can someone please post solutions to pareto optimal questions of dse 2014?

[onionknight]

I can't quite understand what you're saying.

[ABHI1994]

i understand what you have posted,but as u said    Now consider the allocation xa=1/2,xb=1/2,ya=0,yb=1->ua=1/2 ub=1 there is no option in question paper like this.....

On 2 June 2015 at 20:27, onionknight [via Discussion forum] <[hidden email]> wrote:

I can't quite understand what you're saying.

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[onionknight]

That is exactly what I've explained in my post. It's not like you can only choose between the allocations given in the options, you can move anywhere within the edgeworth box.

[ABHI1994]

we will see overall utility too???

On 2 June 2015 at 20:56, onionknight [via Discussion forum] <[hidden email]> wrote:

That is exactly what I've explained in my post. It's not like you can only choose between the allocations given in the options, you can move anywhere within the edgeworth box.

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[ABHI1994]

ahaa!!!got it thank you so much.

plz post the ans. of 16-20 of dse 2014 entrance exam.

On 2 June 2015 at 21:28, SINGH ABHINAV <[hidden email]> wrote:

we will see overall utility too???

On 2 June 2015 at 20:56, onionknight [via Discussion forum] <[hidden email]> wrote:

That is exactly what I've explained in my post. It's not like you can only choose between the allocations given in the options, you can move anywhere within the edgeworth box.

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[Anirban]

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[knowpraveen]

How did you come up with the monotonically increasing function as the one which satisfies the given conditions? Can you demonstrate?

If (a,b) and (c,d) are indifferent bundles, how does this condition follow - (a+c)/2, (b+d)/2 for the utility function ln (x)+ y. Please explain. I couldn't attempt several questions in the previous que. papers as it needs thorough understanding of the graphs and various utility mathematical functions and their patterns. How do I go about this? Please help.

[Aashna]

onionknight /L  -please help - pareto optimality isgoing above my head

[Sris]

ya plz....all the pareto optimality /general equilibruim experts plz help us...

[knowpraveen]

It's given that (a,b) is preferred to (c,d) is a>=c or b>d. Consider a line drawn from the origin cutting across the indifference curves for such a utility function. The points at which it cuts across satisfy the aforementioned conditions, when goods are preferred as we move in the positive direction across the diagonal of an edgeworth box for a two good-two person economy. So, its okay to assume that it's a Cobb-Douglas function, say U(x1,x2)=x1.x2.  

For the second condition, the utility curves are that of perfect complements as is obvious. So, the contract curve would be a straight line y1=y2, for utility function U(y1,y2)=min(y1,y2) as the other utility function for the agent 1 takes it up as well.

So, there are infinite competitive equilibrium allocations possible on this contract curve.

I hope its clear.

[knowpraveen]

For the next one, we have a budget constraint as follows - Px is considered to be numeraire and Py = p. Let's say, which gives p=0, for the price vector (Px, Py)=(1,0).

The budget equation is therefore, x1+p.x2=10p for Agent 1. The equation for x1 and x2 for Agent 2 is (10-x1)/(11-x2) = 1, which is as per the contract curve equation, y1=y2. Therefore, on solving these, with p=0, we get x2=1 and y2=9 ie, the allocation has to be (0,1) and (11,9) for agents 1 and 2 respectively which is not given in the list of options. 

On Sun, Jun 14, 2015 at 11:44 AM, knowpraveen [via Discussion forum] <[hidden email]> wrote:

It's given that (a,b) is preferred to (c,d) is a>=c or b>d. Consider a line drawn from the origin cutting across the indifference curves for such a utility function. The points at which it cuts across satisfy the aforementioned conditions, when goods are preferred as we move in the positive direction across the diagonal of an edgeworth box for a two good-two person economy. So, its okay to assume that it's a Cobb-Douglas function, say U(x1,x2)=x1.x2.  

For the second condition, the utility curves are that of perfect complements as is obvious. So, the contract curve would be a straight line y1=y2, for utility function U(y1,y2)=min(y1,y2) as the other utility function for the agent 1 takes it up as well.

So, there are infinite competitive equilibrium allocations possible on this contract curve.

I hope its clear.

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[onionknight]

You can't really draw indifference curves for Lexicographic preferences as they are just single points. There will be 1 competitive equilibrium in the 6th question. If the price ratio is px/py>0, then in any case, agent 1 will always spend all his money on buying good x whereas agent 2's consumption bundles would consume equal units of good x and good y.

x1(consumer 1's demand of good 1)= 10py/px             y1(consumer 1's demand of good 2)=0
x2(consumer 2's demand of good 1)= 11px/px+py=consumer 2's demand of good 2)= 11py/px+py

now, x1+x2=11 and y1+y2=10

You may solve this to get the competitive equilibrium.
When px=1, py=0, Agent 2 would want 11 units of good 2 to maximize utility (since they are free), there will no equilibrium. When px=0 py=1, agent 1 would demand infinite amount of good 2 as more units give him more utility and they are free. So again, we're left with that one case.

[ABHI1994]

plz give some explanation of Px/Py greater than zero and only one equilibrium allocation.

On 14 June 2015 at 00:36, onionknight [via Discussion forum] <[hidden email]> wrote:

You can't really draw indifference curves for Lexicographic preferences as they are just single points. There will be 1 competitive equilibrium in the 6th question. If the prices ratio px/py>0, then in any case, agent 1 will always spend all his money on buying good x whereas agent 2's consumption bundles would consume equal units of good x and good y.

x1(consumer 1's demand of good 1)= 10py/px             y1(consumer 1's demand of good 2)=0
x2(consumer 2's demand of good 1)= 11px/px+py=consumer 2's demand of good 2)= 11py/px+py

now, x1+x2=11 and y1+y2=10

You may solve this to get the competitive equilibrium.
When px=1, py=0, Agent 2 would want 11 units of good 2 to maximise utility (since they are free), there will no equilibrium. When px=0 py=1, agent 1 would demand infinite amounts of good 2 as more units give him more utility and they are free. So again, we're left with that one case.

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