Mathematics for Economists

Optimal control

Using the initial condition and the transversality condition

x 0 = c 1 +c 2 ,

0 = c 1 eTc 2 eT,c 1 =c 2 e^2 T

x 0 =c 2



1 +e^2 T



,c 2 =x 0 /



1 +e^2 T



= x^0 e

T

eT+eT

Hence

x(t)=

x 0 etT

eT+eT +x^0

eTt

eT+eT.