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Edited on Thu Aug-31-06 11:55 AM by izzybeans
In economic terms it would mean cost vs. benefit. There is nothing in this problem to define cost vs. benefit other than monetary units. So under this notion of rationality than school A would be the choice.
Assuming all other things being equal: School B sets the lbs. limit at the Average of school A, so this would shrink their average below 250 because cost would prohibit the upper limits of the distribution from rising too far beyond 250 lbs. Remember school A reports an average. I would expect the upper limit to be higher in school A because there are no economic constraints on poundage. If they are economically rational, this will drag the average higher. The upper limits of school B will be at or near 250 lbs so the average would have to trend lower. Outliers impact averages and this is perhaps the key to answering this question.
With that in mind, on the other hand, the lower limits of school B would probably increase as well. Because under this definition of rationality it would be rational for those who don't eat that much food to start piling it on at the end of the semester. Combine this raising of the lower limits and lowering of the upper limits then the overall range would shrink. This may nullify any theoretical change in the average of school B. But we can't really tell without specific information about the students of each school. Again that fuzzy word rational pops back into play. It may be rational for some students to eat over the lbs. limit and pay more, say if they are on sports teams requiring heavy diets. We don't have any information about the students of the school to suggest what is rational for them, other than 2+2=4. I would say your prof. probably thinks that this athlete is irrational and he/she would only drive up the average of school B as a consequence.
Now if we define rational in a more well rounded way then this economic analysis is bunk. But pure economics suggests school A. Then again these types of problems drove me into the more social of the human sciences, because the world only works like this in textbooks.
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