You inherit a phosphate mining company and are now in charge of production decisions. You only have two years to extract all of the phosphate because in three years from now, an environmental regulation will go into effect banning mining in that area. There are 300 tons of phosphate to mine. The marginal benefit (marginal revenue) from selling phosphate (which is used in fertilizers) is: MB = 200 - Q and is the same for both periods. The Marginal Extraction Cost is zero and you face a discount rate of 10%. a. Consider year one. When your marginal benefit = 0, how much are your sales of phosphate (Q)? if you do not sell any phosphate, how much is your marginal benefit? if you sell all 300 tons of phosphate, how much is your marginal benefit? [NOTE: there is no “economics” here – this is just plugging in numbers to help you make a graph in the next question] b. The answers to part (a), combined with the fact that MEC = 0, should enable you to graph out the Net Marginal Benefit curve for year one (NMB1). c. Knowing that the NMB is the same for year two (NMB2), graph NMB2 on the same graph as NMB1. d. Discount your curve for NMB2, to get PV(NMB2), and plot that line on the graph as well. e. What is the optimal amount of phosphate to sell in the first year and the second year? Recall that the total amount of phosphate available is 300 tons. Show all of your work and label these amounts on your graph. f. If the discount rate rises, what do you think will happen to your answers in part (c)? (you do not need to use actual numbers, but talk about what happens when discount rates rise)