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.

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