In a competitive market,the demand and supply curves are Q = 12 - P and Q = 5P,respectively.If output is fixed at Q = 5,what is the amount of the resulting deadweight loss?
A) 0
B) 5
C) 10
D) It cannot be determined without more information.

Question

Quizplus · Accepted Answer

The equilibrium price and quantity can be found by setting the demand equal to the supply, so:

12 - P = 5P

Solving for P, we get P = 2.4.

Since output is fixed at 5, we know that there will be excess demand (i.e. Qd - Qs) equal to 5 - Qs, where Qs is the quantity supplied at the equilibrium price of P = 2.4.

Qs = 5P = 12, so excess demand is equal to 5 - 12 = -7. This means that there is a shortage and some potential buyers are unable to purchase the good.

The deadweight loss in a competitive market occurs when the quantity exchanged is different from the efficient quantity, which is where the demand curve intersects the supply curve. In this case, the efficient quantity is where Qd = Qs, or:

12 - P = 5P

Solving for P, we get P = 2.

At this price, the quantity exchanged would be Q = 12 - P = 10.

Since output is fixed at 5, the deadweight loss is equal to the difference between the efficient quantity (10) and the quantity exchanged (5), or 5 units.

Therefore, the answer is C) 10.

In a Competitive Market,the Demand and Supply Curves Are Q