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?

a. Price = $20, Quantity = 4 units

b. Price = $12, Quantity = 2 units

c. Tax revenue = $24

Explanation:

Please see Attachment_1 for part a.

Please see Attachment_2 for part b and part c.

a. price is $60, quantity is 14.

b. price is $36; quantity is 8

c. $96

Explanation:

A) Equilibrium is when demand is equal to supply

Demand: QXd = 14 - (1/2)PX must be equal to Supply: QXs = (1/4)PX – 1

14 - (1/2)PX = (1/4)PX – 1

- (1/2)PX – (1/4)PX = 1-14

- (1/4)PX = -15  

Dividing both sides of the equation with - 1/4, we get  

PX = 60.  

Price at equilibrium is 60.  

Substituting PX=60, into the Supply equation to get the Quantity at equilibrium:

QXs = (1/4)PX – 1

QXs = (1/4)(60) – 1

       = 15 – 1

       = 14

Quantity at equilibrium is 14.  

(please see attachment for graph) EQUILIBRIUM A

B) A $12 excise tax will result in a decrease in demand and supply will remain the same.

QXd = 14 - (1/2)PX + 12

        =26 – (1/2)PX

The new equilibrium price and quantity will therefore be:

26 - (1/2) PX = (1/4)PX – 1

(-1/2 -1/4) PX = -26 – 1

-3/4 PX = -27

Dividing both sides by -3/4, we get:

PX = 36

Substituting the new equilibrium price, into the supply equation  

(1/4)PX – 1

1/4) (36) – 1 = 8

New equilibrium quantity is 8.  

(Please see attached for graph) (EQUILIBRIUM B)

C) Since an excise tax is collected on each unit sold, the amount of revenue received by the government is the amount of the tax multiplied by the quantity sold. Revenue earned by the government from a $12 tax is $12 * 8 = $96.  

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