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eco204_HW_20 - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 20 From Lecture 22 recall that a square node is a decision node, while a circular node is a chance node. In the former, the decision maker has complete control on the path, while in the latter, chance determines the path. Question 1 In Lecture 22 we discussed the oil driller’s problem in which the choices were to {Drill, Not Drill}. By definition, these are mutually exclusive choices: that is, you can do one or the other, but not both. In this problem, you will make a decision under uncertainty where the choices are not mutually exclusive. I hope it makes you think harder about how to setup a problem. You are the CEO of a pharmaceuticals company “Economics‐Man Genetics”. It has replicated Economics‐Man’s genes 1 . The company must decide whether to commercialize Economics‐Man genes ‐‐ aimed at students studying for Economics tests and the final exam (just like you!) ‐‐ using a Biochemical or Biogenetic R&D approach. Suppose the profits and probabilities of the competing approaches are: 1 No relation to Eco‐man. 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain R&D Approach Biochemical Biogenetic Investment $10m $20m Outcome Large Success Small Success Success Failure Gross Profit $90m $50m $200m $0m Probabilities 0.7 0.3 0.2 0.8 Observe how the Biogenetic approach is more “risky”: it has a high upside but also a low downside. In contrast, the Biochemical approach is less risky but also less lucrative. Find the best approach to commercialize the Economics‐Man’s genes. Assume you can commercialize only one approach. Hint: the choices {Biochemical, Biogenetics} are not mutually exclusive. Question 2 Consider this variation of the oil driller problem we saw in Lecture 22. A company must decide whether to drill for oil. The outcome of not drilling is $0. The outcomes of drilling ‐‐ with a cost of $120m ‐‐ are many fold: net profits from oil can be: $600m, $200m, $0m, or ‐$120m (think of these as different amounts of oil; in Lecture 22 there was either oil or no oil) with probabilities 0.2, 0.18, 0.32 and 0.30 respectively. (a) Draw the decision tree for this problem. (b) If the company is risk neutral, what is the decision? (c) Now suppose the company is risk averse. Denote a gamble with outcomes X1 and X2 with probabilities p1 and p2 by: (X1, X2; p1, p2). Suppose the board of directors decides that: U($600, ‐$200; 1, 0) = U($600) U($600, ‐$200; 0.7, 0.3) = U($200) U($600, ‐$200; 0.5, 0.5) = U($0) U($600, ‐$200; 0.25, 0.75) = U(‐$120) Suppose you’re now risk averse (maybe it’s the economy!). Should the company drill for oil? 2 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain (d) (Difficult) Can you reduce the uncertainty for drilling for oil ($600, $200, $0, ‐$120; 0.2, 0.18, 0.32, 0.30) to a gamble between $600 and ‐$200? By doing this question, you’re reducing the drilling option ($600, $200, $0, ‐$120; 0.2, 0.18, 0.32, 0.30) to an “equivalent risk”. This is a technique used by risk managers to transform and understand risk in terms of some benchmark uncertainty. 3 ...
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