General Equilibrium - June 17

classic Classic list List threaded Threaded
32 messages Options
12
Reply | Threaded
Open this post in threaded view
|

General Equilibrium - June 17

Amit Goyal
Administrator
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
This post was updated on .
walrasian equilibrium for n=4 is 2 <p*<3 ( px/py) ,
i had earlier made mistake, consumption bundle would be , i guess, ((1- 1/p) , 2) for first 2 individual and ( (1+ 1/p ), 0 )
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Vasudha
Komal, if these r the consumption bundles then to make total demand=total endowment, v will need p*=1. but at p*=1 these bundles wud nt be demanded in the first place.
i'm getting no walrasian equilibrium! plz correct me if i m wrong..and can't do the first one!
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
u were right those bundles were incorrect
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

rituvv
In reply to this post by Vasudha
yes vasudha i agree...we cant choose a price ratio so that all 4 can trade...apart from 1st person all others attach a higher index to x nd 1 is indifferent btwn them....for example if ratio is btwn 2nd 3 then individusl  3 rd nd 4 th person spend entire income on x nd dd > supply
1,2 on y nd dd> supply
so cant have a comp eqm in this case...

Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Amit Goyal
Administrator
In reply to this post by Vasudha
There is a Walrasian/Competitive equilibrium in this economy:
When price of X is Rs. 2/- and price of Y is Re. 1/-.
Individual 1 will consume only Y: (0, 3)
Individual 2 will consume his endowment: (1, 1)
Individual 3 will consume only X: (1.5, 0)
Individual 4 will also consume only X: (1.5, 0)
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
@ amit sir, this is only one of the equilibrium, right?
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Amit Goyal
Administrator
This is the only equilibrium.
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Vasudha
In reply to this post by Amit Goyal
Thanks. I have understood my mistake :)
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Vasudha
But what about pareto efficiency?
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
In reply to this post by Amit Goyal
i have got really confused, if there is a question that there r 2 individauals with u = 3x1 + y1 and 4x2 +y2,respectively and endowmwnts (1,1) each , then what will the the walrasian equilibrium?
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Amit Goyal
Administrator
Komal, In the economy you mentioned Competitive equilibrium prices are:
Price of X is 3 and price of Y is 1.
Individual with utility function u(x, y) = 3x + y consumes the following bundle: (2/3, 2)
Individual with utility function u(x, y) = 4x + y consumes only X: (4/3, 0)
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Amit Goyal
Administrator
In reply to this post by Vasudha
Vasudha, for set of Pareto efficient allocations, I suggest you do it for the cases N = 2 and N = 3 first. You will observe a pattern. And then you can try and prove it for general N.
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

ritu
sir for N=2 i got PE set as the vertical axis of agent 1 and horizontal axis of agent 2.....how to get it for 3 individuals....?????
AJ
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

AJ
In reply to this post by Amit Goyal
ummmm, i gave my best shot to it....and it's weird answer :/

I am getting pareto efficient allocation something like...

for Nth person, (x,y)= (N,y) or (x,0) ... x, y belongs to [0,N]

Now,
~ When this person is having.. (N,y) .. the remaining can have any distribution of good Y.. and allocation will be pareto optimal.

~ when this person is having .. (x,0) ... the (N-1)th person should have .. either (N-x, y) or (x',0)..
                                                      ~ when he has.. (N-x, y) ... the remaining can have any distribution  of good Y
                                                      ~ when he has.. (x',0) ... the (N-2)th person should have... either (N-x-x') or (x'',0)

...............
and now we continue same way till 1st person...

I am basically trying to say that last person should either have "all X" or "no Y" .... if he has all X... all allocations are optimal.. if he has no Y(and some X).. we move to previous person..

Now he must have "all remaining X" .. or "no Y" .... if 1st case: all allocations b/w remaining people are optimal.... if 2nd case: we move to previous person

Now he must have "all remaining X" .. or "no Y" ... and continues.......
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
In reply to this post by Amit Goyal

 p=4 can also be equilibrium
where  first individual with utility 3x + y consumes (3/4, 2)
 and second with utility = 4x +y consumes (5/4,0) ,
 am i right ?
 i m not able to understand why is there only one walrasian equilibrium ,  even this appears to me as walrasian equilibrium. where m i wrong ?
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

ritu
komal at p=4.....individuals 1,2,3 all will choose to consume only y as for all of them mrs<p1/p2....dd>supply....hence not an equlm
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

ritu
individual 1 has x+y
2 has x+2y
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

komal
In reply to this post by ritu
@ritu, actually i m refering to a question asked in between, plz help me out if u know..
Reply | Threaded
Open this post in threaded view
|

Re: General Equilibrium - June 17

Vasudha
In reply to this post by komal
y do u say he wud consume (3/4,2)?
12