Starting with QD = 60-10P and QS = 10P and supposing that the government imposes an excise tax of $2 per unit collected from producers, find (a) the new equilibrium price and quantity and (b) how much of the tax is actually paid by consumers and how much falls on producers

(a) To find (a), the first step is to determine the equilibrium price and quantity before the imposition of the excise tax.

QD = 60 - 10P

QS = 10P

At equilibrium QS = QD:

• 60 - 10P = 10P
• 60 = 10P + 10P
• 60 = 20P
• P = $3

Substitute 3 in either equation to get equilibrium quantity:

• QS = 10P
• QS = 10(3)
• Q = 30 units

Now, we can determine the equilibrium price and quantity after the imposition of the $2 excise tax. The tax is collected from the producers, so it reduces the price of producers.

• The new supply equation will be: QS = 10(P - 2)
• QS = 10P - 20
• The demand equation remains the same: QD = 60 - 10P

At equilibrium, QS = QD.

• 10P - 20 = 60 - 10P
• 10P + 10P = 60 + 20
• 20P = 80
• P = $4

Equilibrium quantity:

• QS = 10P - 20
• QS = 10(4) - 20
• Q = 40 - 20
• Q = 20 units

The new equilibrium price is $4, and the new equilibrium quantity is 20 units.

(b)

The equilibrium price increased by $1, so because the tax was $2, it means that the tax imposed by the government is shared equally between the consumers and producers.

• Consumers pay $1.
• Producers pay $1.