Car purchase. A student just entering college needs used car so that he can earn part of his college expenses. He has narrowed it down to two choices-a "cheap" used car or a "good" used car-and he estimates the performance probabilities for both as shown in the table. If he buys the cheap car and it is "totaled" through excessive repair costs, he will not buy another cheap car. Rather, he will move up to a good used car like the one he is currently considering, Similarly, if he buys a good used car and it is totaled through excessive repair costs, he will not buy another "good" car, but will move down to a "cheap" car like the one currently under consideration. "Repairs above normal" are $300 per year. while "major repairs" are $600 per year for each of the student's four years of college. Note that normal repair costs represent a zero baseline.
Assume a salvage value or $500 for each car if totaled and no more than one such "total disaster" occurring. Further assume that the replacement cost is simply the purchase cost of the next used! car: that is, neglect future expected costs for the replacement car.
|
| Performance Probability | |||
Car | Cost ($) | Normal Repairs | Repairs Above Normal | Major Repairs | "Totaled" |
Cheap | 4000 | 0.20 | 0.30 | 0.30 | 0.20 |
Good | 6000 | 0.50 | 0.30 | 0.10 | 0.10 |
Which car should be purchased? What is the optimal, four-year expected cost? If the student- experts to be in college for five years instead of four, is the decision changed? What is the new expected cost?
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