2. Suppose that demand for an exhaustible resource is p(t) = 180-Q(t). And suppose that the...

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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 Te = 3td = 150 years. Draw a four-panel diagram showing the equilibrium competitive price path pe(t) and competitive equilibrium production path Qe(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, Ae, for the competitive industry. Draw your price path diagram with t extending to 4 doubling times. (b) Suppose at time ta, 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, p.(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 to 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 <Ae on your graph. Show these in current value at time to and at time t = 0. 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 Te = 3td = 150 years. Draw a four-panel diagram showing the equilibrium competitive price path pe(t) and competitive equilibrium production path Qe(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, Ae, for the competitive industry. Draw your price path diagram with t extending to 4 doubling times. (b) Suppose at time ta, 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, p.(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 to 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 <Ae on your graph. Show these in current value at time to and at time t = 0.

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a The equilibrium quantity is found by setting the marginal cost equal to the marginal benefit which is given by the inverse demand function MC MB 20 ddQ 180 Q 20 1 Qe 160 The equilibrium price is the... View the full answer