Apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions
1. (a) Given that ƒ(x, y, u, v) = 0 and g(x, y, u, v) = 0, determine ∂u/∂x, ∂u/∂y, and ∂v/∂y.
(b) Given that u = ƒ(x,y) and v = g(x,y), prove that there exists a functional relationship between u and v of the form ø(u,v) = 0 if and only if the Jacobian ∂(u,v)/∂(x,y) is identically zero.
Cramer's rule is applied. A Quasi-concavity, Hessian, and Kuhn-Tucker conditions are analyzed.