ISI PEA 2015 discussion

[onionknight]

Not sure about what they asked but pretty sure that only when you club a and b will you get a complete description of lexicographic preferences. Maybe there were some differences in the questions

[onionknight]

My answer was for equilibrium prices and allocations where for 1 the goods are perfect substitutes and for 2 they are lexicographic in X. So, p1=p2=1 x1=0 y1=12  x2=10 y2=0

[amalgamateking]

Nah,I dont think questions were different at all.

If anyone remembers part iv of question 1 (dhruv, since you asked?) Can he or she please write it down here?
Also if what you are saying is true, the  do you mean to say that there were actually no sub sections to that part, and basically it wasnone question only? Or are you saying that we had to asnwer first with a (where he doesnt care about y) and then another time with b (where he in addition to a, likes more Y)?

Also did you attempt this question?

[amalgamateking]

Do youbremember the initial endowment?

[onionknight]

Yes, they were one part. a.) said that he prefers X without caring for Y b.) said that if the amount of X was same then he preferred a bundle with greater amount of Y. Only when a and b are clubbed together will it make compete description of lexicographic preferences in X.

[onionknight]

Yes, X1=4 Y1=8 , X2=6 Y2=4

[amalgamateking]

And you remember that we had to find competitive eq? How did i miss that word? :/ i totally remember reading that the last five words of that question were "set of pareto efficient outcomes"

[onionknight]

Like I said, that is not something I remember clearly. I do remember the a.) and b.) parts precisely since even I thought they are different and had to re-read them to understand what exactly they meant.

[amalgamateking]

So essentially, the paper setter had described lexicographic preferences towards X only. Just that he did it in two steps (a and b). But we only had to find out one answer (either like you did which is the comp eq, or what i did, the contract curve)? This is what you are saying right?
Also did you mention the set of pareto optimal outcomes in that part? I didnt find the comp eq, just the contract curve

[onionknight]

Yes.
No I only wrote the eqm. prices and bundles.

[amalgamateking]

Btw just asking, how many did you attempt in PEA and in PEB (full + some parts)?

[onionknight]

PEA 29, PEB I did 5 complete and in the question on Solow Model I did the first 2 parts and the third part was incomplete. Do you know the answer to the regression question in PEA? I didn't cover that topic and it was the one question I couldn't do so I thought I might as well make a wild guess.

[art]

guys what is the answer for last question of pea...the minimium value wala which had 6th powers of x+1/x...it took a lot of time but couldnt solve

[amalgamateking]

6 is the answer of pea last question

[onionknight]

Yeah, it's 6. The expression can be reduced to 3(x+1/x).

[amalgamateking]

Nice! You had a pretty great exam.. did you attempt the cake cutting one? If yes, how did you show the pareto optimal outcomes and optimal cutting by A. Also what about its last part?

And monopoly MR necessarily negative mein toh I just did derivative of mr which was 2p' +xp" + A" (something like this)

I said in usual cases p is taken to be linear so second term vanishes and also there is no function like A so we only have 2p' which is negative. Here however we are simply told in general p" and A" exists but we dont know its sign, so MR may be positive as well. What did you do?

[onionknight]

All allocations would be pareto efficient since their utilities were just the fraction of cake they got. Whenever one gets more, the other gets less. Optimal cutting would be to cut in two equal pieces because if he cut it in any other ratio B would keep the bigger piece for himself. In the third part when u<1 answer won't change and when u>1 he'd let B keep the entire cake because that would give him the highest utility.

I think you're talking about question 4, I didn't attempt that

[amalgamateking]

Why would the answer not change if u is less than 1?

Take the following value of u=1/2. If he cuts the cake into a part like (1/3, 2/3) where the first is for himself the  his total utility is (1/3)+[(1/2)*(2/3)] = 2/3. This is greater than 1/2 (which A got earlier). Thus optimal cutting may change even when u is less than 1

[amalgamateking]

Ok got it. Bunk.

[onionknight]

With 1/2,1/2 his utility would be 1/2+1/2*1/2=3/4>2/3