The government of a small South Pacific island is considering whether to allow development of a small but valuable deposit of phosphate rock. Not having the resources to develop and mine the deposit themselves, the country has the option to sell a lease to a foreign mining company for an immediate one-time fee of $12 million - resources that can be used to address many development challenges in the country1. The lease will expire (and the deposit will likely be mined out) in 20 years. A panel of experts suggests that the mining of the phosphate, despite the use of best practices to avoid contamination, will eventually result in contamination of surface and groundwater supplies in a manner that will increase health risks for some residents. Best estimates of these health-related damages (willingness to pay to avoid the damage) are a total of $18 million. Moreover, the health effects are not likely to be experienced until the end of the 20 year lease.

a. Suppose that the government of the island choose a discount rate of .04. What is the present value of the damages created by the project? What is the net present value of the project from the vantage of the government? Assuming this is the best (i.e. most efficient) way to develop the phosphate resource, is doing so justifiable on the basis of economic efficiency?

b. Find the breakeven discount rate such that the net present value of this development opportunity is zero (i.e. find the internal rate of return).

c. The government of the country has decided to allow the project to go forward. However, as a measure to deal with perceived inequities across generations, they decide to invest a substantial portion of the lease payment. Assume that $9 million is invested at a 4% annual rate (compounded annually). Will the future value of this investment be sufficient to compensate those that suffer damages in year 20?

d. Read p. 96-100 of Goodstein. How does the "environmental bond" discussed in c) help to foster sustainability in the "neoclassical" sense discussed by economists like Robert Solow?