Posted by
duck on
Jun 11, 2013; 2:20pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2010-Ques-31-34-tp6501930p7582141.html
Hi.. :)
31) Option(d)
32) Option(a)
Reasoning: For any price ratio: Agent 1 demand would be: x1=py/px ; y1=0
And for agent 2: If px>py then, x2=0 and y2= 2px/py
If px<py then, x2=2 and y2=0
If px=py then, {(x2,y2)| x2+y2=2}
Clearly, Market is not clearing for px<py and px>py.
But when px=py then, At (x1=1, y1=0) and (x2=1 , y2=1) clears the market.
So, Competitve equilibirum Allocation is: Agent 1 getting (1,0) and Agent 2 getting (1,1).
33) Now, Agent1 lexicographically prefers y over x.
So, for all price ratio his demand would be: x1=0 and y1=1
Demand for Agent 2 remains the same as above.
Now, when price ratio ≤ 1 then, market is clearing.
Hence, option(c)
34) Agent 1 demand : x1=0 and y1=1 for all strictly positive price ratio.
And as agent2 treats both goods as perfect complements. He would consume the same amount of x and y or all price ratio i.e x2=y2= 2px/px+py
Now, for market clearing we need x2=2 and y2 to be 1 implying x2≠y2.
For (py=0 and px>0) or (px=0 and py>0), agent1 would demand infinite amounts. So, again market will not clear.
Therefore, no competitve equilibirum exists.
:)