Question from MSQE 2011

[Rajat]

Consider two consumer with identical income M and utility function U=xy where x is the amount of restaurant good consumed and y is the amount of any other good consumed. The unit prices of the goods are give. The consumers have two alternative plans to pay the bill. A: Each pays for what she consumes. B: both pay one-half of the bill amount.

1) Find equilibrium consumption under plan A.
2) Find same for plan B.
3) Explain the difference if any.

Please help. Not clear about the approach. Thanks !

[Rajat]

Friends, please help here.
I do not come from economics background. Hence, although I am able to tackle such economics questions based on common sense, I need to learn what is the correct/appropriate approach that should be followed in the final examination.

Moreover, given the unavailablility of mock tests for ISI entrance examination, this forum is my (and possibly of many others) best shot at understanding from others.

[Zen]

I am also stuck in this. I have found the first two answers, but I need some help in the explanation. Can anyone check if the answers are correct and provide the required explanation?
Plan A: For each consumer: x=M/(2*price of x), y=M/(2*price of y).
Plan B: For each consumer: x=2M/(3*price of x), y=M/(3*price of y).
I cannot explain the difference. I just used Lagrange multiplier method.

[hoouin]

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[Zen]

[onionknight]

Your solution is correct. Both will end up spending 2M/3 on the food. I got the same answer when I solved this problem using game theory. Since both consumers think that only half of the load of anything that they order (that they wouldn't order when they were eating alone) would fall on them, they wastefully end up spending too much on food and end up with a lower utility.

A similar example is given here: http://www.investopedia.com/terms/d/diners-dilemma.asp

[Zen]

Thanks for the confirmation, onionknight!

[hoouin]

Ur answer is right . we have to solve simultaneously for x1 and x2 to get nash equilibirium...

[Rajat]

Guys, are you also covering Game thoery/ Nash equilibrium for the exam ???

[Rajat]

@zen, can you pls upload your lagrangian method solution

[Zen]