Question based on imposesing tax

Question

Given equations describe market for widgets

                        Demand: P = 10 - Q Supply: P = Q - 4

Here P denotes the price in dollars per unit and Q denote to the quantity in thousands of units. Assume the government imposes a tax of $1 per unit to decrease widget consumption and raise government revenues. Determine new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive?

Along with the imposition of a $1.00 tax per unit, the demand curve for widgets shifts inward. At each price, the consumer desire to buy less. Algebraically, the new demand function is:
                                       P = 9 - Q.
The new equilibrium quantity is found in the same way as in (2a):
                                  9 - Q = Q - 4, or Q* = 6.5.
To find out the price the buyer pays, PB* , substitute Q* into the demand equation:
                                  P_B* = 10 - 6.5 = $3.50.
To find out the price the seller receives, Ps* , substitute Q* into the supply equation:
                                  P_s* = 6.5 - 4 = $2.50.