Economics · Mathematical Economics
Consider an objective function involving n variables: U = f(X1, X2, ..., Xn) subject to φ(X1, X2, ..., Xn) = 0. Let |H̅r| represent the bordered Hessian determinant of order r. What are the second-order conditions for an extremum?
(A) For a maximum, |H̅2| < 0, |H̅3| < 0, ...
(B) For a maximum, the bordered Hessians alternate in sign starting with positive, i.e., |H̅2| > 0, |H̅3| < 0, ...
(C) For a maximum, |H̅2| < 0, |H̅3| > 0, ...
(D) For a minimum, all bordered Hessians are negative, i.e., |H̅2| < 0, |H̅3| < 0, ...
(E) For a minimum, |H̅2| > 0, |H̅3| > 0, ...
Choose the correct answer from the options given below:
(A) For a maximum, |H̅2| < 0, |H̅3| < 0, ...
(B) For a maximum, the bordered Hessians alternate in sign starting with positive, i.e., |H̅2| > 0, |H̅3| < 0, ...
(C) For a maximum, |H̅2| < 0, |H̅3| > 0, ...
(D) For a minimum, all bordered Hessians are negative, i.e., |H̅2| < 0, |H̅3| < 0, ...
(E) For a minimum, |H̅2| > 0, |H̅3| > 0, ...
Choose the correct answer from the options given below:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(A) and (D) only
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Correct answer
(B) and (D) only
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