Isi peb 2016

[urvashi]

Is anyone interested in discussing it?

[Eco16]

Well I am interested but I haven't tried it yet.

[varnika1880]

I am in

[urvashi]

In question 1 part 4 will the set of pareto efficient allocations be the entire edgeworth box?

[knowpraveen]

How would the entire edgeworth box be Pareto Efficient! The consumer 2 has lexicographic preferences, so its always better to have more of x to make him/her well off. So, let's say x1,y1=(0,12) and x2,y2=(10,0) is a desired point because out of any two bundles for consumer 2 (10,0) would be the most preferred bundle for consumer 2 also maximizing the utility of consumer 1 by consuming the whole of the perfectly substitutable good y.

The Pareto efficient points should come along the line y1=12 or y2=0. For any other points in the edgeworth box, there could be better utility for both consumers in the economy. Let's say you choose x1,y1=(7,4), x2,y2=(3,8)

U2=11 and U1 is greater for any bundle with the x value greater than 7. This could be generalized if we make a close observation. Check for all boundary points, that is important and gets confusing as we get along.

Correct me if I'm wrong. Thanks.

[urvashi]

I realized my mistake thanx how do we attempt Q10

[varnika1880]

So are u implying that the left and top edge would be the Pareto optimum?

[varnika1880]

Do u have any idea about question 10 ?

[knowpraveen]

No Varnika, only the x axis of consumer 2 should be pareto optimal for obvious reasons. Take a point from the axis on the left to clear the air.

[knowpraveen]

There is only one way to go about this problem. The given case is that of a liquidity trap which is why we got the equilibrium point in the fourth quadrant. The interest rate has bottomed and has reached r(min), any increase in the money supply is going to be futile from this point on.

So, what next! To increase r to 0.2 without Y immediately adjusting to 2500 there should be an exogenous increase in Investment by an amount 102.5 which gives us an equilibrium at r=1/5 and IS curve as Y=2090-200r

Draw the graph and that is going to give the question some direction. I hope its going to be a cakewalk if you don't take into consideration the negative equilibrium point. Don't draw the graph by extending it into the fourth quadrant, IS and LM curves should be inside the first quadrant itself. If you doubt the validity of the curves, its a liquidity trap at play.

I hope this is the way to go about the problem. If you have different thoughts kindly let me know, we will complete the problem by taking the discussion further. Thanks Varnika and Urvashi for asking. I skipped the problem at first glance. I never thought this problem would be a tricky one, given the simplicity of sectoral demand functions upon initial inspection.

[varnika1880]

Thnx a lot but what I mean to say suppose consumer 2 is consuming all of X+ some amount of y ..ie on the left edge ...then there can't be a Pareto superior point to this
and also won't we consider the different cases of price ratio in this ...thnx

[knowpraveen]

Yeah, I'm sorry I never took the Y value in lex preferences into consideration. You're right. Lets say  (10,2) is preferred to (10,0) as far as consumer 2 is concerned which gives us another condition for pareto optimality. Left and top axes are the pareto efficient allocations. Sorry again. And, what do you think about q10! I have already posted an answer. Let me know if there's any other way to solve. Thanks.

[varnika1880]

Yeah m working on it

[varnika1880]

I can't think of any other way of solving q.10

[knowpraveen]

Okay. Cool.

[varnika1880]

Have u done q 3 ?

[knowpraveen]

Pure intuition and some graph. Coming to the first question, for I=1 and R=0, the equations are going to E+B=1 for E<=1/2 and 2E+B=1 otherwise. Its easier to understand the budget line from this. The budget line generally would be E+B=I-R for E<=1/2 and 2E+B=I-R otherwise.

Taking this further now, for I=1 and R=0 case, there wouldn't be a case of E>1/2 since we go off limits by exceeding the budget. So, the budget equation remains for E<=1/2 and the utility attains maximum when E is maximum ie. 1/2. So, the utility turns out to be 3/2

You can draw the graph on your own and see for yourself.

The third part, the budget equations are going to look like this - E+B=2 for E<=1/2 and 2E+B=1.5 otherwise (do a bit of back-of-the-envelope calculation, you will come up with this) So here the optimal bundle is going to be (E,B)=(0.5,1.5)

Correct me if I'm wrong. Thanks =)

[urvashi]

I am confused in q3 where they have mentioned per unit price is 1 and 2 and then change it to every additional unit costs p=2 what is the difference also in the second part since the consumer cannot consume more than 1/2 he will consume 1/2 and the first budget equation applies bt if that is so it necessitaies 1/2 of butter to be consumed however mrs is greater than price ratio so only ectricity shud be consumed?

[urvashi]

I n q4 last part how do we provethat the monopolist can charge a lower pricre than mc

[knowpraveen]

It means any unit over and above 1/2 unit of E is going to be charged at p=2.

2(E-0.5)+0.5(1)+B=3-1
2E+B=1.5