The market demand function for wheat is Q^d = 10

Question

The market demand function for wheat is Q^d = 10 - 2P and the market supply function is Q^s = 4P - 2,both measured in billions of bushels per year.Suppose the government wants to increase the price of wheat to $3/bushel and they impose a voluntary production reduction program to achieve their goal.What is the size of the aggregate surplus? A) $4 billion B) $12 billion C) $10 billion D) $6 billion

Quizplus · Accepted Answer

To find the aggregate surplus, we need to calculate the area between the supply and demand curves up to a price of $3/bushel. At a price of $3, the quantity demanded is Q^d = 10 - 2(3) = 4 billion bushels, and the quantity supplied is Q^s = 4(3) - 2 = 10 billion bushels. Therefore, there is an excess supply of 10 - 4 = 6 billion bushels, which will be eliminated through the voluntary production reduction program. The area of the aggregate surplus is the triangular area between the two curves, up to a price of $3/bushel. This can be calculated as: (1/2) x ($3/bushel) x (10 billion bushels - 4 billion bushels) = $12 billion. Therefore, the size of the aggregate surplus is $12 billion.

The Market Demand Function for Wheat Is Qd = 10