Effective consumption shadow price with habit
= Effective consumption shadow price with habit
{title2=$D=V_w-\lambda V_h$}
When habit evolves by $dh=\lambda(c-h)dt$, increasing consumption both costs wealth and increases future habit. Consequently the consumption coefficient in the <Hamilton-Jacobi-Bellman equation> is $V_w-\lambda V_h$. A finite interior optimum requires this effective shadow price to be positive.