Suppose that demand for a depletable and non-recyclable resource is stable over time. This depletable resource is scarce ( S is the fixed stock) with a constant marginal extraction cost c. Suppose that there is a backstop technology that can replace this depletable resource, which operates at a constant marginal cost K>c. Let Rt and Pt denote the quantity extracted and the price of the depletable resource in period t, respectively. Assume that r represents the discount rate. Explain your intuition for the following hypothetical scenarios. You may want to highlight (whenever applicable) the changes in: (1) the time of exhaustion (if the resource is fully depleted), (2) the initial price, (3) the evolution of the price over time, (4) the rate of extraction, and (5) the shadow price. Use the relevant plots to illustrate your answer. a) Write down the Hotelling rule for the price Pt to show the two determinants of price: marginal extraction cost (MEC) and marginal user cost (MUC). Explain how the price evolves over time. [6 marks] b) Describe how the depletable resource is extracted over time. On a plot, depict how the price and quantity change until the backstop technology is utilised. Will the depletable resource be exhausted? Explain your answer. [6 marks] c) Suppose that the discount rate used in parts (a) and (b) is lowered (rc. Let Rt and Pt denote the quantity extracted and the price of the depletable resource in period t, respectively. Assume that r represents the discount rate. Explain your intuition for the following hypothetical scenarios. You may want to highlight (whenever applicable) the changes in: (1) the time of exhaustion (if the resource is fully depleted), (2) the initial price, (3) the evolution of the price over time, (4) the rate of extraction, and (5) the shadow price. Use the relevant plots to illustrate your answer. a) Write down the Hotelling rule for the price Pt to show the two determinants of price: marginal extraction cost (MEC) and marginal user cost (MUC). Explain how the price evolves over time. [6 marks] b) Describe how the depletable resource is extracted over time. On a plot, depict how the price and quantity change until the backstop technology is utilised. Will the depletable resource be exhausted? Explain your answer. [6 marks] c) Suppose that the discount rate used in parts (a) and (b) is lowered (r