Suppose that the market for corn is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as $P = 10 - Q ^ { d }$ ; the supply curve can be expressed as $P = 0.25 Q ^ { s }$ . Quantity is expressed in millions of bushels. Now suppose that the federal government imposes a price floor of $3 per bushel of corn. Which of the following best describes the market after the price floor is imposed?
A) There will be a shortage of 5 million bushels.
B) There will be a surplus of 5 million bushels.
C) There will be a surplus of 7 million bushels.
D) There will be a surplus of 12 million bushels.

Question

Quizplus · Accepted Answer

Before the price floor is imposed, the market is in equilibrium, meaning that the quantity supplied is equal to the quantity demanded:

10 - Qd = 0.25Qs

Solving for Q, we get:

Qd = 40 - 0.25Qs

Substituting Qs = Qd, we get:

Q = 20

This means that the equilibrium quantity of corn is 20 million bushels, and the equilibrium price can be found by substituting Q into either the supply or demand equation:

P = 10 - Qd = 10 - (40 - 0.25Qs) = $8 per bushel

When the government imposes a price floor of $3 per bushel, this means that the price cannot fall below $3. However, the equilibrium price is $8, so the price floor is not binding and has no effect on the market. As a result, the quantity supplied and demanded remain at 20 million bushels, so there is no shortage or surplus.

Therefore, the correct answer is B.

Suppose That the Market for Corn Is Initially in Equilibrium P=10−QdP = 10 - Q ^ { d }P=10−Qd

Suppose That the Market for Corn Is Initially in Equilibrium $P = 10 - Q ^ { d }$