Mathematics for Economists

Optimal control

As

dp

dt

= 2 (x 1 )=



(^2) (t (^1) ) if t< 1 / 2
2 ( 1 t 1 ) if t 1 / 2
p(t) =
Zt
0
2 (s 1 )ds=t^2 2 t+C, t< 1 / 2
0 = p



1

2



=^1

4

1 +C,)C= 3 / 4

p(t) =

Zt

1 / 2

 2 sds=t^2 +^1

4

, t 1 / 2.