dse 2008 Q 48 AND 49...HELP PLEASSE

[Sris]

JUST GIVE ME HINTS...

[Sris]

The next TWO questions are based on the following situation: Consider
a two-person two-good exchange economy: persons/agents are A and B, and
goods are 1 and 2. The agents have the following utility functions:

uA(x;x2) =alpha x1 + x2;  uB(y1; y2) = y1y2

where x1 and x2 denote the allocation to A of good 1 and good 2, respec-
tively. Similarly, y1 and y2 denote the allocation to B of good 1 and good
2, respectively. There are 5 units of each good; i.e., x1+y1 = 5 and x2+y2 = 5.
Now, consider the following allocation: Agent A gets 4 units of good 1
only, but agent B gets 1 unit of good 1 and 5 units of good 2.


QUESTION 34. Suppose an agent i is said to envy agent j, if i strictly
prefers j's allocation over her own allocation. And, an allocation is called
`No-envy allocation' if none of the agents envies the other. In that case,

(a) the above allocation is always `No-envy allocation'
(b) the above allocation is never `No-envy allocation'
(c) the above allocation is `No-envy allocation' if  alpha>= 5/3
(d) the above allocation is `No-envy allocation' if alpha<=5/3

QUESTION 35. The above allocation is
(a) always Pareto optimal
(b) never Pareto optimal
(c) Pareto optimal if alpha<=  5
(d) Pareto optimal if alpha>= 5


i need the second one only,,,,q35...i m getting( a )
but answer key says (d)


plz help...amit sir...pls pls pls

[L]

say alpha =1, then Ua = 4, Ub = 5
Now consider this allocation, A - (2,3) and B - (3,2)
Ua= 5, Ub = 6

So, both are better now. If alpha is greater than 5, given allocation will be pareto optimal. But, if alpha <5, then there are cases for which it is not pareto optimal as you can see from previous question that A will envy B's if alpha is less than 5/3.

[Sris]

ok thank u so much L....GREAT HELP...!1!