GE doubt

[Halflife]

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[happy]

[(5,5),(5,0)] to [(10,5),(0,0)]  only Competitive equilibrium at price (0, Py)

if we set P = (Px, 0) then individual 2 will demand 10 unit of y in order to maximize his utility at these price, which is not possible in competitive equilibrium

and at any positive price => No competitive equilibrium

[Asd1995]

In equilibrium demand=supply

Agent 1's demand of x= his demand of y

Agent 2's demand of x=his demand of y

Total demand of x= total demand of y

but total x=10, total y=5

Hence demand is never equal to supply. So there is no competitive equilibrium.

In the first question the location is pareto efficient.

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[Algaeconomics]

Only 5,5 5,0 to 10,5 to 0,0

[Asd1995]

I just get

5/(1+px)=x=y for person 1

10px/(1+px)=x=y for person 2

px=0 gives a demand of (5,5) for person 1 and (0,0) for person 2

Where am I going wrong?

[Algaeconomics]

Yeah Happy s ans is correct.
Because the first good is in excess price of it can be equated to 0 to reach an equilibrium

[Asd1995]

Can you look at my working and tell me where I went wrong?

[happy]

(5,5) gives 5 utility to individual 1
(0,0) gives  0 utility to individual 2

and there is 5 unit of y still available in the economy , with its price equal 0.

If any person demand good y it neither effect individual utility and nor budget constraint.

So competitive equilibrium  (5,5+e) (0, 5-e) where e belongs to [0,5]

[Halflife]

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[Asd1995]

Had individual 2's utility increased as a result of more x, would this not be an equilibrium then?

So if there's any way to reallocate such that demand is not equal to supply in the true sense, but utility from reallocation does not change the utilities from the demanded sets, then that's a competitive equilibrium too?

[Asd1995]

Also do you mean good x?

[happy]

Yes i mean Good-x

5 unit of good-x is still available in the economy and price of x equal to 0.

Competitive equilibrium condition
total demand = total supply

so competitive equilibrium(5+e,5),(5-e,0) where e belongs to [0,5]

[happy]

max min(x , y)

Solution of the above problem is
x = y  if the price of both good are positive

x may or not equal to y  if the price of 1 good equal to 0, because demanding extra amount a good whose price equal to 0, does not change the optimal solution of the problem just because it doesn't change budget constraint and the utility.

[Asd1995]

Wait this was my bad.

max min(x,y)
0*x + py*y=0 ==>demanded bundle has to have y=0, x=anything

geometrically the budget line is horizontal and coincides with the IC, hence infinite number of values are acceptable/optimal/can be demanded.