GE with discrete commodity space - May 22

[Amit Goyal]

May22_DiscreteGoodsEcon.png

[anon_econ]

Pareto efficient allocations:
(x11,x12)  (x21,x22)
(0,0)        (2,1)
(0,1)        (2,0)
(1,1)        (1,0)
(2,1)        (0,0)

Competitive equilibrium:
px/py=1. (x11,x12)=(0,1), (x21,x22)=(2,0)
and also 1<px/py<2. (x11,x12)=(1,0), (x21,x22)=(1,1).

The First Welfare Theorem does not hold.

[anon_econ]

Sir I've not checked my answer..if it's wrong plz just tell me that it's wrong w/o telling me the mistake..i'll try to work it out again

[AJ]

@vasudha..
Hey....
I am getting same pareto efficient points, But...
Apart from urs .. I am getting this also as competitive equilibrium...

2>Py/Px>1

(x11,x12)=(0,1), (x21,x22)=(2,0).

Did I made some mistake..?? Or Can it also be competitive Equilibrium...??
Please reply......

Ahhh.. just realized.... U must be having JNU exam right now....

[AJ]

@vasudha..
Hey....
I am getting same pareto efficient points, But...
Apart from urs .. I am getting this also as competitive equilibrium...

2>Py/Px>1

(x11,x12)=(0,1), (x21,x22)=(2,0).

Did I made some mistake..?? Or Can it also be competitive Equilibrium...??
Please reply......

Ahhh.. just realized.... U must be having JNU exam right now....

[anon_econ]

Hi AJ :)
Do u mean py/px or px/py?
And I didn't give that exam..

[AJ]

py/px

As in when price of Y is greater than price of x... like for x its 1.. and for y .. between 1 and 2 ...

then can the allocation i mentioned be competitive equilibrium..??

[Amit Goyal]

Excellent Vasudha. Very well done. Keep it up. You are absolutely right about both the set of efficient allocations and the competitive equilibrium.

[AJ]

Ohh.. No thats not equilibrium.. I made a mistake!
Got it now!

[anon_econ]

Thanks a lot sir :)
I'm going to go into hibernation from tomorrow..u please keep posting these interesting questions..i'll look forward to doing them as soon as i get free :)

[aditi5000]

Hey, can you please explain how you got your answer... Would really appreciate it... Thank you in advance :)

[Chinni18]

Vasudha could you explain how you obtained the price ratio and answer. I am rather flummoxed! Thanks in advance

[sid]

can some one pls explain the logic behind price ratio...