1. Suppose demand for an exhaustible resource is p(t) 20 Q(t). There are two competitive types...

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1. Suppose demand for an exhaustible resource is p(t) 20 Q(t). There are two competitive types of producers each producing an identical product. The high cost producers have marginal cost of production equal to CH = 4, while the low-cost producers have marginal costs of cL = 2. The interest rate is r, and doubling times associated with this r are 50 years in length. (a) Explain why both producers cannot produce simultaneously over any interval of time, t₁ < t <t₂. (b) Suppose the high-cost stock owners have sufficient reserves, SH, to last two doubling times if they are the only producers holding positive reserves in the competitive equilibrium. Suppose also that exhaustion occurs at T = 4td. Find the equilibrium path that holds between time 2ta and T and determine the equilibrium price at time 2td. Show this on a price-time graph accurately drawn. (c) Now, suppose the low-cost stock owners have sufficient reserves, S₁, to last from time t = 0 until time t = 2td, given that the price they will receive at 2t, is the price from the high-cost stock producers equilibrium price path. Find the equilibrium path that holds between time 0 and 2td and determine the equilibrium price at time t = 0. Show this on a price-time graph accurately drawn. (d) What are the values of X and X₁ that must occur in this equilibrium? Show the current value of these at time t = 0 and at time t = 2ta on your graph. Explain. 1. Suppose demand for an exhaustible resource is p(t) 20 Q(t). There are two competitive types of producers each producing an identical product. The high cost producers have marginal cost of production equal to CH = 4, while the low-cost producers have marginal costs of cL = 2. The interest rate is r, and doubling times associated with this r are 50 years in length. (a) Explain why both producers cannot produce simultaneously over any interval of time, t₁ < t <t₂. (b) Suppose the high-cost stock owners have sufficient reserves, SH, to last two doubling times if they are the only producers holding positive reserves in the competitive equilibrium. Suppose also that exhaustion occurs at T = 4td. Find the equilibrium path that holds between time 2ta and T and determine the equilibrium price at time 2td. Show this on a price-time graph accurately drawn. (c) Now, suppose the low-cost stock owners have sufficient reserves, S₁, to last from time t = 0 until time t = 2td, given that the price they will receive at 2t, is the price from the high-cost stock producers equilibrium price path. Find the equilibrium path that holds between time 0 and 2td and determine the equilibrium price at time t = 0. Show this on a price-time graph accurately drawn. (d) What are the values of X and X₁ that must occur in this equilibrium? Show the current value of these at time t = 0 and at time t = 2ta on your graph. Explain.

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a Both producers cannot produce simultaneously over any interval of time because of the exhaustible nature of the resource As the resource is being ex... View the full answer