### Create a fundamental-objectives hierarchy for comparision

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Question: Once you decide that you are in the market for a personal computer, you have many different considerations. You should think about how you will use the computer, and so you need to know whether appropriate software is available and at what price. The "feel" of the computer, which is in some sense determined by the operating system and the user interface, can be critical. Are you an experienced user? Do you want to be able to program the machine, or will you (like most of us) rely on existing or over-the-counter software? If you intend to use the machine for number crunching, videos, or gaming, then processor speed may be important. Reliability and service are other matters. For many students, an important question is whether the computer will be compatible with other systems in any job they might eventually have. Finally, of course, price is important.

Create a fundamental-objectives hierarchy to compare your options. Take care in doing this; be sure that you establish the fundamental objectives and operational attributes that will allow you to make the necessary comparisons. (Note that the previously suggested attributes are not exhaustive, and some may not apply to you!) Use your model to evaluate at least three different computers (preferably from different manufacturers). You will have to specify precisely the packages that you compare. It also might be worthwhile to include appropriate software. (Exactly what you compare is up to you, but make the packages meaningful.) Be sure that your utilities are such that the best alternative gets a 1 and the worst a 0 for each attribute. Assess weights using pricing out, swing weighting, or lottery weights. Calculate overall utilities for your alternatives. Try using the utility functions for money and computer reliability that you assessed in Problems I and II. You may have to rescale the utility functions to obtain scores so that the best alternative in this problem scores 1 and the worst scores 0.

Problems I: Assess your utility function in three different ways.

a. Use the certainty-equivalent approach to assess your utility function for wealth over a range of \$100 to \$20,000.

b. Use the probability-equivalent approach to assess U(\$1,500), U(\$5,600), U(\$9,050), and U(\$13,700). Are these assessments consistent with the assessments made in part a?

c. Use the trade-off method to assess your utility function for values ranging from \$100 to \$20,000.
Plot the assessments from parts a, b, and c on the same graph and compare them. Why do you think they differ? Can you identify any biases in your assessment process?

Problems II: Assume that you are interested in purchasing a new model of a personal computer whose reliability has not yet been perfectly established. Measure reliability in terms of the number of days in the shop over the first three years that you own the machine. (Does this definition of reliability pass the clarity test?) Now assess your utility function for computer reliability over the range from 0 days (best) to 50 days (worst). Use the assessment technique with which you feel most comfortable, and use computer assessment aids if they are available.

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