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. What is the dead-weight loss (per million bushels) associated with the price floor when the most efficient producers are active?
A) $\$ 9.375$
B) $\$ 2.25$
C) $\$ 1$
D) $\$ 0.63$

Question

Quizplus · Accepted Answer

First, we need to find the equilibrium price and quantity in the market without the price floor. Set the demand equal to supply:

$$10 - Q ^ { d } = 0.25 Q ^ { s }$$
$$Q ^ { d } = 40 - 4P$$
$$Q ^ { s } = 4P$$

Setting these equal gives $P=2.50$. Substituting this into either demand or supply gives the equilibrium quantity of 10 million bushels.

Next, we need to determine the impact of the price floor of $3.00 per bushel. Since this price floor is above the equilibrium price, it is binding, and the market price will be set at $3.00. At this price, quantity demanded is:

$$Q _ { d } = 40 - 4P _ { f } = 40 - (4 * 3) = 28$$

And quantity supplied is:

$$Q _ { s } = P _ { f } / 0.25 = 3 / 0.25 = 12$$

Thus, the market is in disequilibrium, and there is a surplus of 16 million bushels (28 - 12). This surplus represents the deadweight loss of the price floor. To determine the magnitude of this deadweight loss, we need to determine the area of the triangle between the quantity supplied and quantity demanded at the price floor:

$$\text{Deadweight Loss} = \frac{1}{2} * (28 - 12) * (3 - 2.5) = 3$$

Therefore, the deadweight loss per million bushels is $3 / 16 = 0.1875$, which is equal to $\$0.63$ per million bushels.

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 $P = 10 - Q ^ { d }$