Mathematics for Economists

Optimal control, explanation, interpretation

One can interpretp(t)as the shadow price for the state variablex(t).At

every moment of time the inÖnitesimal contribution is

dW(t)

dt

=f(t,x(t),u(t))+(x(t)p(t))^0 =

=f(t,x(t),u(t))+x^0 (t)p(t)+x(t)p^0 (t)=

=f(t,x(t),u(t))+p(t)g(t,x(t),u(t))+x(t)p^0 (t)=

=H(t,x(t),u(t))+x(t)p^0 (t).

the direct ináow and the indirect change of the wealth. (Direct cash ináow

and change of the value of the stocks.)