Mathematics for Economists

Optimal control, Bolza problem

H = u^2 x+pu,p=Hx= 1 ,p=t+C

p( 1 ) = 1 +C= 2 x( 1 ),C= 2 x( 1 ) 1 ,p(t)=t+ 2 x( 1 ) 1

0 = Hu^0 = 2 u+p= 2 u+t+ 2 x( 1 ) 1 ,

u = x( 1 )+ 1 / 2 t/ 2.