DSE 2013 Paper Discussion

[kangkan]

any luck with inter temp question...its driving me nuts

[Granpa Simpson]

it cannot be a, because if its a it has to be d too...actually I solved it in a grt hurry so might have missed a few points..so plz check and do let me know...!!!!

[Granpa Simpson]

Q17) b.

[Dreyfus]

I agree for q17 ...subhayu

[Granpa Simpson]

Vaibhav yar plz solve the second part of the intertemporal one..its really driving me crazy...

[Dreyfus]

Subhayu..even I m also scratching my head on second part....

[kangkan]

@subh..can you show working for 22...i am not getting the ans :(

[kangkan]

guys..what is the final consumption bundle x=1/2 and x2=? (for intertemp question)

[Granpa Simpson]

The second derivative will be (3x^2-3*x-6), the function will be convex if f''(x)>0, now this will be possible if either both (x-2) and (x+1) are positive or they are negative, now consider two cases:
Case 1: if both are positive then x>2, and x>-1, the set of points are (2,inf) intersection (-1,inf)=(-1,2).
Case 2: if both are negative then, x<2 and x<-1, the set will be (-inf,2) int (-inf,-1)=(-inf,-1)
Now it is clear that the function is convex on (-1,2) by Case 1, so it cannot be concave in that region so we rule out option b as it says the function is concave on (-1,2)
Now a can be ruled out since in the interval (-inf,2) f''(x) is not always negative, take x=-3,
Also d can be ruled out because in the interval (2,inf) f''(x)>0, so it cannot be negative and hence cannot be concave too.
Option c satisfies all the criterion, in the interval (-1,2) the function will be convex, as given in Case 1, also in the interval (-inf,-1), f''(x)<0.  
so answer is option c.

[Granpa Simpson]

Sorry kangkana it was my mistake that in the solution i wrote a, but it shud be c...!!!!

[neha:)]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/qp-ma-option-a-2013.pdf
 
Someone please help me with Q. 7 and 8th..

[kangkan]

Hi Neha..for 7th..you have to solve it as cournot equilibrium of two firms..after doing all the algebra ,you will get p= a+c-b^2*c/(2+b)(1-b)..now you have to assume that b is so small that b^2 can be ignored.the above expression simplifies to a+c/2-b which is option a i tink.

For the second one,its maimaztion of profit for a single monopolist...differentiate with respect to q1 and q2...you will get q1 =q2....use this in the expression for price..the option will be c

[neha:)]

Thanks a lot!

[Granpa Simpson]

for Q33 the answer will be option a...at last solved...

[Granpa Simpson]

Procedure: Consider the case of a single person where the person will consume x1 only if slope of the IC will be greater than the slope of the budget line, which means 1/β>(1+r), on rearranging it will come down to β<(1/1+r). For a single cnsumer the demand will depend on Pr(β<(1/1+r)) which for a continuous distribution can be written as Pr(β<=(1/1+r)) which is nothing but F(X=1/1+r)=C.D.F. For a uniform distribution defined on [a,b] the C.D.F is given by F(X)=(X-a)/(b-a), here in this case X=1/1+r and the pdf is defined on [1/2,1], using the formula we get Pr(β<=(1/1+r))=F(x=1/1+r)=[(1/1+r)-(1/2)/1/2]=(1-r)/(1+r)............................(1)
(1) gives the demand for a single consumer, so for N consumers the demand will be N*[(1-r)/(1+r)].
Spent almost an hour on this solution and got this as the only way to proceed, however plz do check and comment on the validity.

[Dreyfus]

Gr8 subhayu........

[bhavya jain]

@ Kangan for q6 i think u wrote wrong option c) by mistake. ur working is correct, & the right option is d)

[kangkan]

@bhavya....yes i meant 51/221 :)
@subh ...i can see that nof customers who wud demand x1 in period 1 is N(1-r/1+r)..but will they all demand the exactly 1 unit in period  :(

[kangkan]

guys..please join in my 2012 paper discussion thread..thanks :)

[Granpa Simpson]

The function (1-r)/(1+r) is the demand of x1 for a single consumer...so for N consumers it will be N*[(1-r)/(1+r)]...e.g if suppose for a single consumer the the demand is 4 units, if there are 3 consumers and each has the same preference then total demand will be 12 units...in this case it has been specified in the question that all the N consumers are identical..so for 1 consumer if demand is (1-r)/(1+r) so for N it wud be N*[(1-r)/(1+r)]..isnt it so..??