Mathematics for Economists

Optimal control, Bolza problem

Asx( 0 )= 1 C 1 +C 2 = 1 .By the transversality condition

0 =Fx^0 ( 1 )= 2 x( 1 ),

x( 1 )= 0 ,

0 =C 1

1

e+C^2 e,C^1 =C^2 e

2

soC 1 =e^2 /

1 +e^2

andC 2 = 1 /

1 +e^2

.