ISI interview slot 1 question

[Asd1995]

Posting so that people can get an idea-

Let a comsumers preference be such that if bundle vector x is preferred to bundle vector y then qx is preferred to qy for all q>0.

Give an example of such preferences, and give a utility function consistent with the same.

Suppose a consumer has such preferences. Define a budget set with prices pi and income m. Let optimal consumption be bundle vector c. Now make all prices 3/4th of original prices, and let optimal consumption vector be d.

Relate c and d.

[Econ17]

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[Asd1995]

Better than expected. Solved it completely and was in and out within 5 minutes. Discussed an alternate method on assumption that preferences are convex. Rest they asked me my background, where did I hear about ISI, if I had a job in hand, if I had applied for other colleges etc.

They were friendly and asked good questions. Key is to be absolutely detailed as possible, like you're explaining it to a 10 year old.

[Econ17]

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[Asd1995]

Good luck for yours. Campus and rooms are pretty disappointing though.

[Econ17]

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[Econ17]

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[Asd1995]

Yes, these preferences mean MRS(ij) =f(qi/qj)  ie. Consumer only cares about the ratio of any two quantities in his budget set. This is a property of homothetic preferences.
U=any homothetic function of n goods.

Assume function is convex, set up lagrangian for both problems/budget sets and write MRS(ij) for both, it'll be the same. So consumer demands same ratio of any two quantities for both budget sets.

So d=4c/3

To prove for nonconvex preferences, say there's a bundle y preferred to 4c/3 in the second budget set. Multiply by 3/4 both sides (using property described in beginning of question) to get 3y/4 is preferred to c. But then 3y/4 must not be affordable if c is brought under original budget set. But it satisfies the first budget constraint as y satisfying the second budget constraint gives the same condition. So there's a contradiction.

[Econ17]

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[ElPsyCongroo]

Any idea when the results come out?

[Econ17]

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[Asd1995]

The coordinator said ten days but we all know how their reliability is. Either its out in a couple of days or after ISIK interviews IMO