Part I. You are the exclusive owner of a depletable resource, a private mine. Yo

Question

Part I. You are the exclusive owner of a depletable resource, a private mine. You want to extract gold and use it in a way that is dynamically optimal over two periods (period 1 (today) and period 2 (next year)). Gold is scarce so there is not enough within the mine for the static solution to be the dynamic solution for both periods. Total gold available -Q-12 MC of extraction in period 1-50 MC of extraction in period 2-20 P-MB (for both periods 1 50-10q Discount rate-r-5% 1.) What is the dynamically optimal quantity of gold to be extracted in period 1? (round to 2 decimal places) 2.) What is the dynamically optimal quantity of gold to be extracted in period 2? (round to 2 decimal places) 3.) Compared to the scenario explained in part one, if all else is held equal and there is an increase in the stock of gold available from the beginning, the amount of gold extracted in period one would a.) increase b.) decrease c)not be affected

Explanation / Answer

a) For dynamic efficiency, PV NMB period 1 = PV NMB period 2

150 - 10q1 - 50 = (150 - 10q2 - 20)/1.05

1.05(100 - 10q1) = 130 - 10q2

105 - 10.5q1 = 130 - 10q2

10q2 - 10.5q1 = 25

And we know that q1 + q2 = 12

Solve these equations to get q1*= 4.63 and q2*= 7.37

b) In period 2, quantity is 7.37

c) When stock of capital is increased the extraction in period 1 would increase.

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