The state government is considering whether to allow mining in a current wilderness area. This area provides two benefits: recreation opportunities (backpacking) and biodiversity (a unique habitat for endangered wildlife and plants). Mining is expected to reduce backpacking visits from the current level of 10,000 recreation visitor-days (RVDs, a measure of recreational use) per year to 4000 RVDs/year for the next 10 years; after that time, recreational use would partially rebound to 7000 RVDs/year into perpetuity. If the mine is not opened, recreational use is expected to continue at current levels into perpetuity. Mining is expected to bring profits of $1 million/year for the 10 years of the mining operation. You can assume that all benefits and costs begin in one year's time. The state government has a planning horizon of 50 years.

For all of the following questions please include your detailed workings and explanations. Use of a spreadsheet to do the computations is highly recommended but your answer must include any formulas you used to compute the values.

(1) Compute the present value of mining profits in the area (i.e. excluding effects on recreation) if the discount rate is  a) 6 percent b) 3 percent

(2) Suppose that travel cost studies estimate than a RVD of backpacking is worth $90. Compute the following using both a 6 percent and a 3 percent discount rate:  a) The present value of recreation in the area if it is mined.   b) The present value of recreation in the area if it is not mined.

(3) Continue to assume that a RVD of backpacking is worth $90. Considering only the benefits and costs of mining and recreation, and not biodiversity, would preservation be the efficient solution if the discount rate is  a) 6 percent? b) 3 percent?  If preservation is not efficient, how much would the habitat need to be worth in present value to make mining not worthwhile?

(4) Which discount rate makes the best case for mining and why?