4. Scenarios A and B are identical in every respect (e.g. demand function, initial resource stock, and extraction cost function), except for the following: in Scenario A, a backstop with constant marginal cost 5 is available at time t = 0; in Scenario B it is known at time t = 0 that the backstop will not become available until t = 49. (a) Suppose that in Scenario A, the backstop begins to be used at time t = 50. What, if any, is the difference in price trajectories in the two scenarios? Explain your answer briey. (b) In Scenario C everyone knows that the backstop will be available at t = 51, but not earlier. Draw a gure showing (only) the equilibrium price trajectory in scenario B (corresponding to the arrival times of the backstop, t = 49) and in Scenario C (corresponding to the arrival time t = 51). Briey explain the difference in the two trajectories. (Hint: The initial price in Scenario C must be higher than, lower than, or the same as the initial price in Scenario B. Those are the only three possibilities. Consider each of these possibilities. You should be able to quickly conclude that two of these possibilities are not consistent with equilibrium in Scenario C. Therefore, the remaining scenario is the correct one. Your gure should reect this fact.) (c) Now consider Scenario D, where there is uncertainty. At t = 0 everyone knows that the backstop will become available either at t = 49 or at t = 51. Each of these outcomes is equally likely. (The uncertainty is \"resolved\" at t = 49: either the backstop becomes available, and everyone knows this, or it does not become available; in the latter case, everyone knows that it will become available to t = 51. In either case, there is no more uncertainty after t = 49.) Reproduce your gure from part (b) and draw the equilibrium price trajectory prior to t = 49 for the scenario with uncertainty. Your goal is to gure out the relation between this trajectory and two trajectories under certainty with different times of availability