Mathematics for Economists

Calculus of variations

2 π

ZT

0

x(t)

r

1 +



x

 2

dt!min

x( 0 )=a

The solution of the EulerñLagrange equation is still of the form

x(t)=α
ch



tβ

α



but we should also have the conditionx( 0 )=aand the transversality

0 = φ^0 b(x(b))=Fx^0



b,x(b),x(b)



=

rx(T)x(T)

1 +



x(T)

 2.

That isx(T)orx(T)is zero which is impossible for functionch(t)..