Question

Question 6:

Suppose that the market for cigarettes in a particular town has the following supply and demand curves: QS=PQS=P; QD=60−PQD=60−P.

What is the equilibrium quantity and price?

Suppose that the town council wants to reduce cigarette consumption. It imposes a quantity tax per unit of cigarettes on the consumer side. Find the new equilibrium quantity, the equilibrium price paid by the consumer, and the equilibrium price received by the producer.

Suppose the flat tax is 20. What is the new equilibrium quantity, the price paid by consumer, and the price received by the supplier?

Compute the consumer surplus before and after tax. Draw the supply and demand curve and label the equilibrium quantity and prices. Also shade the area of the consumer surplus before and after tax.

If the council wants to reduce cigarette sales to 5, what would the appropriate tax be?

Answer 1

Equilibrium at demand= supply,

60-p=p

P=60/2=30

Q=30

Let assume per unit tax=t

New demand after tax, p=60-q-t or q=60-p-t

New Equilibrium,

60-p-t=p

P=(60-t)/2=30-0.5t{ price producer received pay}

Price CONSUMER pay=30-0.5t+t=30+0.5t

Q=60-(30-0.5t)-t=30-0.5t

t=20

P=30-0.5*20=20

Price CONSUMERs pay=30+0.5*20=40

Q=30-0.5*20=20

Before tax,

CS=1/2*30*(60-30)=450

PS=1/2*30*(30-0)=450

After tax,

CS=1/2*20*(40-20)=200

PS=1/2*20*(20-0)=200

Q=30-0.5t

Initial Q=30

Desired Q by council=30-5=25

25=30-0.5t

t=5/0.5=10

So t=10 ,lead to Q reduce by 5 units.