# Quasi-Concavity, Hessian, and Kuhn-Tucker Conditions

Apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions

1. (a) Given that Æ’(x, y, u, v) = 0 and g(x, y, u, v) = 0, determine âˆ‚u/âˆ‚x, âˆ‚u/âˆ‚y, and âˆ‚v/âˆ‚y.

(b) Given that u = Æ’(x,y) and v = g(x,y), prove that there exists a functional relationship between u and v of the form Ã¸(u,v) = 0 if and only if the Jacobian âˆ‚(u,v)/âˆ‚(x,y) is identically zero.

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#### Solution Summary

Cramer's rule is applied. A Quasi-concavity, Hessian, and Kuhn-Tucker conditions are analyzed.

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