The demand curve and supply curve for a good are given by Q^D = 100 - 5P and Q^S = 1.25P - 2.5. Suppose the production of this good generates a negative externality, where the external marginal cost is constant at $2. To achieve the socially optimal output level, the government wants to implement a quota. The size of the quota should be ____ units of the good. A) 24 B) 20 C) 16 D) 14

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Quizplus · Accepted Answer

To find the socially optimal output level, we first need to adjust the supply curve to account for the external marginal cost. The original supply equation is QS = 1.25P - 2.5. Including the external cost of $2, the new supply equation becomes QS = 1.25P - 2.5 - 2 = 1.25P - 4.5. To find the equilibrium, we set the demand curve equal to the adjusted supply curve: 100 - 5P = 1.25P - 4.5. Solving for P gives P = 18.9. Substituting P = 18.9 into the demand curve (or the adjusted supply curve) to find Q gives Q ≈ 16. Therefore, the size of the quota should be 16 units to achieve the socially optimal output level.

The Demand Curve and Supply Curve for a Good Are