Dynamic Optimization with a Nonsmooth, Nonconvex Technology: The Case of a Linear Objective Function
This paper studies a one-sector optimal growth model with linear utility in which the production function is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for a general form of irreversible investment. We show that every optimal path either converges to zero or reaches a positive steady state in finite time (and possibly jumps among different steady states afterwards). We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a minimum safe standard of conservation. They extend the conditions known for the case of S-shaped production functions to a much large class of technologies. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the golden rule capital stock.
Keywords: Nonconvex, nonsmooth, and discontinuous technology; extinction; survival; turnpike; linear utility.
Department of Economics
Southern Methodist University