Micro doubt.

[Nikkita]

Can anybody help for this ques.?

[Asd1995]

Don't have a notebook/pen nearby but I can see the the utility function is concave so preferences are well behaved and convex so Lagrangian method of critical points will give me maxima.

Try finding lagrangian conditions by maximising U(C,D) w.r.t constraint p(C).C+(1+T)D=M ------- (0)

to get

DU/DC=k.p(C)

DU/D(D)=k.(1+T)

Take the ratio to get

(DU/DC)/(DU/D(D))=P(C)/(1+T)

U(C)/U(D)=P(C)/(1+T)

Differentiating the above w.r.t. C,

U(CC)= -U(D)*P(C)/(1+T)^2 * D(T)/DC ----------- (1)   (U(D) IS INDEPENDENT OF C)

Differentiating the above wrt D,

0=U(DD)*P(C)/(1+T) - U(D)*P(C)/(1+T)^2 * D(T)/D(D)  (Since U(CD)=0)

OR 0=U(DD) + U(D)/(1+T) * D(T)/D(D) ==> D(D)/DT= U(DD)(1+T)/U(D) < 0 ------(2) so cutting tax would increase charity.

Expression ke liye dekhle yaar eliminate U(D) in (2) by using (1) and (0), ho jaana chahiye.. btw what book is this?

[Nikkita]

Thanks a lot Asd1995!

i would still like to ask the following points:
1. H, in solution is Hessian, i guess..
2. it should be (1-t) in the Budget Equation.

This is not any book, just got this ques. unexpectedly from coaching assessment, that too without any solution mentioned.. and correct ans. as written there is C option..
I am getting 'Unambiguous effect' as in option c, still not reaching the full answer./

[Asd1995]

Hessian negative ho toh raha hai, you've evaluated D3 as <0 - <0, it should be <0+<0= <0. So a negative semidefinite hessian means convex preferences.

But jitni meri knowledge hai Hessian just confirms convexity of preferences, which I agree with. Overall effect can be only judged by evaluating D(D)/D(t).

I may have read the question wrong then, did it say it is given a subsidy of t on donations? If donations are "taxed" then effective price of donations in the budget equation should increase, so it should be 1+t.

Are we in agreement on this?

To me the answer is still b, I can't find anything wrong with my expression of DD/Dt

[Nikkita]

much mistake still in my ans..

[Asd1995]

Evaluate D3 again, first term will have an extra negative in front of it.

[Nikkita]

yes, still D1<0, D2>0, D3>0, so unambiguous effect..

[Asd1995]

So as far as I know hessian is evaluated to find convexity of preferences. Negative semidefinite hessian just implies convex preferences and it has nothing to do with the sign of dD/dT.

I've evaluated it myself in this image, link below : it is negative semidefinite so you may have gone wrong in evaluating it.

http://imgur.com/GMg4YxS