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

[Aashna]

[onionknight]

If you could post a screenshot or the questions in text it'd make things easier.

[amianand]

Hi an someone please help me on this.

[onionknight]

ua= xa(1+ya-yb)= xa(1+ya-1+ya)=2*xa*ya when ya>yb
       xa(1+0)=xa     otherwise
Similarly you can write the function for ub. Now draw an edgeworth box and draw indifference curves for both consumers that pass through the 4 given points. The indifference curves would be vertical lines in the bottom half(below ya=yb=1/2) for each consumer and cobb douglas type in the upper half. There'd be a change in shape of the indifference curves at the line (ya=yb=1/2). For part d, you'll find there is no allocation that makes both consumers better off than the endowment (Both consumers can't together be shifted to higher indifference curves than the ones they are at presently).

[Aashna]

please help with these two as well @onionknight

[Aashna]

also please tell me one thing - how do we decide how many pareto solutions it will have? how do we find if it will have multiple optimal points or just one ?

[onionknight]

For 31(Answer: b), consider the utility functions for the two consumers to be lnxi+yi and lnxj+yj (these functions satisfy the given condition and are also monotonically increasing). For these utility functions, dyi/dxi=dyj/dxj when
1/xi=1/xj, and all such allocations are pareto optimal, so the bundles needn't be equal.

For 32 (Answer: c), if you have identical allocations then the edgeworth box will be rectangular and the endowment point would be at the center of the rectangle. Now the indifference curves of both the consumers passing through the endowment point will have some finite slope(it will also be the same as the their preferences are identical) and at some price ratio of the two goods, this slope will become equal to the slopes of the two indifference curves. Hence, the utilities of both the consumers would be maximized subject to their respective budget constraints and this will be a competitive equilibrium.

[onionknight]

When you're given two consumers and their respective utility functions and some endowment and you need to find pareto optimal solutions, draw the edgeworth box and the indifference curves. Now, consider points in different areas inside the edgeworth box/on the edgeworth box. Mostly, all points in a particular area have similar properties so if one of them is not pareto optimal you can extend it to all the points in that area. So check in the bottom triangle, upper triangle, between the xa=ya and xb=yb line (if it's a rectangle), on the edges etc.

[L]

@Onionknight

For Q.57, I didn't understand how the indifference curve will be discontinuous at xa = ya or xa = yb. Also, I think the dividing line should be ya = yb = 1/2 as the indifference curves change when ya > yb.

And although, the highest overall utility is for part (d) {(Ua, Ub) : (1/4, 3/2)}, but for part c and b {(Ua, Ub) : (1/2, 3/4)} A's utility is higher as compared to d while B's utility is lower. So, if going from allocation c (or b) to d, overall utility is increasing at the expense of A. Isn't this pareto improvement is coming at the expense of A. Infact, why should it be called pareto improvement?
So, isn't b, c,d all are pareto optimal?

[onionknight]

Thank you for pointing that out. It's indeed the line ya=yb=1/2 where the indifference curves change shape but the answer and the approach still remain the same. When you're assessing pareto optimality, you don't have to restrict yourself to switching between the allocations given in the question or as you are doing, moving to the pareto optimal point. You can move anywhere within the edgeworth box and if any movement results in an increase in the utility of at least one consumer and this increase is not at the expense of the utility of the other, then it is a pareto improvement.

Take the third allocation for instance, xa=1/4, xb=3/4, ya=1, yb=0 -> ua=1/2 ub=3/4. Now consider the allocation xa=1/2,xb=1/2,ya=0,yb=1->ua=1/2 ub=1. Clearly, this is a pareto improvement and thus we can rule out option c. You can rule out options a and b in similar fashion but not option d because no pareto improvements exist.

[L]

Yeah, got that. Thanks

[L]

Also, there won't be discontinuity in indifference curve. I think it should be a kink at the point of change.

[onionknight]

I know, that's why I say they change shape at that line (got rid of the word discontinuity)

[ABHI1994]

plz provide solution of 2014 dse paper

On 1 June 2015 at 05:05, onionknight [via Discussion forum] <[hidden email]> wrote:

I know, that's why I say they change shape at that line (got rid of the word discontinuity)

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[Akshay Jain]

Detailed solutions of dse 2014 ppr are available at the dse fotocopy shop.... U can get ur copy

[ABHI1994]

THANK YOU

On 1 June 2015 at 10:43, Akshay Jain [via Discussion forum] <[hidden email]> wrote:

Detailed solutions of dse 2014 ppr are available at the dse fotocopy shop.... U can get ur copy

Akshay Jain
Masters in Economics
Delhi School of Economics
2013-15

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[ABHI1994]

i need only ans. key,if you have plz provide it....

On 1 June 2015 at 21:18, SINGH ABHINAV <[hidden email]> wrote:

THANK YOU

On 1 June 2015 at 10:43, Akshay Jain [via Discussion forum] <[hidden email]> wrote:

Detailed solutions of dse 2014 ppr are available at the dse fotocopy shop.... U can get ur copy

Akshay Jain
Masters in Economics
Delhi School of Economics
2013-15

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[ABHI1994]

@onionknight from utility function it is coming Ua=1/4,Ub=3/2 from option d and from option b it is coming Ua=1/2,Ub=3/4 from c it is coming same only option from option a pareto improvement seems possible from my calculation,Iam plunged in this situation which is suitable plz help

On 1 June 2015 at 22:27, SINGH ABHINAV <[hidden email]> wrote:

i need only ans. key,if you have plz provide it....

On 1 June 2015 at 21:18, SINGH ABHINAV <[hidden email]> wrote:

THANK YOU

On 1 June 2015 at 10:43, Akshay Jain [via Discussion forum] <[hidden email]> wrote:

Detailed solutions of dse 2014 ppr are available at the dse fotocopy shop.... U can get ur copy

Akshay Jain
Masters in Economics
Delhi School of Economics
2013-15

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[onionknight]

Please read my reply to L's post carefully.

[ABHI1994]

but in option d Xa=Xb is not given it is the case of option b??

On 2 June 2015 at 19:31, onionknight [via Discussion forum] <[hidden email]> wrote:

Please read my reply to L's post carefully.

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