doubt:P.O and Gen eq

[Mauli]

situation:An exchange economy is populated by three consumers: 1, 2, and 3. There are two goods—good x and good y. The consumers’ preferences are characterized (respectively) by
the three utility functions: u(1) = min{x, y}, u(2) = 2log(x) + y, u(3) = x + 2y
Total endowment of good x and y in the economy is 10 units each.


q1)Which of the following allocations is pareto efficient?
a)((1, 1), (1, 0), (8, 9))
b)((4, 4), (1, 2), (5, 4))
c) ((2, 2), (8, 0), (0, 8))
d)((1, 1), (0, 1), (9, 8))

q2)
Suppose the endowment is the pareto efficient allocation of the problem above. Then competitive equilibrium prices are
 a) (1, 1)
 b)(1, 3)
 c)(1, 4)
  d)None of the above
kindly tell me the approach to solve this question.

[Sumit]

Hey Mauli,
I do it like that
Lets take option b)((4, 4), (1, 2), (5, 4))

Here U(1)=4, U(2)=2 and U(3)=14..
Now,try to find a reallocation which increase any one person Utility without reducing others utility...
Here is one- ((4, 4), (0, 2), (6, 4))...Now  U(1)=4, U(2)=2 and U(3)=15...The utility of third person has increase from 14 to 15 this mean this is not PO point....

As you try this method on each option...you will get answer a)((1, 1), (1, 0), (8, 9)) as PO allocation..coz we are unable to find any other reallocation which increases any person utility without reducing others utility....

The only problem I faced in this question is that I need to look up log values... which I didn't remember correctly...

N I tried q2 as well but I stuck in btw....

Any one who got it plz show how to do it....

[Mauli]

wow sumit!
that was a fab answer:)
!and it is the right answer. please keep trying the other one too. i am sure you will reach a conclusion:)
i am trying it too!
thanks a lot:)

[rohan]

2) none of the above

[Mauli]

hi rohan:)
i have access to the answer key.
it wud be great if you would share your approach.