Optimal investments with increasing returns to scale

I analyze the firm optimal investment policy, assuming a pure increasing-returns-to-scale technology and adjustment costs. The existence of an optimal plan is proved by applying a new set of necessary and sufficient conditions for optimality. The analysis is carried out in a linear-quadratic framework that enables one to study a general nonlinear problem in a neighborhood of the long-run equilibrium. The investment policy shows a reverse accelerator effect. In a general setting I prove that the saddle-point characterization is a sufficient condition for a stationary competitive equilibrium to be a finitely optimal trajectory.