Question

Suppose demand and supply are given by

QXd = 14 - (1/2)PX and QXs = (1/4)PX - 1

Instructions: Round your answers to the nearest whole number.

a. Determine the equilibrium price and quantity. Show the equilibrium graphically.
b. Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium price and quantity.
c. How much tax revenue does the government earn with the $12 tax?

Answer 1

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

`QXd = 14-(1)/(2) Px\\\\QXs = (1)/(4) Px-1\\\\QXd =QXs\\\\`

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 =
`14-[(1)/(2) (Px+12)]`

= 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.

Answer 2

a. Price = $20, Quantity = 4 units

b. Price = $12, Quantity = 2 units

c. Tax revenue = $24

Step-by-step explanation:

Please see Attachment_1 for part a.

Please see Attachment_2 for part b and part c.