Suppose that the market for cigarettes is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as $P = 60 - Q ^ { d }$; the supply curve can be expressed as $P =$ $0.5 Q ^ { s }$. Quantity is expressed in millions of boxes per month. Now suppose that the federal government imposes a production quota on cigarettes of 30 million boxes per month. What is the deadweight loss (per million boxes) associated with the quota?
A) $\$ 275$
B) $\$ 75$
C) $\$ 50$
D) $\$ 25$

Question

Quizplus · Accepted Answer

Before the quota, the market was in equilibrium at a price of $45 and a quantity of 30 million boxes per month, where the supply and demand curves intersected.

With the quota, the quantity supplied is fixed at 30 million boxes per month. At this quantity, the demand exceeds the supply, so the price increases. To find the new equilibrium price, set the quantity supplied equal to 30 million boxes and solve for price:

$60 - Q^d = 0.5Q^s$

$60 - Q^d = 0.5(30)$

$Q^d = 45$

So the new equilibrium price is $60 - 45 = $15 per box.

The deadweight loss associated with the quota is the area of the triangle formed by the new equilibrium price, the old equilibrium price, and the quantity difference between the two equilibria (i.e. the amount by which the quantity demanded exceeds the quantity supplied at the new higher price).

The quantity difference is 45 million boxes per month minus 30 million boxes per month, or 15 million boxes per month.

The height of the triangle is the difference between the old and new equilibrium prices, or $45 - $15 = $30 per box.

The base of the triangle is the quantity difference, or 15 million boxes per month.

Therefore, the deadweight loss per million boxes is:

(0.5 x $15 x 15 million boxes per month) / 15 million boxes per month

= $7.50 per box

Multiply by 10^6 to get the answer in dollars per million boxes:

$7.50 x 10^6 = \boxed{\$75}$

Suppose That the Market for Cigarettes Is Initially in Equilibrium P=60−QdP = 60 - Q ^ { d }P=60−Qd

Suppose That the Market for Cigarettes Is Initially in Equilibrium $P = 60 - Q ^ { d }$