Question: 1. The private marginal benefit for commodity X is given by 10-X. where X is the number of units consumed. The private marginal cost of producing X is constant at $5. For each unit of X produced, an external cost of $2 is imposed on members of society. In the absence of any government intervention, how much X is produced? What is the efficient level of production of X? What is the gain to society involved in moving from the inefficient to the efficient level of production? Suggest a Pigouvian tax that would lead to the efficient level. How much revenue would the tax raise?

2. Consider the interactions between a chemical firm situated on the banks of a river and a fishery located downstream from the chemical firm. The chemical firm benefits from polluting the river while the fishery suffers from any pollution of the river. Specifically, let the marginal benefit of pollution C of the chemical firm be MB_C = 12 - C, and let the marginal cost of pollution of the fishery be given by MC_F = 6. Suppose also that property rights favour the chemical firm.

(a) What pollution level will the chemical firm choose in the absence of any bargaining?

(b) If both parties bargain, what pollution level will emerge as a result of this mutually beneficial bargaining? As an outcome of the bargaining process, who will make a transfer to whom, and what is the minimum required level of transfer? Explain and provide a graphical representation.

Now suppose that the fishery does not know the chemical firms true marginal benefit curve. Instead, the chemical firm persuades the fishery that its marginal benefit of pollution is MB_C = 2A - 2C rather than the true curve (given by MB_C = 12 - C). Property rights favour the chemical firm and bargaining takes place accordingly.

(c) What pollution level will be chosen through bargaining now? And what is the minimum required level of transfer?

(d) What is the gain to the chemical firm from misrepresenting the marginal benefit curve when the minimum transfer identified in (c) takes place? Does the chemical firm have an incentive to misrepresent the position of its marginal benefit curve? If so, what implications does this have for the efficiency of the Coasian solution?

3. Suppose that two firms emit a certain pollutant. The marginal cost of reducing pollution for each firm is as follows: MC₁ = 300e₁ and MC₂ = 100e₂ where e₁ and e₂ are the amounts (in tons) of emissions reduced by the first and second firms, respectively. Assume that in the absence of government intervention. Firm 1 generates 100 units of emissions and firm 2 generates 80 units of emissions.

(a) Suppose regulators decide to reduce total pollution by 40 units. In order to be cost effective, how much should each firm cut its pollution?

(b) What emissions fee should be imposed to achieve the cost-effective outcome? How much would each firm pay in taxes?

(c) Suppose that instead of an emissions fee, the regulatory agency introduces a tradable permit system and issues 140 permits, each of which allows the emission of one ton of pollution. Firm 1 uses it political influence to convince the regulatory agency to issue 100 permits to itself and only 40 permits to firm 2. How many, if any, permits are traded between the firms? What is the minimum amount of money that must be paid (total) for these permits? By how many tons does each firm end up reducing its pollution?