Mathematics for Economists

Constrained local su¢ cient conditions

By the conditions that

F^0 (x 0 )h= 0 )hTL^00 xx(x 0 ,λ)h> 0

ifγis large enough andh 6 =0 the quadratic form

Q(h)$hTLxx^00 (x 0 ,λ)h+γ

(^)
F^0 (x 0 )h
(^2)

0. Hence for someUaroundx 0
   Q(xx 0 )+o



kxx 0 k^2



 0.