Discussion Problem_ (5)

[duck]

Find Pareto Efficient Points:

U1 = x1+y1 , endownment = (0,5)
U2 = x2+y2 , endownment = (5,0)

[maahi]

my ans is that initial endowment is pareto efficient . am i wrong ?

[duck]

There are other Pareto Efficient Points also.

[pbansal]

the whole edgeworth box including boundary

[Maahi]

Its a case of perfct subst. Any combn frm 0 2 5 wud b feasible

[Sumit]

Infinite Pareto efficient points If goods are not discrete and finite PE points If goods are discrete..
In other words, all the solutions of the First diagonal of edgeworth box (i.e the straight line from top left corner of edgeworth box to bottom right corner)....
Mathmatically---
Given=U1 = x1+y1 , endownment = (0,5)
         U2 = x2+y2 , endownment = (5,0)

suppose a set X={x: 0<=x<=5}
Now the pareto efficient points set={(x1,y1) & (x2,y2): x1+x2=5, y1=(5-x1) & y2=(5-x2), for all x1,x2ϵX}

Note: we got this solution bcoz good X & y are perfect substitutes which we can easily conclude from utility fn of both the consumer.
 

[duck]

The Entire Edgeworth Box (including boundary) is PE.

[Sumit]

@could you plz explain why the entire edgeworth box is PE?????

[duck]

Hi Sumit.. :)

Just use the definition of Pareto Efficiency.