Suppose there are 12 units of a depletable resource that will be distributed across 2 generations of people, so that 91 +92 = 12. The inverse demand curve (marginal value curve) for the resource for both periods is p: = 10 - 2t, fort = (0,1), wheret = 0 corresponds to the current (first) generation and t = 1 corresponds to the next period. The discount rate is r=0.1 (10%). The cost of acquiring the good (eg. extracting and processing it) is 2 per unit. Answer the following questions. a) Graph the dynamically efficient equilibrium of this resource-constrained allocation problem. Take care to clearly and completely label the axes and the equilibrium user cost and resource allocation. Upload your graph. b) Show the dynamic equimarginal condition and how the resource constraint is used. That is show the equation(s) that you can use to solve for the efficient allocation of the resource across the two periods. c) show with math and numbers that the user cost of the good is higher in period 2 and the amount received in period 2 is lower. This requires solving the equimarginal condition subject to the resource constraint with the numbers given. d) Show with math that the consumer surplus received in period 2 is lower than in period 1, and explain why the sustainability criterion is therefore not satisfied. e) Explain and show how the Sustainability Criterion can be satisfied if the first generation invests all of the resource rent and receives a return on the investment equal to the discount rate r=0.1