2. Suppose that demand for an exhaustible resource is p(t) = 180-Q(t). And suppose that the marginal cost of production is c = 20. The interest rate is r, and doubling times associated with this r are 50 years in length. (a) Suppose the competitive equilibrium exhausts in T. = 3td = 150 years. Draw a four-panel diagram showing the equilibrium competitive price path po(t) and competitive equilibrium production path Q.(t), with the demand curve drawn in the upper left quadrant, the price path in the upper right quadrant, and quantity path in the lower left quadrant. Find the equilibrium scarcity rental price, de, for the competitive industry. Draw your price path diagram with t extending to 4 doubling times. (b) Suppose at time td, the competitive industry forms a cartel, which then operates until the time of exhaustion, Tm (which you will determine). Explain why the marginal revenue to the cartel, MR(t), cannot equal the competitive price path, pe(t). (c) Now, find the equilibrium cartel price path, Pm (t), marginal revenue path MR(t), and quantity path, Qm(t), that uses up the same remaining stock as existed at time td under the competitive equilibrium. (Do this in pencil until you get the areas on the quantity paths to be correct, then draw it in pen.) Show these on your graph. (d) Explain why Am