Optimal pricing in a diffusion model with concave price-dependent market potential

Using optimal control theory, a diffusion model of new product acceptance is studied. We consider a profit-maximizing firm faced with the problem of determining its optimal pricing policy under the assumption that the total market potential is a concave decreasing function of price. For an infinite planning horizon it is shown by phase portrait analysis that the optimal price is steadily increasing and converging to a saddle point equilibrium.