Model of a depletable resource

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Consider the following two-period model of a depletable resource (e.g., fossil fuel). The demand for the resource in period 1 is MB1 = 20 – Q1 and in period 2 is MB2 = 20 – Q2. The marginal extraction costs is MXC = 5 in each period.a. To start, only consider a single period. First, assume that there is no scarcity. That is, that the total known stock of the depletable resource is S > 15. On a graph, depict the demand and supply curve for the depletable resource, depict the equilibrium level of production, and illustrate the net benefits of production (consumer surplus minus total variable cost). On a separate graph, show the marginal net benefits (MNB) (subtract the marginal cost of extraction/production from the marginal benefits).b. Now consider the two period model. Assume no discounting (r = 0). The total known stock of the depletable resource is S = 50. What is the efficient allocation of the depletable resource between period 1 and period 2? What is the marginal user costs of the resource at the equilibrium level of production in period 1?c. Continuing with the two period model, now suppose that S = 24. What is the efficient allocation of the depletable resource between period 1 and period 2? What is the marginal user costs of the resource at the equilibrium level of production in period 1? Illustrate the efficient allocation of resources between period 1 and period 2 using the figure from class where the period 1 and period 2 marginal net benefits (MNB) curves are represented on the same graph. d. Use the figure where the period 1 and period 2 marginal net benefits (MNB) curves are represented on the same graph to illustrate how the efficient allocation of resources between periods 1 and 2 would change as a result of the following:An increase in the marginal extraction cost (MXC) in period 1 (i.e., MXC’ > 5).An increase in the demand for the resources increased in period 2 (i.e., MB2′ > MB2 forall Q2 > 0).Suppose that the discount rates were 10% (r = 0.10) instead of zero (r = 0).Suppose that new stocks of the resource are discovered so that S = 28 rather in S = 24.

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