Your company manufactures iPhone cases There are rumors that

Your company manufactures iPhone cases. There are rumors that Apple will introduce the iPhone 6 in the coming months. If you wait until the phone is announced to develop cases that fit, you expect to make a profit of $1 m. If you make cases based on the rumors, then there is a 60% chance that you make $1.5m in profit because you will be able to sell your cases before your competitors. However, there is a 40% chance that your cases won\'t fit and you will need to redevelop your cases after the phone is announced, giving you an expected profit of only $300k. Construct the decision tree. Make sure to label the nodes. Don\'t forget the probabilities. Solve the decision tree. Make sure to prune the sub-optimal branches and label each node with its payoff. You are considering paying a reward of $100K for more accurate information about the phone\'s dimensions. How accurate must the information be (i.e., with what probability will the cases fit), for this to be worth S100K or more? Construct the decision tree and solve it.

Solution

The decision tree is as follows:

Without any information as such expected profit=

E(P) = 0.5 ( 1) + 0.5[0.6(1.5)+0.4(0.3)]

= 0.5+0.5(0.9+0.12) = 0.605 million

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If the information is accurate you can aim for profit of 1.5 million.