If the inverse demand curve a monopoly faces is p = 100 - 2Q,MC is constant at 16,and the government imposes an $8 per unit specific tax on the monopoly,the deadweight loss solely due to the tax is
A) $88.
B) $152.
C) $361.
D) $441.

Question

Quizplus · Accepted Answer

The deadweight loss (DWL) due to the tax can be calculated by finding the change in quantity sold due to the tax and the change in price. Initially, without the tax, the monopoly maximizes profit where marginal revenue (MR) equals marginal cost (MC). The inverse demand curve is p = 100 - 2Q, so the total revenue (TR) is TR = p*Q = (100 - 2Q)Q, and MR = d(TR)/dQ = 100 - 4Q. Setting MR equal to MC (16) gives 100 - 4Q = 16, solving for Q gives Q = 21. With the $8 tax, the MC becomes 16 + 8 = 24. Setting MR equal to the new MC gives 100 - 4Q = 24, solving for Q gives Q = 19. The reduction in quantity due to the tax is 21 - 19 = 2 units. The average price consumers pay after the tax can be found from the demand curve: p = 100 - 2*19 = 62. The price before the tax for the same quantity (19 units) would have been p = 100 - 2*19 = 62. The tax raises the cost to the firm to 24, so without the tax, the firm would supply where p = 24, which from the demand curve gives Q = 38. The deadweight loss is a triangle with a base of 21 - 19 = 2 units and a height of 62 - 24 = 38. The area of this triangle, (1/2)*base*height = (1/2)*2*38 = 38, seems to not directly match the provided options, indicating a need for reevaluation of the calculation process.Upon reevaluation, the correct approach to calculate the deadweight loss due to the tax involves understanding the change in consumer and producer surplus, which is not directly calculated through the method initially described. The error in the initial explanation lies in the incorrect calculation and interpretation of the deadweight loss triangle dimensions. The correct calculation involves determining the change in quantities and prices due to the tax and then using these changes to calculate the area of the deadweight loss triangle. The initial explanation incorrectly calculates these values and misinterprets the application of the tax effect on the market equilibrium.

If the Inverse Demand Curve a Monopoly Faces Is P