Mathematics for Economists

Constrained positive deÖnite matrixes

Example

Solvex 32 x 12 x 22 !max,x 12 +x 22 +x 32 = 1.

The solution isx 3 = 1 ,x 1 =x 2 = 0 .The (wrong) bordered Hessian is

H=

0

BB

@

0 0 0 2

0 4 0 0

0 0 4 0

2 0 0 0

1

CC

A.

The determinant is64 which is Öne. But

(^)
(^)
(^)

0 0 0

0 4 0

0 0 4

(^)
(^)
=^0 .(The
problem is that the basis is at a wrong place.)