Consider a market characterized by the following inverse demand and supply functions: P_X = 40 − 4Q_X and P_X = 10 + 2Q_X.Compute the surplus received by consumers and producers.

Question

Quizplus · Accepted Answer

To find consumer surplus, we need to find the area under the demand curve and above the market price, which is given by P_X = 10 + 2Q_X. Solving for Q_X, we get Q_X = 5 + 0.5P_X. Substituting this into the demand function, we get P_X = 40 − 4(5 + 0.5P_X), which gives us P_X = 20. Therefore, the equilibrium price is $20. To find producer surplus, we need to find the area above the supply curve and below the market price, which is given by P_X = 40 − 4Q_X. Solving for Q_X, we get Q_X = 10 + 0.25P_X. Substituting this into the supply function, we get P_X = 10 + 2(10 + 0.25P_X), which gives us P_X = 40. Therefore, the equilibrium price is $20 and the equilibrium quantity is 15. Consumer surplus is then given by the area of the triangle below the demand curve and above the price, which is (1/2)(20-10)(15) = $75. Producer surplus is given by the area of the triangle above the supply curve and below the price, which is (1/2)(20-10)(15) = $75. Therefore, the consumer surplus is $75 and the producer surplus is $75, giving a total surplus of $150. Thus, the correct answer is B) $20 and $40, respectively.

Consider a Market Characterized by the Following Inverse Demand and Supply