dse 2013...doubt

[SoniaKapoor]

[Akshay Jain]

suppose that A's utility function is U(d)a=da and utility function of B is U(d)b=db
where da = |plant location in [0,1] - 0.2| and db = |plant location in [0,1] - 0.7|

If the plant is at extreme position say 0 den da= 0.2, db=0.7 and when plant is at extreme position 1 dn da=0.8, db=0.3

now take a plant location in interval (0,0.2) dn
da<0.2 and db<0.7, so both of them are worse off (position 0 pareto dominates (0,0.2)

similarly take a plant location in interval (0.7,1) dn
da<0.8 and db<0.3, so both of them are worse off (position 1 pareto dominates (0.7,1)
therefore option (a) is ruled out

now take a location 0.5 dn
da=0.3 and db=0.2 which means utility of A increases but dat of B decreases when compared with location 0 but it is pareto dominated by location 1 so option b and c are also ruled out


hence option D

[Dreyfus]

0.5 is the Pareto optimal location.... Because when you deviate from 0.5 to:
The left, let's say 0.3, A's utility will fall and B's utility will rise ie B is made better off by making A worse off.
The right, let's say 0.6 B is clearly worse off and A is better off
Also if we deviate to the extreme point 0, A will be worse off and B will be better off, and to the extreme point 1 A is better off and B is we worse off!

[Dreyfus]

@Akshay..please help..where I am missing!

[Akshay Jain]

@vaibhav...just compare the utilities at both locations 0.5 and 1
u vl find that at 1 both of their utilities dat is distance from their initial locations increases as compared to dat of 0.5.....imlies dat both are better off at 1

[SoniaKapoor]

Thnxx akshay..

[Dreyfus]

Thnkx Akshay....I got it...both are getting better off when deviated from 0.5 to 1