DSE 2013 Paper Discussion

[kangkan]

and for 51,i am getting this.....C=1/2 *Yd=0.5(Y-0.4Y)=0.3Y  M=1/10(Y) (since it is function of total income)


Y= C+3200+4000+800-0.1Y
Y=0.3Y+3200+4000+800-0.1Y
0.8Y=8000
Y=10000

Now with this the other ans also change..can you please verify :)

[kangkan]

43 is C..i plotted them

[kangkan]

i think 27 is 27/99...lte x=0.272727.... now 100x=27.2727..... subtracting both we get 99x=27 ..x=27/99

[kangkan]

can you help with 22...if differentiated it twice but m getting a crazy ans.....

[kangkan]

21 is d i think..we only discussed it a few days ago...remeber?

[kangkan]

i think 6 is C.... here is my working

expected waelth is she doesnt buy =100 expected utility= 10 rootover 100=100

If she buys, her expected U= 10root49*(1-p)+10root400*p

since she is an expected utility maximizer she will buy when the second term is >100

equating i get p>3/13=51/221

Please verify...

[kangkan]

please help with the Cumulative distribution question..also any luck with the intertemporal choice question?

i got the ans to the monoplist question with the assumption that b<<1..dnt knw if thats the way to go

[Dreyfus]

For intertemporal ques....I m getting r=1/2 as utility function is of perfect subs...but we should not forget that its intertemporal choice ! I mean consumer would never exhaust her income entirely in either period
The budget constraint given here is P*x1 +P*x2/(1+r)=P*1/(1+r) equivalently x1+x2/(1+r)=1/(1+r)
Optimal choice condition MRS=Price ratio
                                          →1/beta=(1+r)
                                          →r=1/beta -1
Now x1=1/2
So BUDGET CONSTRAINT must be satisfied with these two values
1/2 + x2*beta = 1*beta
x2=1-1/(2beta)
Beta belongs to (0,1)
When beta <1/2
x2<0 (not possible)
When beta>=1/2
x2>=0
This implies r=1/2 is the only option that satisfies constraint
Anyone with the second part of this ques..?

[kangkan]

for the second part: the number of people who wud consume in period A is intergration from 1/2 to 1/1+r of 2..(uniform distri)...which comes out as N(1-r/1+r)..so if the optimal choice period 1 is 1/2..the demand will be N/2(1-r/1+r)

[kangkan]

but vaibhav...since the indifference curve will be a straight line,does not it mean that we will have border solution?

[Dreyfus]

Border solution is der only when prices of two commodity differs!
Here u can't say that prices differ....so here in this case I used the normal optimization for interior solution!

[kangkan]

can you please upload a snapshot of the diagram...wud be obliged..thanks :)

[Dreyfus]

Sry to say....I hvnt drawn any curve or dig for this ques

[Homer Simpson]

check the other thread

[kangkan]

but here the optimization problem will be max x1+Bx2 sub to x+x2/1+r=1/1+r right?this will be linear programming one..will it have an interior solution,?..and lets take a hypo case..lets assume Beta is nearly 1...lets say 0.99999 ...and r=0.75...in this case i wud be better of consuming in period 2 only cuz the the cost of period 1 consumption will be too high...do you think the consumption smoothing objective will apply here?

[Dreyfus]

I don't think it won't be apply here...as u hv absolute values of r and beta in this case!

[kangkan]

linear programming or consumption smoothing? :)

[Dreyfus]

For the DSE ques....consumption smoothing! And for ur hypo ques linear programming

[kangkan]

alright...can you verify the other questions....thanks

[Granpa Simpson]

Yes 27 will be (27/99)...