In the market for cotton, the quantity demanded and quantity supplied are expressed mathematically as Q^D = 400 - 250P and Q^S = 250P - 100, where P is the price per pound of cotton and Q measures pounds of cotton. Suppose the government sets a price ceiling of $0.50 per pound of cotton. The deadweight loss with the price ceiling is: A) $26.25. B) $40.00. C) $62.50. D) $1.25.

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To calculate the deadweight loss due to the price ceiling, we first need to find the quantities demanded and supplied at the price ceiling of $0.50. Substituting P = 0.50 into the demand and supply equations:Quantity demanded (QD) = 400 - 250(0.50) = 275 poundsQuantity supplied (QS) = 250(0.50) - 100 = 25 poundsThe price ceiling causes a shortage, and the quantity traded in the market will be the lesser quantity, which is 25 pounds (the quantity supplied).To find the equilibrium price without the price ceiling, we set the quantity demanded equal to the quantity supplied:400 - 250P = 250P - 100500 = 500PP = 1At the equilibrium price of $1, the quantity demanded and supplied is:Q = 400 - 250(1) = 150 poundsThe deadweight loss is the loss in total surplus, represented by the area of the triangle formed by the demand and supply curves between the quantities of 25 and 150 pounds at the price ceiling of $0.50 and the equilibrium price of $1. The base of the triangle is 150 - 25 = 125 pounds, and the height is the difference in price, $1 - $0.50 = $0.50.Deadweight loss = 0.5 * base * height = 0.5 * 125 * 0.50 = $31.25However, given the options provided and the calculation, it seems there might have been a mistake in the calculation or interpretation of the options. The correct approach to find the deadweight loss involves calculating the area of the triangle formed by the difference in quantities and prices due to the price ceiling. The provided options do not match the calculated value, suggesting a possible error in the calculation steps or a misunderstanding of the provided options. The correct calculation method involves identifying the equilibrium quantity and price without the price ceiling, the quantities demanded and supplied at the price ceiling, and then calculating the area of the triangle that represents the deadweight loss.

In the Market for Cotton, the Quantity Demanded and Quantity