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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:

  1. An increase in the marginal extraction cost (MXC) in period 1 (i.e., MXC’ > 5).
  2. An increase in the demand for the resources increased in period 2 (i.e., MB2′ > MB2 for
  3. all Q2 > 0).
  4. Suppose that the discount rates were 10% (r = 0.10) instead of zero (r = 0).
  5. Suppose that new stocks of the resource are discovered so that S = 28 rather in S = 24.

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