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 change in producer surplus (per million boxes) associated with the quota?
A) $\$ 175$
B) $\$ 75$
C) $\$ 50$
D) $\$ 25$

Question

Quizplus · Accepted Answer

The producer surplus is the area below the supply curve and above the equilibrium price. The equilibrium price is found by setting the demand and supply curves equal to each other:$$60 - Q ^ { d } = 0.5 Q ^ { s }$$$$Q ^ { d } = Q ^ { s } = 40$$The producer surplus is then:$$PS = \int_{0}^{40} (0.5 Q ^ { s } - 60) dQ = 800$$With the quota, the quantity supplied is fixed at 30 million boxes per month. The producer surplus is then:$$PS = \int_{0}^{30} (0.5 Q ^ { s } - 60) dQ = 450$$The change in producer surplus is:$$\Delta PS = PS_{quota} - PS_{equilibrium} = 450 - 800 = -350$$The change in producer surplus per million boxes is:$$\frac{\Delta PS}{Q} = \frac{-350}{30} = -11.67$$The correct answer is A) $\$ 175$.

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 $P = 60 - Q ^ { d }$