ISI Interview Question

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ISI Interview Question

happy



Anyone plz
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Re: ISI Interview Question

ALIBABA
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Re: ISI Interview Question

Asd1995
probably convex ICs and positive marginal utilities.
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Re: ISI Interview Question

Asd1995
In reply to this post by happy
Perhaps the question is incomplete. If I assume a Rawlsian welfare function I'll get a different result than I'll  get from maximising sum of utilities which would be different from weighted sum of utilities.

The only other thing I can think of is he may want the allocation to be fair i.e no one envies each other and locations are pareto optimal.

If Utility is convex analysis for each kind of welfare function changes but again idk.
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Re: ISI Interview Question

happy
In reply to this post by ALIBABA
concave increasing means utility of x increases at decreasing rate

An example of concave increasing function



X-Axis = qty of x
Y-Axix = U(x)
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Re: ISI Interview Question

Econ2017
In reply to this post by Asd1995
Can you please help me in solving this problem ?



A ‘success’ is defined as picking an ‘A’ such that the polynomial x2 − Ax + 1 has at least one real root. Mr. X is picking A from uniform distribution over [0, 5]. Mr. Y is picking A ∈ [0, 5]
with the probability distribution function fA(a) given by : fA(a) = 2a ∀a ∈ [0,5]. Which
 person has a higher probability of success?
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Re: ISI Interview Question

Asd1995
If you're preparing for ISI interview, they scrapped asking math questions last year.

ANnyway,

If a polynomial with real coefficients has 1 real root, then imaginary roots occur in conjugate pairs (a+bi,a-bi)

Since this has a degree of 2, it must have both roots real. Discriminant (b^2-4ac) >=0

so A^2-4>=0 or A belongs to the set of all real values except from -2 to 2.

So permitted values in our set are [2,5] so success= 0.6

Probability Mr. Y picks out something from [2,5]= F(5)-F(2) where F is cdf of the distribution.

First I believe we have to normalise the pdf here, so that INTERGRAL f for all values of a=1

so f(a)=2a/25

F(a)= a^/25

So success= 1-4/25=21/25

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Re: ISI Interview Question

Econ2017
Thanks buddy.
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Re: ISI Interview Question

Econ2017
R u done with ques 4?
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Re: ISI Interview Question

happy
In reply to this post by Asd1995
last year they asked 2 micro question or just 1?
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Re: ISI Interview Question

Asd1995
One
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Re: ISI Interview Question

Asd1995
In reply to this post by Econ2017
Which question?
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Re: ISI Interview Question

Asd1995
In reply to this post by happy
So after a bit of thought, here's my two cents;

Since we dont have a defined welfare function, we know that if preferences are convex, there exists an allocation which is fair and pareto optimal (Hal Varian). If everyone has the same preferences, the only such allocation is where everyone has the same utility.

Now if transfer from c1 to c2 results in a loss, and we still want to ensure fairness, we still need to give everyone the same bundle since everyone still has the same preference. So both cities will have same bundle, but this will not maximize total utility. Still, it is a fair and a pareto efficient outcome.

If preferences are concave a fair and PE allocation may not exist, it would depend on the nature of the function.

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Re: ISI Interview Question

Econ2017
This one . You already did . Thanks again :)
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Re: ISI Interview Question

Asd1995
Sure, happy to help. Obviously I may be wrong so keep that in mind.
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Re: ISI Interview Question

ElPsyCongroo
In reply to this post by Asd1995
If they scrapped math questions then what do they ask?

One micro and one macro?

Or just one micro?
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Re: ISI Interview Question

Asd1995
Only micro last year
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Re: ISI Interview Question

ElPsyCongroo
What? Like one micro question?

Sure hope they don't flip the pattern and ask one math question this year :S
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Re: ISI Interview Question

Asd1995
Hahaha micro will always be there. Math or no math can't say.
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Re: ISI Interview Question

Econ2017
Hey what's the relevance of CRS in this question ?


Suppose a monopolist faces constant returns to scale. Answer the following parts:
(a) Why he never produces on the inelastic side of the demand curve?
(b) Why does total revenue increase on the inelastic side as price increases?
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