Consider a privately owned lithium mine making extraction decisions. a. Suppose today's market price for a unit of lithium is $100 and the extraction costs are constant and $20 per unit. What is the firm's net price today, i.e. what is the marginal resource rent? b. Suppose the firm's discount rate is 15%, extraction costs are unchanging, and the market price is not expected to change in the next period. Using the notion of present value, argue whether the firm should extract and sell today or extract and sell tomorrow. c. Suppose the discount rate is still 15%, extraction costs are unchanging, and the market price is now expected to increase to $110. Again using the notion of present value, argue whether the firm should extract and sell today or extract and sell tomorrow. d. Re-evaluate your decision in part (c) using a discount rate of 5%. e. Re-evaluate your decision in part (c) if, due to your firm's R&D, you expect to have successfully innovated by next period so you expect your future extraction costs to fall to $10 per unit