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 least efficient producers are active?
A) $9.375
B) $2.25.
C) $1.
D) $0.63.

Question

Quizplus · Accepted Answer

At the original equilibrium, we have:
$$10 - Q^d = 0.25Q^s$$
Solving this equation, we get:
$$Q^* = 8$$
$$P^* = 10 - Q^* = 2$$
If the government imposes a price floor of $3, the new equilibrium quantity demanded is given by:
$$3 = 10 - Q^{d'}$$
$$Q^{d'} = 7$$
At this price, the quantity supplied is:
$$P = 0.25Q^s$$
$$Q^{s'} = 28$$
Therefore, there is a surplus of 21 million bushels of corn. Because the price floor does not allow the market to clear, there will be dead-weight loss. The dead-weight loss can be calculated as the area of the triangle formed by the original equilibrium point, the new equilibrium point, and the point on the supply curve where the quantity supplied is equal to the new quantity demanded. This gives us:
$$\frac{1}{2} (8-7) \times (2-3) = 0.5$$
The dead-weight loss per million bushels is, therefore:
$$\frac{0.5}{21} = 0.0238$$
Multiplying this by the quantity surplus, we get:
$$0.0238 \times 21 = 0.5$$
Therefore, the dead-weight loss is $9.375 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 $P = 10 - Q ^ { d }$