DSE 2007

[NM]

Can someone please help me out with question 38? As per my reasoning I think it should be 'b' but the answer key says 'a'.

Thanks. :)

[Gayyam]

Simplifying the utility function as a Cobb-Douglas function, we have -
U(c1,c2) = c1*(c2)^(1/(1+∂)). The budget constraint is c1 + c2/(1+r) = w1 + w2/(1+r).

Solving, we get c1 = (w1 + w2/(1+r))/(1+(1/(1+∂))).

Now, if c1 increases, the borrowing increases. c1 increases if ∂ increases. Thus the answer is (a).

[Dreyfus]

Since optimal borrowing, b = [(1+§)*(w1*(1+r) + w2)/(2+§)*(1+r)] - w1
differentiating wrt § yields [(w1*(1+r)+w2)/(1+r)*(2+§)²] is positive, thus b increases!

[SoniaKapoor]

Gayyam..How did you get the cobb douglas version?

@drefus..how did you find optimal borrowing?

[Dreyfus]

The given utility function is monotonically transformed version of Cobb Douglas function.
The optimal borrowing in period 1, b = C1* - W1
Where C1* is optimal consumption level in period 1

[Gayyam]

Since utility functions are the same up to a monotonic transformation, you can choose to transform any utility function as you like with a suitable monotonic transformation. (DSE 2008 q31, q32 are good examples)

Often, this simplifies calculations. e.g. here, we have U(c1,c2) = log(c1) + log(c2)/(1+∂)
Using the properties of log (log(a) + log(b) = log (a*b)), we get U(c1,c2) = log (.c1*(c2)^(1/(1+∂)))

But, y=e^x is a monotonic transformation. So, e^U(c1,c2) is equivalent to the utility function, which is c1*(c2)^(1/(1+∂)).

Do let me know if this is clear.

[NM]

Thank you so much! :D

I didn't think of converting the utility function into Cobb-Douglas.

[SoniaKapoor]

gayyam..Thanx I got that
Bt i still didnt get how u got c1 value?Please help.I'm stuck.

[phelps.phan]

This is my approach and I'm getting the answer
Qn 36:
MU1=1/c1
MU2=1/(c2.(1+d))
MRS=(c2.(1+d))/c1

Slope of the intertemporal budget line is (1+r)
So the optimal choice condition is (c2.(1+d))/c1=(1+r)
=> c1/c2= (1+d)/(1+r)

Since the endowment(wage) is also a possible consumption bundle, when he borrows
c1/c2 will be greater than w1/w2
ie. (1+d)/(1+r) > w1/w2
(1+d)*w2 > w1*(1+r)

Qn 37: c1/c2= (1+d)/(1+r)
as d increases c1 increases, he borrows more

[phelps.phan]

guys pls explain 44,45,56. thanks.

[The Villain]

@phelps
57 The standard error is given by root(p*(1-p)/n)
where p=215/400, 1-p=185/400 , n=400
put in above formula u'll get it .025 :)

[phelps.phan]

thank u Ron, can u tell how we arrive at this formula.

[The Villain]

This is the formula for a proportion value.
Refer any stats book degroot , or freund..any..u'll get it.Cheers!!

[yuganshi]

For ques 44 and 45 the following rules are used
rule 1: intersection of an open set is always a closed set hence 44 ans is d

rule 2: union of a closed set is always an open set hence 45 ans is c ....

[Anjali]

@Gayyam , could you please explain ques 37 ?

[Akshay Jain]

[Anjali]

Thanks Akshay !!