1. Coltan is an ore that is used to manufacture tantalum capacitors, which are a major component in cell phones. Suppose that the static market for virgin coltan (i.e., the coltan that comes out of the ground) is characterized by the following market conditions: Pp = 250 - Q (1) Ps = 50 (2) Suppose that the total current reserves of coltan are limited to 250 units and the discount rate is 1%. Further suppose that we are only interested in two periods, t = 0 and t = 1, where t = 1 is 70 years later than t =0 and that supply and demand do not change over time. a) (10 points) If the goal of society is to maximize TS across the two time periods, what will be Qo and Q1? b) (10 points) Now suppose that due to advances in recycling, the demand for virgin coltan actually decreases in the second time period ( = 1). This means that (inverse) demand in t = 0 is still PD = 250 - Q, but demand in t = 1 is Pp = 220 -Q. If supply does not change over time and the discount and time period remain the same, what are the efficient allocations (the allocations that maximize TS across time) for Qo and Q1? (Don't over-think this, it is no harder than the previous portion of the question.) c) (5 points) Briefly explain the intuition of why, in both a) and b), Qo > Q1