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 due to both the monopoly and the tax is
A) $529.
B) $1332.
C) $1764.
D) $441.

Question

Quizplus · Accepted Answer

The deadweight loss (DWL) due to both the monopoly and the tax can be calculated by finding the DWL due to the monopoly power and the additional DWL due to the tax. The inverse demand curve is p = 100 - 2Q, and the marginal cost (MC) is constant at 16. When a specific tax of $8 per unit is imposed, the effective marginal cost becomes MC + tax = 16 + 8 = 24.1. Without the tax, the monopoly maximizes profit where marginal revenue (MR) equals marginal cost (MC). The MR curve, derived from the demand curve, is MR = 100 - 4Q. Setting MR = MC (16) gives 100 - 4Q = 16, solving for Q gives Q = 21 units, and the corresponding price is p = 100 - 2*21 = 58.2. With the tax, the effective MC is 24. Setting MR equal to the new MC (24) gives 100 - 4Q = 24, solving for Q gives Q = 19 units, and the corresponding price before tax is p = 100 - 2*19 = 62.The DWL of a monopoly without tax is the triangle formed by the quantities produced by the monopoly and the socially optimal quantity (where price equals the original MC, 16). The socially optimal quantity is found by setting p = MC in the demand equation: 100 - 2Q = 16, solving for Q gives Q = 42. The base of the triangle is 42 - 21 = 21, and the height is the difference in price from the monopoly price to the price at the socially optimal quantity, which is 58 - 16 = 42. The area of this triangle is 0.5 * 21 * 42 = 441.The additional DWL due to the tax is the triangle formed by the change in quantity due to the tax, from 21 to 19 units. The base of this triangle is 2 units (21 - 19), and the height is the tax of $8. The area of this triangle is 0.5 * 2 * 8 = 8.The total DWL is the sum of the DWL due to the monopoly (441) and the additional DWL due to the tax (8), which equals 449. However, none of the provided options match this calculation directly. Given the options and the typical approach to such a problem, the closest match or intended answer based on the standard calculation method seems to be a misunderstanding in the calculation process. The correct approach to calculating the total DWL involves understanding both the monopoly's effect on the market and the tax's impact. However, the provided options and the calculation steps outlined do not align perfectly with the standard economic analysis for such a scenario. The answer provided as A) $529, is selected based on the options given, but it's important to note that the explanation and calculation steps do not lead directly to any of the provided choices, indicating a potential error in the question or a misunderstanding in the calculation process.

If the Inverse Demand Curve a Monopoly Faces Is P