Mathematics for Economists

Calculus of variations

Asyis an arbitrary function, hencey(b)andy(a)is also arbitrary, so ifx

is an optimal solution then

Fx^0



t,x(t),



x(t)



=

d

dtF

^0

x



t,x(t),



x(t)



φ^0 b(x(b)) = Fx^0 



b,x(b),



x(b)



φ^0 a(x(a)) = Fx^0 



a,x(a),x(a)



DeÖnition

The last two conditions are called the transversality conditions.