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1. Consider a proposal to build a dam on a pristine river that is currently a popular recreational area. The primary purpose of the dam

1. Consider a proposal to build a dam on a pristine river that is currently a popular recreational area. The primary purpose of the dam is to generate electricity. The dam is expected to have a useful life of 50 years, after which it will be decommissioned and removed due to sediment buildup. The con- struction of the dam is expected to be completed in one year. Here are some key characteristics of the project:

Initial construction cost: $100,000,000 (assumed to be incurred in year 0)

Annual electricity production: 100,000 MWh (Megawatt-hours) at a rate of $100 per MWh

Cost of decommissioning the dam: $10,000,000 (to be incurred in the year following the dam's closure)

Annual value of recreational activities lost due to the dam: $5,000,000 per year

Now, your task is to analyze this dam project from an economic perspective and answer the following questions:

(a) If the social discount rate is 3% per year, is building the dam a good idea?

(b) If the social discount rate is 10% per year, is it a good project?

(c) Calculate the "cut-off" discount rate, c, such that the dam is a good idea for discount rates lower than c, and a bad idea for discount rates greater than c.

d) Assess the economic feasibility of the dam project based on your calcu- lations. Should the project move forward from a purely economic stand- point? Why or why not?

2. Consider two firms, Firm 1 and Firm 2, located in the same region. Both firms emit pollutants into the atmosphere. The government is interested in reducing pollution in this area and decides to implement a pollution reduction policy. Assume that in the absence of regulation both firms would emit 100 unit of pollution (P). The marginal cost of pollution reduction (abatement) for each firm if given by:

Firm 1 has a marginal cost of abatement given by MC1(Q1) = 0.5Q1, where Q1 represents the level of pollution reduction by Firm 1.

Firm 2 has a marginal cost of abatement given by MC2(Q2) = 0.2Q2, where Q2 represents the level of pollution reduction by Firm 2.

(a) Plot both functions on the same graph with pollution on the horizontal axis.

(b) If the government aims to reduce air pollution by half, mandating that each firm reduces emissions by the same amount, calculate the cost of pollution reduction for each firm and the overall cost of pollution reduc- tion.

(c) Calculate the efficient level of pollution reduction for each firm under a Pigouvian tax to achieve the same level of pollution as in the uniform mandate.

(d) Calculate the pigouvian tax.

(e) Demonstrate that the overall cost of pollution reduction is lower under the Pigouvian tax and explain why this is the case.

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