Re: JNU 2006-2002 Doubts

Posted by akanksha on May 09, 2014; 7:58am
URL: http://discussion-forum.276.s1.nabble.com/JNU-2006-2002-Doubts-tp7588757p7589109.html

Can somebody please try out these qs.
Q.1   Suppose we say that an allocation x is Pareto optimal if and only if there does not exist an allocation, say y, such that : every individual in the economy considers y to be at least as good as x, and at least one individual considers y to be strictly better than x. Now, consider a society of four individuals. This society has five allocations to choose from a, b, c, d and e. Individual preferences over these allocations are as follows :
     
       1st individual : a > b >c > d>e
       2st individual : b >c > d >e > a
       3st individual : c >d >e >a >b
       4st individual : d >e >a >b >c
     where a>b >c>d>e means that the 1st individual prefers allocation a over b, b over c, .... d over e.      Likewise for the preferences of other individual. Find out the Pareto optimal allocations for this society.

Q.2     Suppose there are 4 alternatives, x,y, a and w. Further suppose that there are 7 individuals, 1,2,3,4,5,6 and 7. The individuals' rankings (ordering) of the four alternatives, Ri, i=1, ....7 are given by
R(1):(xy)zw
R(2): yzwx
R(3): zw (xy)
R(4): (xy) (zw)
R(5): yzwx
R(6): zw(xy)
R(7): (xy) (zw)

Determine which of the alternative are Pareto-optimal. ExplAIN YOUR ANSWER.
(Alternatives inside the parentheses are indifferent to each other. If an alternative is written to the left of another alternative, then the former is preferred to the latter.)