ps3 - whether dams are built today or tomorrow Dams are...

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EC313-Fall 2010 Problem Set 3 (Updated 18 August 2010) Matt Turner When you write up your answers, your goal should be to (1) be correct, and (2) convince your reader that your answer is correct. Answers which do not achieve these goals will not be awarded full credit. To accomplish the second objective, it is helpful if your work is legible and if all steps are presented, possibly with a line of explanation. Problems 1. You own a coal mine and would like to exploit it in the wealth maximizing way. Suppose that the demand for coal is Q = 10 - 2 p for p < 5. Let T denote the time at which your mine is exhausted and suppose that a is the amount of coal in the mine. Extracting coal is costless. The price of coal at time 0 is p 0 and the discount rate is γ . Verify that you exhaust your mine in finite time. 2. Let d 1 and d 2 be the proportions of rivers that are dammed in the present and in the future. Once built, dams cannot be unbuilt, and it is not possible to dam more than all of the rivers. Let bd be the benefit from dams. This benefit occurs tomorrow,
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Unformatted text preview: whether dams are built today or tomorrow. . Dams are costless to construct, but there is some probability that building dams will hurt salmon runs in the future. Let c s d denote this cost, where c s is a random variable that takes the value 0 with probability p and the value 2 c with probability 1-p . Assume that b-2 c < 0, b > 0, c > 0. (a) Suppose you are required to make a choice of d 1 today and must choose d 2 = tomorrow. If you want to maximize the expected value of dam building, what do you do? What is your expected benefit from dam building? (b) Suppose that the planner is able to delay construction of the dam until the future. What is the expected value today of an optimal construction policy tomorrow? (c) For the situation described above, what is the option value of non-use? (d) When is it likely to be important to think about option values? 1...
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