# General Equilibrium - May 18

19 messages
Open this post in threaded view
|

## General Equilibrium - May 18

 Administrator Solve the attached problem by tonight. May18_GenEq.png
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 Umm i'm getting the set of pareto efficient outcomes as all allocations (x11,x12)=(12,m) and (x21,x22)=(0,n) where m>=0,n>=0, m+n=8. And the competitive equilibrium is p1/p2=1. Demands are (12,0) and (0,8) for 1 and 2 respectively.
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 Administrator Well done Vasudha. You correctly found the set of efficient allocations. But the competitive equilibrium in this problem does not exist. At price ratio 1, consumer 1 will demand (0, 12) and not (12, 0).
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 Oh yes!
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by Amit Goyal Sir for pareto efficient outcomes, I am only getting (12,2) for consumer 1 and (0,6) for consumer 2. I went according to consumer 1's preferences - either the total consumption has to increase from (10+2 = 12) to 12+2 = 14 or the total consumption can stay constant at 12 units but > or = of good 2 needs to be present in the bundle but definitely not < 2. So his PO outcome must be (12,2) and thus for the other consumer its (0,6). How did m+n=8 situation arise? Maybe I am interpreting the question wrong? And for competitive equilibrium, yes indeed it doesn't exist because consumer 1's demand would be (0,12)...
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 hey aditi u don't hv to take the endowment as the starting point. all allocations from which nobody can be made better off w/o making anyone worse r PO. for eg (12,6) and (0,2) is PO bcoz u can't make either of them better off w/o making the other one worse off starting from this point..
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by Vasudha i got the pareto efficient points as the y=axis for consumer 2??????
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 and yes at any ratio of prices ie..<1,=1,>1 good 2 's demand exceeds its total endowment in economy so no equilibrium...
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by ritu yeah ritu ur PO allocations r right
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 Achha, yes! Got it.. Thanks. That makes so much more sense!!! Thank you!! :)
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by Vasudha Haha, the competitive equilibrium bit got me too!
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by Vasudha When the price ratio = 1 consumer 2's income becomes m2 = 2p1+6p2 so demand for good 2 = m2/p2 = 2p1+6p2 /p2 = 2p1/p2 + 6 = 8 when p1/p2 = 1 Also, consumer 1 - income = (10p1+2p2) he needs to have minimum 12 in his consumption bundle (total of 1+2) , so if we give him 12 of good 1 and 0 of good 2, consumer 2 gets 8 of good 2 , isn;t that a competitive equilibrium? (10p1+2p2) / p1 = 10 + 2 p2/p1 = 12 and both markets clear... what's wrong with my approach?
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 can anyone please walk me through this .... I am having problem understanding the logic ... why 1 would demand (0,12) ??
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 Also I am not even sure if I understood the preference of consumer 1 properly ... what does it say ?
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 In reply to this post by Vasudha can someone pls explain why demand by consumer 1 is (0,12)
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 @pbansal ..when price ratio is 1 agent 1 will demand only good 2..check his utility fn
Open this post in threaded view
|

## Re: General Equilibrium - May 18

 COuld someone illustrate the second part of this question?