or if the basic price exclusive of taxes is changed.