ISI INTERVIEW PREP

[deepak]

Neha, I would think the answer is option b) ? Option a doesn't seem likely at the going prices, as Agent 1 would be stepping down from a Utility of 2 to a Utility of 1

[Hargun]

@neha: I don't think that in the case where preferences are of min type, but the total amounts of two goods are different, we can say that every pareto-efficient point can be reached competitively. because if we draw say a slanted line of 45 degrees through the endowment point passing through the contract region(parellelogram), then the ICs highest tangent to the price line will not be tangent to each other, thus there will be no equilibrium for these prices. but where one of these goods is free, the price line is horizontal or vertical.
it cannot be horizontal because the parellelogram is such that, the horizontal price line with px=0 cannot be bargained for (try and start from equal prices and think that prices are bargained progressively making the price line steeper or flatter. if you make it flatter, you will reach a point where price line intersects the point (0,1). this isnt an equilibrium price ratio and there is no reason to reduce price of x further) i think the only option left is a vertical price line, which means option b is correct.
I'm sure of the first para i wrote but not about the explanation given in the second para. what do you think?

[Preet]

No. Think like this now. Px= 0 and Py=1 i.e. i now make good x to be a free good. Agent 1 now has zero income.Take this case now(only an e.g.): Agent 2 will prefer to consume (999,999) than (999,1000) since good y is costly as he needs to minimize his expenditure. Agent 1 will not consume the excess of good y since he has zero income and good y has a price attached to it. Hence, such a price combination results in a pareto inefficient allocation

[Hargun]

Yes preet you're right. thanks

[Preet]

So buddy u have ur interview on 6th. How's the prep? Any tips from the DSE cracker?

[Hargun]

@neha: its 'a' because it lies on the price line and passes through both the endowment and final equilibrium points.

[Hargun]

Ha ha. no tips, just doing what you're doing, and revising the concepts. when is your interview?

[Preet]

same day. same slot. Probably one name ahead of yours!

[Preet]

Not 'c'? Coz endowment is wht agents can sell at given market prices and then buy the bundles which achieve pareto efficiency at given prices. and endowments in both options satisfy that. as per your logic also, the price line can pass through both the points..

Hargun wrote

@neha: its 'a' because it lies on the price line and passes through both the endowment and final equilibrium points.

[Hargun]

Yes, you're right, i made a mistake reading the options .
:)

[deepak]

Guys, I'm not sure about option a. The utility derived from the 2 goods is complementary and much as possible, they'd like to have more of both than more of just one. So if agent 1 had an endowment of (2,5) (which leaves him with an income 7 and a utility of 2), for equal prices of x and y, why woud he trade away from a position of higher utility to (6,1)?

[Hargun]

Deepak, only 1's util function is given, not two's. we don't know if its min or any other function

[Hargun]

sorry, i meant only two's is given

[Preet]

@Deepak- i would rather see this case as one where Agent 1 has no utility function and he's consuming the leftover! :D
@Hargun-you can also edit a post instead creating a fresh one :)

Hargun wrote

Deepak, only 2's util function is given, not two's. we don't know if its min or any other function

[deepak]

Ah yes. I went with the rigid assumption that both had min Utility functions.

Also, had that been the case, the given situation wouldn't be competitive equilibrium! So like you guys say, we only have agent 2's utility to work with and 1 does seem to treat x and y as perfect substitutes.

[deepak]

Ok, digging up some old bones now, ISI 2012 MQE paper, Question 15 Part b)
Gist of the question goes
Production of Food F = (T*Lf)^0.5 and Production of Manufacturing M = (K*Lm)^0.5. Also K=36,T=49, Lm+Lf-100 and all factors are completely employed.
Part b of the question asks how much labor each firm would employ given land were free.
Now, the cost functions for food and manufacturing respectively are (after substituting the values for T,K):
C(F) = 1/49 * w * F^2 + 7 * 0 (since land costs nothing)
The marginal cost of Food still remains the same. So the fact that land costs nothing doesn't really change anything? Or is there a flaw here?

[n.saish]

@ Deepak: Ya, I also thought the same way, as land is a fixed cost, whether its zero or a million bucks they will have to pay in the short term and in the long term when the amount of land can be optimized they will use as much of land there is in the economy as its free.... But either ways the labor employment I don't think would change...

@ Neha: Sorry for troubling you so much over this problem...
I've understood how to find the pdf from the df... But still don't get the problem thats occurring when you directly write the pdf because when you're directly writing the pdf the case you've mentioned would not occur, because if all xi's are less than z it becomes the highest no.... not the second highest... (that is the case to be included while writing the df)
But nevermind that... Thanks a lot :)

[anon_econ]

Those who hv their interview on 6th or 7th, plz do share ur experience here once it gets over!

[neha]

@preet ,, what you are saying makes sense to me,, but i have one more doubt.

Instead of minimizing the total expenditure we can think in terms of maximizing the utility. Since at Px=0 and Py=1 agent 1 has no income,, so agent 2 cant think of selling any of his y units to him and to maximize his utility he would want 1000 units of x [(1000,1000) is preferred over (999,1000)]  and there is no price attached to it,he can very well afford to do that. so he would want 1000 of x which leads to excess demand of it.. so thats why it can be competitive.  What do you think?

[anon_econ]

i agree with u, neha. that's how i thought about it.