JNU Doubts

[Arushi :))]

1.
Consider a society of 2 individuals in which a single commodity id produced , individual 1 getting x units and individual 2 getting y units of the commodity.
Suppose only three outcomes are possible in any time period:
A: x=10, y= 10, B: x=7, y=5, C: x=5, y=12
Then
a) society will prefer B over C
b) society will prefer C over B
c) society will be indifferent between B and C
d) we cannot say which of a,b,c will hold .

2.
A utility maximizing choice of a consumer's equilibrium occurs necessarily
a) where the marginal rate of substitution equals the price ratio.
b) where the marginal rate of substitution equals the price ratio and all income is spent.
c) where the marginal rate of substitution equals the price ratio and all income is spent and all goods are consumed in positive quantities.
d) where none of the above is necessarily true.
Should it be 'd' ? considering concave preferences and others.

3.
It is known that in an examination , 5% of the examinees cheat . However, whenever an examinee cheats, a black dot appears on his/her answer script.
An examiner receives an answer script with a black dot. What is the probability that the answer script came from a cheater?>
a) 0.05
b) 1.00
c) There is insufficient information to answer the question.
d) None of the above

4.
Suppose a perfectly competitive firm has a production function Q= A*K^0.4*L^0.6 where A>0
Q is the amount of output produced and K and L are the amounts of capital and labour employed respectively , during a unit time period.
What is the equilibrium ratio of wage bill to total revenue for the firm?
a) 0.6
b) 0.4
c) 0.67 approximately
d) cannot be determined based on this information alone
I go with d

[Granpa Simpson]

Q2. d.
Q3. 1.
Q4. 0.6

[Granpa Simpson]

Q3) use conditional probability and find P(Black dot appears/The student is a cheater), also since whenever a student cheats black dot appears in his sheet so P(Black dot appears)= P(he is a cheater) = 0.05....Now using the formula for conditional probability you will get 1 as the answer.(Guess!!!!!)

Q4) For a competitive firm w=p.MP(L)....also Total Revenue= p.Y
Now MP(L)=0.6*A*(K)^0.4*(L)^-0.4
Also (w/R)= {p.(0.6)*A*(K)^0.4*(L)^-0.4}/{p*A*(K)^0.4*(L)^0.6}
therefore, (w/r)= 0.6*(1/L)
or, (wL/R)= 0.6....hence option a.

[Amit Goyal]

1. (d) we cannot say which of a, b, c will hold.
2. (d) where none of the above is necessarily true.
3. (c) There is insufficient information to answer the question.
4. (a) 0.6

[Granpa Simpson]

Thank you Sir..!!!!

[The Villain]

Pls explain me quest 1

[Arushi :))]

@ Ron
What I think for the first one is:
B : x=7, y=5
C: x=5, y=12
If we go from B to C second person is better off and first is worse off.
And from C to B , first is better off and second is worse off.
So they won't prefer either of them over the other.

[The Villain]

@Arushi

Was it so simple..hehe thanxx.. :-)
I was making it complicated ..

[Arushi :))]

HAHHA ! It was'nt , thats why i posted it here
Actually i was baised towards 'd'.
But its JNU !
They give such options in almost every question, so i thought maybe i am missing out on some imp point .

[Arushi :))]

@ Amit Sir
Please can you explain the third one

[Amit Goyal]

Let B be the event that there is a black dot in examinee's answer script and C be the event that the examinee cheat. We want to find the probability that the answer script came from a cheater given that his answer script has a black dot. That is, we wish to find
Pr(C|B) = Pr(B|C)Pr(C)/ [Pr(B|C)Pr(C)+Pr(B|C')Pr(C')]
We know Pr(B|C) = 1, Pr(C) = 0.05 and Pr(C') = 0.95
But we don't know Pr(B|C'). That is, the missing information is the probability of the event that the answer script has a black dot given that the script belongs to someone who did not cheat.

[kangkan]

I guess it will be insufficient information for question 3 beacuse although we know that a balck dat will definitely appear for cheater,we do not know if a balck dot can appear for non cheater too.

[aman]

But it is given that whenever an examinee cheats, a black dot appears.. Should'nt that mean , whenever he does'nt cheat, black dot will not appear?