ISI 2015 Q.7 and Q.8 - Difficult

[Rajat]

Hi,
can someone share their solution to questions 7 and 8 from 2015 sample paper.
I am kind of clueless about most parts of the questions. to start with (what is intensive and extensive
form !! ?)

[Rajat]

Looks like 2015 is same as 2014 paper.
Those who had taken the paper last year, could you please throw some light here

[onionknight]

Intensive form of the production function is just a form where the function has been reduced to a function of (k,1) or simply k by introducing k=K/L.

The properties you need to check would be
1.) f(0)=0 which is true in this case
2.) f'(k)>0 which is not true
3.) f''(k)<0 which is not true
Inada conditions
lim k->0 f'(k) = infinity , not true
lim k->infinity f'(k) =0 , not true

Part b:
The capital growth equation is
(1+n)*k[t+1]= (1-delta)*k[t] + s*( f(k) )               [where s is the savings rate]
One steady state would be at k=0
divide both sides by 0 and rearrange and your equation would boil down to
(n+delta)/s = k3 - 6k2 + 11k -6 = (k-2)(k-1)(k-3)

The curve of the function on the RHS is something like this: http://s18.postimg.org/k7fy37gx5/20150426_201658.jpg

Now if n+delta is positive and is such that n+delta/s has a value that is attained by this curve at the local maximum that lies between 1 and 2,then we have two more solutions(apart from 0). One is the local maximum between 1 and 2 and once it will be attained after 3. So the total number of solutions is then 3.


I'm not entirely sure how to check stability. It's somewhere in these slides but I can't quite remember it.
Look it up if you want to: http://economics.mit.edu/files/7181

[kk]

how to do question 2 of isi peb 2015

[Rajat]

Can anyone who has solved  Q.7 of 2015 sample paper share their solution to the first part.

What i got is:
In steady state equilibrium, Y(t) = delta* k(t)/[1 - phi + sigma (lambda -1)]

Also, i am not too sure about the law of motion of capital. I hope the K that is being referred to in the question is capital-labour ratio.
Someone please confirm.
Thanks !

[Ansuman7]

Hi how many questions we have to answer for PEB