Mathematics for Economists

Optimal control

The partially optimized Hamiltonian is

Hb(t,x,p(t)) = max

u 2 [ 0 , 1 ]

u^2 x+(t 2 )u

=

=



x if t 2 [ 0 , 1 ]

x+t1 if t 2 ( 1 , 2 ]

which is concave for everyt.Hence we can use Arrowís theorem.