Conditional Probabilities Assignment 1

Conditional Probabilities Assignment 1

Case 6.3

Electronic Timing System for Olympics275not occur, they assess that there is a 10% chance that the competitor will buy the land during June. If Westhouser does not take advantage of its current option, it can attempt to buy the land at the beginning of June or the beginning of July, provided that it is still available. Westhouser’s incentive for delaying the purchase is that its financial experts believe there is a good chance that the price of the land will fall significantly in one or both of the next two months. They assess the possible price decreases and their probabilities in Table 6.2 and Table 6.3. Table 6.2 shows the probabilities of the possible price decreases during May. Table 6.3 lists the conditional probabilities of conditional probabilities of conditional the possible price decreases in June, given the price decrease in May. For example, it indicates that if the price decrease in May is $60,000, then the possible price decreases in June are $0, $30,000, and $60,000 with respective probabilities 0.6, 0.2, and 0.2. If Westhouser purchases the land, it believes that it can gross $3 million. (This does not count the cost of purchasing the land.) But if it does not purchase the land, Westhouser believes that it can make $650,000 from alternative investments. What should the company do?

Table 6.2 Distribution of Price Decrease in May

Price Decrease                    Probability

$0                                               0.5

$60,000                                     0.3

$120,000                                  0.2

Table 6.3 Distribution of Price Decrease in June

Price Decrease in May

$0           $60,000 $120,000

June Decrease               Probability          June Decrease        Probability          June Decrease         Probability

$0                                           0.3                          $0                           0.6                          $0                              0.7

$60,000                                 0.6                          $30,000                  0.2                           $20,000                   0.2

$120,000                               0.1                          $60,000                 0.2                           $40,000                    0.1

CASE

Sarah Chang is the owner of a small electronics company. In six months, a proposal is due for an electronic timing system for the next Olympic Games. For several years, Chang’s company has been developing a new microprocessor, a critical com-ponent in a timing system that would be superior to any product currently on the market. However, progress in research and development has been slow, and Chang is unsure whether her staff can produce the microprocessor in time. If they succeed in developing the microprocessor (probability p1), there is an excellent chance (probability p2) that Chang’s company will win the $1 million Olympic contract. If they do not, there is a small chance (probability p3) that she will still be able to win the same contract with an alternative but inferior timing system that has already been developed. If she continues the project, Chang must invest $200,000 in research and development. In addition, making a proposal (which she will decide whether to do after seeing whether the R&D is successful) requires developing a prototype timing system at an additional cost. This additional cost is $50,000 if R&D is successful (so that she can develop the new timing system), and it is $40,000 if R&D is unsuccessful (so that she needs to go with the older timing system). Finally, if Chang wins the contract, the finished product will cost an additional $150,000 to produce.

1. Develop a decision tree that can be used to solve Chang’s problem. You can assume in this part of the problem that she is using EMV (of her net profit) as a decision criterion. Build the tree so that she can enter any values for p1, p2, and p3 (in input cells) and automatically see her optimal EMV and optimal strategy from the tree.
2. If p25 0.8 and p35 0.1, what value of p1 makes Chang indifferent between abandoning the project and going ahead with it?”

“c. How much would Chang benefit if she knew for certain that the Olympic organization would guarantee her the contract? (This guarantee would be in force only if she were successful in developing the product.) Assume p15 0.4,  p25 0.8, and p35 0.1.

1. Suppose now that this is a relatively big project for Chang. Therefore, she decides to use expected utility as her criterion, with an exponential utility function. Using some trial and error, see which risk tolerance changes her initial decision from “go ahead” to “abandon” when p15 0.4, p25 0.8, and p35 0.1.”

Conditional Probabilities Assignment 1

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