Consider a market characterized by the following inverse demand and supply functions: P_X = 10 − 2Q_X and P_X = 2 + 2Q_X. Compute the loss in social welfare when an $8 per unit price floor is imposed on the market.

Question

Quizplus · Accepted Answer

To find the loss in social welfare, we need to first find the equilibrium price and quantity without the price floor. This is where the demand and supply curves intersect: 10 - 2Q_X = 2 + 2Q_X. 8 = 4Q_X Q_X = 2 Plugging this quantity back into either the demand or supply function will give us the equilibrium price: P_X = 2 + 2Q_X. P_X = 2 + 2(2) P_X = 6 Therefore, without the price floor, the equilibrium price is $6 and the equilibrium quantity is 2 units. With the price floor at $8, the quantity demanded will be less than the quantity supplied, since consumers will not be willing to pay the higher price. Therefore, the quantity sold will be the same as the equilibrium quantity of 2 units, but the price will be $8. The consumer surplus with the price floor is: CS = (1/2)(6-8)(2) = -$2 Note that consumer surplus is negative; this means that consumers are worse off with the price floor than without it. The producer surplus with the price floor is: PS = (8-2)(2) = $12 The total surplus with the price floor is: TS = CS + PS = -$2 + $12 = $10 The loss in social welfare is the difference between the total surplus without the price floor and the total surplus with the price floor: Loss in social welfare = TS without price floor - TS with price floor TS without price floor = (1/2)(6-0)(2) + (1/2)(10-6)(2) = $8 Loss in social welfare = $8 - $10 = -$2 Therefore, the loss in social welfare when an $8 per unit price floor is imposed on the market is $2. The answer is choice C, $2.

Consider a Market Characterized by the Following Inverse Demand and Supply