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.How much would the government have to pay farmers?

Quizplus · Accepted Answer

To find out how much the government would have to pay farmers, we first need to determine the quantity of wheat that would be supplied and demanded at the target price of $3/bushel. Using the demand function: $$Q_d = 10 - 2P = 10 - 2(3) = 10 - 6 = 4$$ billion bushels.Using the supply function: $$Q_s = 4P - 2 = 4(3) - 2 = 12 - 2 = 10$$ billion bushels.At $3/bushel, the quantity supplied (10 billion bushels) exceeds the quantity demanded (4 billion bushels) by 6 billion bushels. To achieve the target price, the government would need to reduce the supply from 10 billion bushels to match the demand of 4 billion bushels, meaning they would need to reduce the supply by 6 billion bushels.If the government pays $3/bushel (the target price) for each bushel of wheat not produced, the total cost to the government would be:$$6 \text{ billion bushels} \times \$3/\text{bushel} = \$18 \text{ billion}.$$

The Market Demand Function for Wheat Is Qd = 10