Mathematics for Economists

Calculus of variations

0 = ψ^0 ( 0 )$

d

dλ

Zb

a

F



t,x(t)+λy(t),x(t)+λy(t)



dt=

=

Zb

a

d

dλ

F



t,x(t)+λy(t),x(t)+λy(t)



dt=

=

Zb

a

Fx^0 y+Fx^0 y dt $

$

Zb

a

q(t)y(t)+p(t)y(t)dt.