DSE 2013 Doubts

[rmabides]

Series 01 : question 31

[xyz123]

X1=X2

Case 1) Px=1
2X1 + X2 = M (Substituting X1=x2)
This gives X1=M/3

Case 2)
(2-theta)X1+X2+T=M (X1=X2)
X1= M-T/3-theta

Equate X1, you'll get the answer

[rmabides]

I was adding the fee with (2-theta), that is, price in second case was equal to (2-theta +T)..

Thanks!

[rmabides]

Series 01 : question 32.

It is related to inter-temporal consumption. So the solution will entail

C1(1+r) + C2 = Y1(1+r) + Y2

c1 = 1/2 , c2 = (beta)? , y1 = -1/2 (?) , y2=1

Where do i go wrong?

Also, what happens in the case with N agents with different discount factors?

[rmabides]

Can it be solved like this?

c1(1+r) + c2 = y1(1+r) +y2

=> c2 = -c1(1+r) + ...

Now when we draw an Indifference curve for c1 and c2.. the slope is -(1+r)[absolute slope being 1+r], this slope must be equal to the ratio of marginal utilities in period one and period 2. MU for P1 is 1 and MU for p2 is beta.

so, 1+r = 1/beta => r = (1/beta) - 1

Am I doing it right ? Whats wrong with earlier approach?