DSE 2006 q30

[Mauli]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/24_june_2006_option_a.pdf

my doubt here, is that the answer says PO is where A has x=2, y=0.
and B has x=0,y=2.
However , there is no way in which either of the two can be made better off. even if
B gives to A one unit of y.
still , the utility of A remains the same. he is neither better off nor worse-off . but B is now worseoff.
can somebody explain this.
or is it simply because in case of a max function the consumption is at either of the two corners which makes option B correct.
please help !

[Sumit]

Hey Mauli,
Look closely n Lets do it by elimination method.All you need to find a feasible allocation in each option in which any or both became better off without making other worse off...
Lets see Option a) Here Ua=1 n Ub=1, Now suppose if we transfer one unit of X of person A to B then we will see.... A now has x=0 n Y=1 and B now has x=2 n y=1...So now we can see Ua=1 n Ub=2...that is we are able to make B better-off without making A worse-off...thats why this is not a optimal solution...

Similary for option c)If we transfer a unit of X from B to A...we will find Ua increase to 1 from zero...n Ub remain same...so this too is not a PO allocation...

N finally for option.d)If we transfer 1/2 unit of Y from A to B...we will find Ub increase to 2 from 1.5...n Ua remain same...so this too is not a PO allocation.

Also If we try to find out feasible solution for option.b) that make any or both person better-off...We unable to do this....thats why option.b) is PO allocation...

[Mauli]

sumit, thanks for replying:)

but see in d ) what if we transfer x=1.5 from A to B .
then A will be left with 0 of x and 0.5 of y . which makes him worse off . ( since now his utility falls from 1.5 to 0.5)
 and B now will have 2 units of x and 1.5 units of y . which will make him better off.  ( utility rises from 1.5 to 2)
hence this should be a P.O allocation.

idk why but i am still confused.
sorry.
let me know if or rather why my argument seems baseless.

[Sumit]

Hey Maahi,
I think you didn't get what pareto efficient allocations are....just read the definition given by amit sir...in the following link...
http://discussion-forum.2150183.n2.nabble.com/dse-entrance-2012-question-doubt-tp7579873.html...

How could you say a point is pareto optimal If utility of one is decreasing n of one is increasing.(which you did in ur example.)..
A simple method of checking weather a point is pareto optimal or not is to fix one person utility n try to increase other person utility in case of two person....If you able to increase second person utility thats means the point is not pareto optimal....n If you not..which means point is pareto optimal...thats all you need to do in this question too...

[Mauli]

cool!
i think i got a bit ''carried away'' with my perception.
but, this definition just seems so perfect:)
thanks sumit:)