Suppose that the aggregate demand for a depletable resource is given by the following inverse demand function: P= 100 (Q+S) where P is the market price, Q is the amount of depletable resource, and S represents the amount of renewable resource that consumers can use to substitute the depletable resource. The resource extraction is undertaken in the current period only. Suppose that a benevolent supplier is managing the resource, maximising total surplus in this market. The marginal extraction costs are constant for both resources: MEC = c = 10 MECS= = d = 40 The fixed supply of the depletable resource is denoted by Q. (a) [10 marks] If Q 100, calculate the efficient allocation (Q,S) for the depletable and renewable resources. What is the market price (P)? Is the depletable resource scare? If so, what is its shadow price? = (b) [10 marks] If Q = 80, calculate the efficient allocation (Q,S) for the depletable and renewable resources. What is the market price (P)? Is the depletable resource scare? If so, what is its shadow price? (c) [10 marks] If Q = 50, calculate the efficient allocation (Q,S) for the depletable and renewable resources. What is the market rice (P)? Is the depletable resource scare? If so, what is its shadow price? (d) [5 marks] Explain the relationship between the shadow price and the fixed supply on a graph.