Final answer:
To find the deadweight loss from a price ceiling of $306, we calculate the difference between the equilibrium price and quantity and the price and quantity supplied at the ceiling. The deadweight loss is the area of the triangle formed between the supply and demand curves, which amounts to $7,524.80 when rounded to two decimal places.
Step-by-step explanation:
To calculate the resulting deadweight loss caused by a price ceiling of $306, we first need to determine the equilibrium price and quantity without the price ceiling. The demand curve is given by P = 1000 - 5Q, and the supply curve is given by P = 5Q. At equilibrium, the quantity supplied equals the quantity demanded, so we set the two equations equal to each other: 1000 - 5Q = 5Q. Solving for Q gives us an equilibrium quantity (Qe) of 100 units and an equilibrium price (Pe) of $500.
With the government-imposed price ceiling of $306, the supply curve remains the same (P = 5Q), and we solve for the quantity supplied at this price (Qs): 306 = 5Qs. This yields a quantity supplied of 61.2 units. The quantity demanded at this price, from the demand curve, is found by solving 306 = 1000 - 5Qd, which yields a quantity demanded of 138.8 units.
Due to the price ceiling, the market is no longer at equilibrium. Consumer surplus and producer surplus have changed, and there is a shortage equal to the difference between quantity demanded and quantity supplied (138.8-61.2). The deadweight loss represents the loss in total surplus due to the market not being at equilibrium. It can be represented graphically as the area of the triangle that lies between the supply and demand curves, above the price ceiling, and between the quantities supplied and demanded at the price ceiling.
To calculate the deadweight loss, we use the formula for the area of a triangle: 0.5 * base * height. The base is the difference between the quantities demanded and supplied at the price ceiling (138.8 - 61.2), and the height is the difference between the equilibrium price and the price ceiling ($500 - $306). This gives us a deadweight loss of 0.5 * (77.6) * (194) = $7,524.80. When rounded to two decimal places, the deadweight loss is $7,524.80.