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

The price floor of $3 per bushel creates a surplus of corn as the quantity supplied at this price is greater than the quantity demanded. At the price floor, the quantity supplied is 12 million bushels [(3/0.25) million bushels], and the quantity demanded is 7 million bushels (10 - 3 = 7). 
The dead-weight loss (DWL) is the loss of consumer and producer surplus that results from the price floor. In this case, the DWL is equal to the area of the triangle between the supply and demand curves, above the equilibrium quantity and below the price floor. 
The equilibrium quantity is 8 million bushels [(10-0.25P)/2 = 0.25P => P = $4 => Q = 8]. Therefore, the DWL is (1/2) x (12-8) x (3-4) = $2. 
The least efficient producers are those whose marginal cost of producing a bushel of corn is greater than $3. At the price floor, these producers can stay in business and sell their corn, but they are less efficient than the other producers who can sell at a higher price. The efficiency loss associated with the least efficient producers being active is the difference between their marginal cost and the price they receive, multiplied by the quantity they produce. 
The marginal cost of producing a bushel of corn is 0.25Q, where Q is the quantity of corn produced in millions of bushels. At the price floor of $3, the quantity produced by the least efficient producers is 3/0.25 = 12 million bushels. Their total cost is 0.25 x 12 x 12 = $36. 
The revenue they receive is 3 x 12 = $36. Therefore, the efficiency loss is $0.375 per bushel ($36 - $35.625) and the total efficiency loss is (0.375) x (12) = $4.5 million. 
The total dead-weight loss is the sum of the DWL and the efficiency loss, which is $2 + $4.5 = $6.5 million or $6.5 per million bushels. However, this is not an option in the given choices, and the closest choice is A) $9.375.

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 $P = 10 - Q ^ { d }$