ajaz_eco204_2009_HW_18

# ajaz_eco204_2009_HW_18 - University of Toronto Department...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 – 2010 S. Ajaz Hussain HW 18 Please help improve the course by sending me an e mail about typos or suggestions for improvements _____________________________________________________________________________________ Note: Please don’t memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you’ll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 We have seen various methods for decision making under uncertainty (Expected utility, Expected Value, Decisions with testing, etc). These methods are frequently used in oil exploration and drilling (see for example the March 6 th 2010 Economist magazine article Plumbing the Depths ). In this question you will see a simple model of oil drilling. An oil company must decide whether to drill or not drill for oil. The outcome of not drilling is \$0. The outcomes from drilling are the following net profits (i.e. revenues minus cost) and corresponding probabilities: ሼ\$600݉, \$200݉, \$0݉, െ\$120݉; 0.2, 0.18, 0.32, 0.30ሽ ሼݔ ;݌,1െ݌ሽ ݌ ܷሺ\$600݉ \$200݉; 1, 0ሻ ൌ ܷሺ\$600݉ሻ ܷሺ\$600݉, െ ݉; 0.7, 0.3ሻ ൌ ܷሺ\$200݉ሻ Recall that the statement: Means that we will observe ݔ with probability ݌ and observe ݔ with probability 1െ . (a) Draw the decision tree for this problem. (b) If the company is risk neutral, will it drill or not drill for oil? (c) Now suppose the company is risk averse. Suppose the board of directors decides that: , െ \$200 1

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ܷሺ\$600݉ െ\$200݉; 0.5, 0.5ሻ ൌ ܷሺ\$0ሻ ܷሺ\$600݉, െ\$200݉; 0 5, 0.75ሻ ൌ ܷሺെ\$120݉ሻ
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ajaz_eco204_2009_HW_18 - University of Toronto Department...

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