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 $P = 0.5 Q ^ { 5}$ . 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 correct answer is A.The producer surplus is the area above the supply curve and below the market price. Before the quota, the market price is 60 and the quantity supplied is 30. The producer surplus is therefore:$$PS = \int_{0}^{30} (P - 0.5Q^5) dQ = 175$$After the quota, the quantity supplied is fixed at 30. The market price is now 60 - 30^2 = 30. The producer surplus is therefore:$$PS = \int_{0}^{30} (P - 0.5Q^5) dQ = 100$$The change in producer surplus is therefore:$$\Delta PS = PS_{after} - PS_{before} = 100 - 175 = -75$$The change in producer surplus per million boxes is therefore:$$\frac{\Delta PS}{Q} = \frac{-75}{30} = -2.5$$The correct answer is therefore A.

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 $P = 60 - Q ^ { d }$