Consider the market for gin is in perfect competition where market demand is given by P=20-4Q and supply is given by P=Q. Suppose that alcoholism is a major problem in this community. Not only does it affect the health of the people who consume the gin, but it also effects community members who do not buy or sell alcohol. Thus, while the private marginal cost of gin is given by P=Q, the Social Marginal cost is given by P=6Q. What policy would you recommend to the local government to bring the economy to the socially optimal allocation?

Question

BlackTom AI · Accepted Answer

Question restatement: We’re in a perfectly competitive gin market with private MC given by P = Q and demand P = 20 − 4Q. The social marginal cost is P = 6Q due to externalities. The task is to identify the policy that brings the economy to the socially optimal allocation.

Option 1: A per unit tax on the supply of gin of the amount T = $10.
To evaluate this, set up the market with a per-unit tax t on producers. The price received by producers is P − t, so the private supply condition becomes P − t = Q. The demand condition remains P = 20 − 4Q. Solving simultaneously: P = 20 − 4Q and P − t = Q ⇒ P = Q + t. Substituting gives Q + t = 20 − 4Q ⇒ 5Q = 20 − t ⇒ Q = (20 − t)/5. The socially optimal quantity, using the social marginal cost, is found from P = SMC: 20 − 4Q = 6Q ⇒ 20 = 10Q ⇒ Q = 2. Set (20 − t)/5 = 2 to achieve Q = 2, which yields t = 10. Therefore a tax of $10 per unit aligns private incentives with the social optimum. This option (T = 10) is consistent with the standard Pigouvian tax approach to internalize a negative externality.

Option 2: A per unit tax on the supply of gin of the amount T = $12.
If the tax were $12, the resulting equilibrium quantity would be Q = (20 − 12)/5 = 8/5 = 1.6, which is below the social optimum Q = 2. This tax overcorrects the market, reducing output below the efficient level and not achieving social optimality.

Option 3: I would not recommend any government intervention because it will create deadweight loss.
In this scenario, there is a negative externality captured by the difference between private MC and social MC (SMC = 6Q vs private MC = Q). This external cost means the private market equilibrium (Q = 4) yields a higher quantity and lower price than is socially optimal, producing deadweight loss. Government intervention that internalizes the externality is appropriate to reach the social optimum, so rejecting intervention ignores the external costs and is not consistent with the problem data.

Option 4: A per unit tax on the consumption of gin of the amount T = $12.
Taxing consumption rather than production changes the incidence and the price paid by consumers, but with a competitive market and a standard per-unit tax, the body of reasoning is similar; however, the optimal tax to internalize the externality is computed from the production side (tax on suppliers) in this setup. A consumption tax of $12 would not necessarily align the market to the socially optimal quantity in the same way as a production tax of $10, so this option does not target the correct channel given the household and producer behavior described.

Option 5: None of the other answers are correct.

Summary of reasoning across options: The core idea is to internalize the external cost by adjusting the price producers receive so that the private quantity supplied equals the socially optimal quantity. The social optimum is found where demand equals social marginal cost (P = SMC), which gives Q = 2. Matching the private supply to this outcome via a Pigouvian tax on producers requires t = 10. Among the options, the production tax of $10 is the only policy that directly leads to Q = 2, while the other choices either misstate the mechanism, miscalculate the tax, or ignore the externality.

ECON1001 (ND) Quiz 4

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