how to solve for competitive equillibrium

[Viren]

DSE 2004 question 6 :
agent 1,2 have utility function min {xi, yi} and their endowments are
1=(999,0)
2=(0,1000)
what is the set of all competitive equillibrium allocations for this economy.

Also what is the general method to solve for competitive equillbrium allocations.

[duck]

hi viren..

when the price would be (1,0) then only we will be having competitive eqm..
so , set of competitive eq in this case is where x1= 999 , y1=999 while
x2= 0 and y2= 1

and for further help follow the given link:

http://discussion-forum.2150183.n2.nabble.com/DSE-2006-td5161871.html#a5161871

[Viren]

HI Nidhi! that was really helpful.however can you please answer the following queries also:-
1. the solution you have provided , is one in which only 1 person maximises his utility and person 2 does not.So why is it a competitve equillibrium ?
2.Also for that matter , can x1,y1=(999,1000) and x2,y2=(0,0) be an answer?

thanks

[duck]

hi viren..
see, for the given economy, a competitive allocation is that allocation where,
1>for a given price, each consumer is maximising his utility such tht value of endownmnt equals value of good they are demanding.. and
2>demand = supply for all commodities.. (or markets clear)

 so,  if you want to find competive allocations, u must find the price ratio first where both would be maximising their utility and then u must check whether demand = supply or markets clear..

now, in the given que.. we ll hav competitive eqm only whn p1=1 and p2 = 0
and at this price, set of competitve eqm is where x1= 999 , y1=999 while
x2= 0 and y2= 1
and also, x1,y1=(999,1000) and x2,y2=(0,0)

sorry..i forgot to write the latter bundle.. thanks.. :)

i hope i cleared ur doubt.. :)