Aksahay..please help

[kangkan]

Hi..Aksahy please help with the following DsE 2013 question..i am at my wits end

[kangkan]

and the follow up

[kangkan]

what i could get for the 1st one is as long as 1+r>1/b the person wud prefer to consume entirely in period 1,since the indiffrence curve is a straight line..but she can borrow only 1/1+r in period 1....it seems the nescesaay condition is 1+r>1/b and r=1..but this is not among the options :(

[kangkan]

for the second part: the number of people who wud consume in period A is intergration from 1/2 to 1/1+r of 2..(uniform distri)...which comes out as N(1-r/1+r)..so if the optimal choice period 1 is 1/2..the demand will be N/2(1-r/1+r)..but why is it 1/2 in the 1st period?whr m i going wrong?. please help

[kangkan]

sorry i got your name wrong

[Homer Simpson]

Kangkan, i think 32 should be (d). The endowment here is (0,1) - which means anything consumed on the line indicates borrowing. since the IC is linear and i am aware that the person definitely consumes in period 1 and period 2, i must be anywhere on the budget line except at x1 = 0 or x2=0 which means we cant have that inequality prevailing as you mentioned. (think perfect substitutes ka condition - if inequality is there, then i choose an extreme)

if x1 = 1/2 , x2 also consumed in positive amounts - that only happens when slope = 1+r and MRS = 1/beta are equal.

[kangkan]

hi..tsuki..i to think it shud be d,but i am not sure...and how do i know he definitely consumes in both period 1 and 2?....can you please show the diagram...i wud be obliged :)

[Homer Simpson]

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[Dreyfus]

But the extreme point on x axis ie when consumer consumes her entire income in period 1 should be present value of 1 not only 1 as if she consumes 1 unit in period 1 she hv to pay (1+r) in period 2! And her period 2 income is only 1!

[kangkan]

hi tsuki..why are the red dots not included..?the question says x1,x2>=0....so they can be zero.... but even if we assume that conumption is on the BC line, how is it that optimal point is (1/2,1-0.5(1+r)) ?..m confused

[Homer Simpson]

haan, x-axis extreme is the one u mentioned. made a silly mistake while labeling the diagram!

[kangkan]

ok..now m totaly confused..do we have a consensus on the ans?

[Homer Simpson]

kangkan, they have given that x1 = 1/2 in the subpart, which means x1 cant be 0 and asked u find the interest rate with it. since he isnt on his endowment point and has borrowed a bit that means he must consume a positive amount in period 2. thats why for 32, i am not considering the red dots. we cant have an extreme solution in this case!

and i rectified the diagram (x-axis labelling thoda galat ho gaya tha pehle)

[kangkan]

Hi....you have said that if X1=1/2 then X2 must also be positive...but if r=1 then ,then he must pay back 1 uit of rice in period 2 right..hence his period 2 consumption will be zero.... :( can you please do me big favor..can you please write down your steps?..thanks a lot

[Homer Simpson]

i did it by intuition actually

[kangkan]

ok..can you verify the other answers?

[Akshay Jain]

the only twist in the question is the formation of the budget constraint of the consumer
now let m1 be production in period 1 = 0
and m2 be production in period 2 = 1
if the consumer is not requared to pay the amt of rice dat he borrows in period 1 den his budget constraint vl be x1+bx2<=1/(1+r) (discounted value of intertemporal budget constraint
but the consumer has to pay back x1(1+r) to period 2, so the discounted value of loan payback for period 2 vil be x1(1+r)/(1+r)=x1
so the new budget constraint is
x1+bx2<=1/(1+r)+x1 (new discounted budget constraint)
now the budget constaint binds at the optimum and
x1 cancels out from the equation leaving
bx2=1/(1+r)
in period 2 the consumer vl consume x2=1
so b=1/(1+r)
r=(1-b)/b
option d
(It would be great if Amit Sir or some1 else confirms my approach)

[kangkan]

Hi akshay..thanks a lot for responding..i cudnt understand this point: x1+bx2<=1/(1+r) (discounted value of intertemporal budget constraint )...can you please clarify..cuz all i nkow is that V of consmptions must be the PV of income stream..please help

[Akshay Jain]

its just dat the total consumption (discounted) in both periods must be less than equal to the total production/income (discounted) in the two periods
for consumption the discount factor is given as beta and for production we use discount factor (1+r)

[kangkan]

thanks askshay..didnt know that use of Beta...one question..the new 50% reservation for DU..do u know how the system will work?also, is it something very significant..given that most people who wud writing the paper will be DU students(i am not Du though)