A firm must decide how to optimally extract a deposit of phosphorous. The total deposit is 1000 tons. The marginal net benefit function facing the firm is: P=500-2Q (for each time period). Assume that the firms marginal costs are zero and in each time period and buyers are willing to purchase 1000 tons of phosphorous. The firm has chosen to examine the problem using two discount rates 10% and 20%.

a) Calculate the optimal rate of extraction and price for each time period under the different discount rates.

b) Calculate the marginal user cost (MUC) associated with each discount rate.

c) Does the Hotelling Principle hold in each instance? Verify your response.