A. The equilibrium price = $20
The equilibrium quantity = 4
b. The equilibrium price = $12
The equilibrium quantity = 2
At equilibrium
The quantity demanded = Quantity supplied
[tex]QXd = 14-\frac{1}{2} Px\\\\QXs = \frac{1}{4} Px-1\\\\QXd =QXs\\\\[/tex]
Qxd = 14-0.5Px
QXs = 0.25Px-1
14-0.5Px = 0.25Px-1
Collect like terms
14+1 = 0.25Px+0.5Px
15 = 0.75Px
Px = 15/0.75
= 20
The equilibrium Quantity
= 14-0.5Px
= 14-0.5*20
= 14-10
= 4
B. With a 12 dollar excise duty
QXd = [tex]14-[\frac{1}{2} (Px+12)][/tex]
= 14-0.5Px-6
QXd = QXs
14-0.5Px-6 = 0.25Px-1
14-6+1 = 0.75Px
Divide through by 0.75
9/0.75 = Px
12 = Px
The equilibrium quantity
= 14-0.5Px-6
= 14-0.5*12-6
= 2
The equilibrium price is $12 and the quantity = 2
3.
