DSE 2010 Q31

[The Villain]

Q31.
I got the eqm price as p1=p2 =1
now...
my doubt is on q31..
Is option a not a compt eqm becaz when we check for it p2 comes out to be zeroso as p2 =1??...so this is contradiction..is my approach right..pls solve this confusion..

[kangkan]

is the bertrand duoploy question..i think my series is difrnt..question 31 is a mtahs question

[The Villain]

here kangkan..please help out

[Akshay Jain]

try 31st question using the edgeworth box.......acc. to me option d
or u can use options and chek for welfare increases or decreases compared to the initial endowment
for 32..the exchange will take place on the indifference curve of 2nd consumer (x+y) so price ratio=1

[The Villain]

Thanku so much Akshay. :-)
Can you please tell me how to solve q31 using edgewarth box.I'm unable to proceed with it..

[SoniaKapoor]

how does welfare inc or dec ??how to do this>

[Akshay Jain]

the 2nd consumer will consume in such a way that he gets utility atleast 2 (endowment utility)option a.. allocation = endowment (can be competitive eqm)option b..cannot b comp eqm as 2nd onsumer is gettin worseoff than that of the endowmentoption c..same arguement as in option boption d...here comes the role of lexicographic preferencesalthough consumer 2 is at same utility level but 1st consumer's welfare increases in this new allocation as he is better off with more of x...so this new allocation is comp equilibrium and thus pareto efficient (and pareto dominates the endowment)

[The Villain]

@Akshay...thats v well explained.Thanks mate.Cheers

[Akshay Jain]

cheers dude...

[kangkan]

@Akshay..t thought the condition MRS =price ratio is valid only when both agents are consuming both goods..but we have a boundary solution here..also if px=py,then at the margin both agents must value both goods as one for one..agent 2 does..but will agent 1 be willing to exchange 1 for 1?