Discussion Problem_ (3)

[duck]

Q1)Find Pareto Efficient points:
Consumer 1 lexicographically prefers good 1 to good 2 , endowment (10,0)
Consumer 2 utility = x21+x22 , endowment (0,6)

[Sumit]

Isn't consumer 2 utility Fn should be 21x+22y???? If it is so, then pareto efficiency point should be Initial endowment (i.e(10,0) & (0,6)respectively) bcoz consumer 1 has lexicographic preference ..

P.S: I'm not sure...

[duck]

Sorry for the confusion.

x21: Amount of good1 consumed by individual 2.
x22: Amount of good 2 consumed by individual 2.

[maahi]

consumer 1 completely prefers good 1 to good 2 so being a rational consumer he wud want to consume more of it he wud nt involve in exchange and choose to consume (10.0) and this is pareto efficient as there is no way to make consumer 2 better off without reducing consumer 1 's welfare .

[Sumit]

@ maahi: exactly what i was thinking.....

@Duck: plz provide sol....

[duck]

Hi.. :)

Lexicographic preference is different. Please read its definition. And then attempt this question again.. :)

[laracroft]

Consumer 1 completely prefers good 1 .Pareto efficient points are:
ans- consumer 1 (10,0)
consumer 2 (0,6)

[maahi]

po allocations are points on the bottom and right edges of the edgeworth box . price ratio is 0.

[maahi]

@ duck pls provide d sol.

[duck]

Correct Answer:

{(x11,x12); (x21,x22) | x12=0 and x11+x21 = 10 and x12+x22=6} UNION
{(x11,x12); (x21,x22) | x21=0 and x11+x21 = 10 and x12+x22=6}

[ss]

@duck can you please explain how did you get this ?

thankyou

[maahi]

please give digramatic representation

[duck]

@Maahi:
Diagrammatic presentation is not possible. Lexicographic preferences do not have utility representation.

@ss:
Please follow the definition of PE. And try to check.