Question

1. In Country Faraway, cigarettes are forbidden, so people trade cigarettes in a black market. The cigarette demand is QD = 12 − P, and the cigarette supply is Qs = 2P.

1. Find the equilibrium price and quantity in the black market.
2. The government becomes aware of the black market and reinforces the police so that half of the cigarette supply would be seized and destroyed. Under this circumstance, what are the demand and supply functions? Show the change by using a supply and demand diagram.

Answer 1

In Country Faraway, cigarettes are forbidden, so people trade cigarettes in a black market.

The demand for cigarettes is given as

Qd = 12-P

And, the cigarettes supply is given as

Qs = 2P

Now, using the above information, we have to solve the following questions.

(a) At equilibrum, the quantity demanded would be equal to quantity supplied in the black market. Hence, at equilibrum

Qs = Qd

or, 2P = 12-P

or, P* = $4

And, let us say, the equilibrum quantity is Q*.

Hence, Q* = Qs = Qd

Q* = Qs = 2.P* = 2×4

or, Q* = 8 units

Hence, equilibrum price is $4 and equilibrum quantity is 8 units in the black market.

(b) Now the government becomes aware of the black market and reinforces the police so that half of the cigarette supply would be seized and destroyed.

Now, previously the cigarettes supply was

Qs = 2P

Now, half of the cigarettes supply is destroyed. Hence, the new cigarettes supply is

Qs' = Qs/2

or, Qs' = 2P/2

or, Qs' = P

This is the new supply finction under the circumstances.

And, there would ne no effect on the demand side. Because, the givernment did not imposed any taxation or limitation in consumption of cigarettes. Hence, the demand function would remain same. Hence,

Qd' = Qd

or, Qd' = 12-P

This is the demand function under the circumstances.

Under this circumstances,

Demand Function: Qd = 12-P and

Supply Function: Qs = P

The change is shown in a diagram below.

The change in supply from Qs to Qs' is shown in the diagram.

Hope the solution is clear to you my friend.