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# Tripos pt 1A economics maths question Watch

1. Okay I get the principles behind these questions but I'm am finding the algebra difficult. I can prove the first part by taking the determinant of the Hessian but judging by the wording of the question this method won't get the highest marks. Basically if I do it their way I get a quadratic form of the form (d1)^2*fxx +(2d1d2)fxy + (d2)^2*fyy. Clearly the third and last term are negative and the middle one is positive but how do I show that the modulus of the outer terms is larger than the modulus of the middle term? For the other parts again I understand the principles but am not sure about the maths. According to examiner reports this wasn't a well answered question (it's a short answer question so we don't get long so long algebra is annoying!).
2. (Original post by stefl14)

Okay I get the principles behind these questions but I'm am finding the algebra difficult. I can prove the first part by taking the determinant of the Hessian but judging by the wording of the question this method won't get the highest marks. Basically if I do it their way I get a quadratic form of the form (d1)^2*fxx +(2d1d2)fxy + (d2)^2*fyy. Clearly the third and last term are negative and the middle one is positive but how do I show that the modulus of the outer terms is larger than the modulus of the middle term? For the other parts again I understand the principles but am not sure about the maths. According to examiner reports this wasn't a well answered question (it's a short answer question so we don't get long so long algebra is annoying!).
Can you be a bit more specific about what you're having issues with?

For part a), one way to prove the question is to explicitly find the Hessian, and compute d'Hd for an arbitrary vector d
3. (Original post by Mark13)
Can you be a bit more specific about what you're having issues with?

For part a), one way to prove the question is to explicitly find the Hessian, and compute d'Hd for an arbitrary vector d
That's what I did do as I say. The problem is I get the quadratic form mentioned after expanding it out and cant show that the quadratic form is strictly less than zero. As I said I am able to prove that it's strictly concave by the determinant method but the wording of the question suggests that's not what they're looking for.

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