Question for the economic gurus out there.

[Idioteque]

I'm just starting a macroeconomics course at school and I'm stumped by a homework problem.

"The meal plan at school A lets students eat as much as they like for a fixed fee of $500 per semester. The average student there eats 250 lbs of food per semester. School B charges $500 for a book of meal tickets that entitles the student to eat 250 lbs of food per semester. If the student eats more than 250 lbs, he pays $2 for each additional pound; if he eats less, he gets a $2 per pound refund. If students are rational, at what school will average food consumption be higher?"

My initial thought is that average consumption would be the same. Since the $500 cost is sunk at school A, 250 lbs would be the point of being full for a rational student. Since the marginal cost of eating an extra pound at school B is the same as the marginal benefit of each pound not eaten, I would think the average would still be 250 lbs. That doesn't seem right, however.

Any help would be much appreciated. :)

[MrCoffee]

1. a suffusion of yellow

[chat_noir]

2. non sequitur - just go with it

[hfojvt]

3. definitely school A

It should be obvious. They have no cost if they eat 300 pounds (other than a health cost, perhaps) whereas at school B, they are rewarded if they only eat 200 pounds and thus have an incentive to reduce what they eat, the same with the cost for eating every pound past 250.

The sad part is that in school A there is no disincentive to taking more food than you can or will eat and thus some is fed to the garbage cans.

[Gormy Cuss]

4. School B

Because School B has quantified the value per pound students understand that they have purchased 250 lbs and have an incentive to maximize the value of the book of meal tickets by eating the full amount. School A's students, on the other hand, understand the unit to be one semester and thus see maximizing the value as eating a certain number of meals or days as the unit of value rather than in terms of pounds.

Edited because I need more coffee.

:-)

[izzybeans]

5. I'd ask the prof. to define "rational" before answering.

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.