Mathematics for Economists

Constrained positive deÖnite matrixes

The Hessian

A=

0

@

2 + 2 λ 0 0

0  2 + 2 λ 0

0 0  2 + 2 λ

1

A,B= 2 x 1 2 x 2 2 x 3 
.

Ifx 1 = 1 ,x 2 = 0 ,x 3 = 0 ,thenλ= 1

H=

0

BB

@

0 2 0 0

2 0 0 0

0 0 4 0

0 0 0 4

1

CC

A

The determinant is64. As there are three variables for maximum the

sign must be( 1 )^3.