(a)  What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution. (b)  What is the marginal user cost (or scarcity rent) of the resource in each period? (c)  Suppose that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Justify the answer.

Micro Economics For Today
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Author:Tucker, Irvin B.
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Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth
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Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal beneÖt is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8.

(a)  What is the efficient quantity of resources extracted in each period? Provide a graphical representation of the solution.

(b)  What is the marginal user cost (or scarcity rent) of the resource in each period?

(c)  Suppose that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Justify the answer.

(d)  Suppose that it is now expected that because of an extraction technol- ogy improvement, while the Örst period marginal cost of extraction will still remain MXC1 = 40, the second period one will now de- crease to MXC2 = 20. Answer the previous questions (a)-(c) under this alternative premise.
 

(e)  How will the answers to questions (a)-(c) change if, because of new discoveries, the known reserves of the natural resource become Q = 400.

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